The presented development of radio detectors in VHF and microwave band showed the possibility and the assets of the coincident detection with the surface detector of the Pierre Auger Observatory. The installation of a first prototype in the VHF band led to the detection of 36 events in approximately 4 months of operation. The exponential decrease of the lateral distribution of the radio signal at ground supports a coherent emission beamed forward around the shower axis. With the current sensitivity, this limits the distance of detection for vertical showers to around 200 m. In the microwave band, we developed and installed in total 61 radio detectors at the Pierre Auger Observatory site. We reported the first detections of air showers in the C-band. However, if the expected emission mechanism, the MBR, is emitted isotropically, the events observed seem to indicate a beamed emission just as in the VHF band. The original purpose of EASIER is to achieve the detection of radio emission from air showers at distances of the order of 1 km. Until now, this distance is limited to 200 m by the radiation pattern of the emission mechanism. Improvements of the sensitivity are underway to possibly explore other emission mechanisms. vi

More than a hundred years after the discovery of cosmic rays, the origin of Ultra High Energy Cosmic Rays (UHECR) remains uncertain. Nowadays several experiments agree on the shape of the energy spectrum above 10 18 eV [1]. The ankle, a flattening of the spectrum at about 4 ⇥ 10 18 eV and a decade higher in energy a cut o↵, are observed by all recent experiments. The origin of those spectral features remains unknown. In both cases, it can be due to the source distribution and acceleration mechanisms or be the signature of energy losses during transport from the distant sources to the Earth. Indeed, the ankle could reflect the transition from a Galactic dominated cosmic ray sky to an extragalactic one, or the energy loss via e + /e pair production of proton against the cosmic microwave background. Similarly the cut o↵ could either sign the GZK e↵ect (the energy loss via pion production of protons against the cosmic microwave background) or indicate an exhaustion of sources at the highest energies. To distinguish between these scenarios, the knowledge of cosmic ray composition and anisotropies is crucial. If the ankle is due to the Galactic to extragalactic transition, this should be visible in terms of anisotropies, while if it is a consequence of the e + /e pair production, a proton composition should be clearly dominant over the ankle energy range. In the same way, if the cut o↵ is due to the GZK e↵ect, the composition should be dominated by protons at the corresponding energy, while if it is the sign of the source acceleration limitation, with a maximum energy proportional to the atomic number Z, the composition should become increasingly heavy with energy. The Pierre Auger Observatory [2] detects UHECRs via the Extensive Air Shower (EAS) they induce in the atmosphere, using two detection techniques: a surface detector array (SD) and fluorescence telescopes (FD). The SD is composed of 1660 water Cherenkov detectors that sample the air shower at the ground. The FD consists of 27 telescopes installed at five sites and measures the shower development in the atmosphere by observing the fluorescence light from the decay of ionized nitrogen atoms. The SD measures the lateral distribution of the shower at one stage of its development, and is weakly sensitive to the primary mass. In contrast, the FD reconstructs the longitudinal profile of the air shower and thus observes the maximum development of the shower which is strongly related to the cosmic ray cross section (hence its composition). However, FD only operates on clear moonless nights, that is about 10% of the time, limiting its total exposure. The detection of radio waves from the EAS holds the promises to combine a 100% duty cycle with a mass sensitivity comparable to the FD. I describe in this thesis, the developments, the installations and the data analysis of a special radio detection system called EASIER for Extensive Air Shower Identification using Electron Radiometer. Before explaining the detection setups, I briefly describe the potential emission mechanisms EASIER could be sensitive to.

ii

Radio emissions

The radio detection of EAS was already developed with some success in the 1960s, and several experiments detected strong pulses in coincidence with EAS at frequencies from a few MHz to hundreds of MHz. The radio pulses were explained by a coherent emission of shower particles due to charge separation in the geomagnetic field and a "Cherenkov like" emission from an excess of negative charges in the shower. The dependence of the radio signal was summarized by Allan [3] in the following expression:

E ⌫ = 20 ✓ E p 10 17 ◆ sin ↵ cos ✓ exp ✓ R R 0 (⌫, ✓) ◆ [µV/m/MHz] (0.0.1)
where ↵ is the angle between the arrival direction and the geomagnetic field direction, ✓ is the zenith angle, and R is the distance to the shower axis. The parameter R 0 was found to be (110 ± 10) m at the frequency ⌫ = 55 MHz and with rather vertical shower ✓  35 . At that time, the limited extension of the signal with distance, the di cult interpretation of its amplitude and the development of other techniques such as the fluorescence technique slowed down the developments of radio detection. A renewed interest started at the beginning of the years 2000 with the need for an increased aperture at ultra high energy and the progress in low noise electronics and data processing. Recent experiments like CODALEMA [4], LOPES [5] or AERA [6] confirmed the potential of this technique at energies around 10 17 eV by instrumenting radio detector arrays with a spacing of about one hundred meters.

In addition to these recent developments in the VHF band, in 2008, a beam experiment was designed to observe the continuum emission in the band [1.5-6 ]GHz upon the passage of an electron beam in an anechoic chamber [7]. The emission, interpreted as Molecular Bremsstrahlung Radiation (MBR) produced by low energy electrons of the plasma induced after the passage of the shower, was reported su cient to be observed from EAS. This radiation is emitted isotropically and the expected flux from air shower deduced from the measurement in laboratory is expressed as:

F (t) / F ref • ✓ d R(t) ◆ 2 • ✓ N (t) N ref ◆ ↵ [W/m 2 /Hz] (0.0.2)
where the F ref = 4⇥ 10 16 W/m 2 /Hz and N ref ' 2 ⇥ 10 8 are a reference flux and the number of particles of a 3.36 ⇥ 10 17 eV reference shower as deduced from the laboratory measurement. The parameter ↵ indicates the level of coherence of the emission, i.e. its dependence with the number of particles. The beam measurements seem to indicate a full coherence that is ↵ = 2.

EASIER

The EASIER detectors are developed to detect extensive air shower radio signal in a complementary way to the Pierre Auger Observatory surface detector. It is flexible in terms of the frequency it is sensitive to. The radio detector is integrated with the water Cherenkov tank, and while the latter triggers at the passage of particles at ground, the former is recording the radio emission from the air shower. The measured radio profile will provide a calorimetric measurement of the electromagnetic shower by integration of the signal and two

iii key informations for mass discrimination: firstly the depth of shower maximum development directly related to the primary composition can be deduced from the position in time of the maximum in the radio trace, secondly the muonic signal at ground can be inferred by subtraction of the electromagnetic component, as estimated from the radio, to the total signal recorded by the water Cherenkov detector.

The EASIER design includes a wide field of view antenna pointing at the zenith followed by an amplification and a filtering stage to select a bandwidth free from RFI (Radio Frequencies Interferences). Then, a power detection stage transforms the RF signal in its power envelope. Finally, a dedicated electronics adapts the power detector signal to the electronics input of the Auger SD detector unit which performs the acquisition. This scheme has been applied successfully to the VHF band and at microwave frequency where MBR from EAS is expected.

VHF band

The purpose of EASIER in this band is to explore a possible emission that could be detectable at further distances and higher energies than the coherent radiation reported by previous experiments. In this band the sensitive part of the detector, the antenna and the amplifier are the one developed for the CODALEMA experiment. The antenna is a fat dipole made of two aluminum blades of 0.6 m each and 0.1 m wide. It is tuned to a resonance frequency of ⇠ 113 MHz and is matched with an amplifier to obtain an approximately flat frequency response from 1 kHz to 90 MHz. We developed an electronic board whose function is a filtering between 30 and 80 MHz, and to adapt the signal to the Auger SD electronics. This last function is performed by the power detector, that transforms the RF signal to a DC voltage proportional to its power in logarithmic scale, and by an amplification that allows us to select a dynamic range of around a factor 10000 in power.

The calibration of the electronic boards was performed in laboratory, however, due to the large amount of background noise at these frequencies in urban conditions the whole setup could not be tested completely until the installation on site. The installation of seven of these detectors was carried out at the Pierre Auger Observatory in March 2011 and several modifications were brought to the initial setup to guarantee a good data taking. After a selection to reject noisy radio traces, we reported the detection of 36 radio events in coincidence with air shower detected by the SD with energy ranging from a few 10 17 eV to more than 3 ⇥ 10 19 eV. The main characteristics of these events are a short distance to the shower axis, a large zenith angle and an excess of detection from the southern direction. The e↵ect of the water Cherenkov detector on the radio sensor, crucial to perform the coincident detection, has been explored in detail. A study of the noise induced by the tank was achieved by emitting fake signal in the water Cherenkov tank and estimating the resulting amount of noise measured by the antenna. This study has shown that the tank is not the origin for the radio events. Nevertheless, electromagnetic simulations showed that the position of the antenna with respect to the tank could influence the radiation pattern and favor the detection of event coming from the south. Finally, the distribution of the signal with the distance from the shower axis shows an exponential decrease supporting a coherent emission. The excess of detection of radio events from southern direction also confirms a geomagnetic origin of the emission but this e↵ect is enlarged by the detector e↵ect. This first setup has shown the feasibility of the coincident detection with the surface detector of the Pierre Auger Observatory in the VHF band. It has raised experimental issues such iv as the importance of a steep filtering and the influence of the tank on the antenna pattern.

A second demonstrator has been developed to overcome these e↵ects and to improve the sensitivity.

Microwave

The developments in the microwave band were triggered by the measurement in beam experiment of an emission between 1.5 and 6 GHz from a shower of particles. The purpose of EASIER in this band is to confirm the possibility of detection in the microwave band and to evaluate if the parameters measured in laboratory, F ref and ↵ of Eq. 5.1.1 are identical in extensive air shower condition. After a noise survey at the Pierre Auger site, the C-band [3.4-4.2 ]GHz was chosen for its atmospheric transparency and the availability of low cost commercial equipment. The antenna we used is a feed horn equipped with an integrated Low Noise Block which amplifies and shifts the RF signal at frequencies between 0.95 and 1.75 GHz. The RF signal is then fed to a power detector and adapted to the Auger SD electronics to obtain a dynamic range of a factor 100.

In April 2011, a first installation of one hexagon, i.e. seven surface detectors, led to the first detection of an air shower in the GHz range. This success triggered the installation of 54 more units one year later. An important work on calibration has been carried out to determine the sensitivity of the detector, defined by the minimum flux detectable. The sensitivity reads:

F signal = k B • T sys A ef f (✓, ) • p ⌧ • ⌫ [W/m 2 /Hz] (0.0.3)
with k B T sys the noise power density, ⌫ the frequency bandwidth, ⌧ the time of integration of system and A ef f the e↵ective area of the antenna. The e↵ective area is imposed by the required field of view. T sys was measured by di↵erent means to around 50 K, i.e. compatible with the detection of MBR as parameterized in [7]. We performed also a calibration of the complete detector on site using an external source carried by an octocopter and flying above EASIER setup. The calibrated power from the source allowed us to estimate our level of noise. It indicated a level of sensitivity in the proper range for MBR detection even if large systematic uncertainties prevented us from reporting a precise number. The microwave detectors have been running in a stable way up to now. The data analysis performed allows us to report four unambiguous radio detections. The origin of these signals is still under investigation. The short distances from the antenna to the shower axis ( 300 m) support a coherent emission origin and the mechanism could indeed be due to a geomagnetic e↵ect, like in the VHF band. However, due to propagation e↵ect in a medium with a refractive index greater than one, even an isotropic emission is greatly enhanced at short distance.

To disentangle the possible mechanisms of emission, we developed a detailed simulation chain.

The particle profile of an extensive air shower is simulated and the microwave emission is estimated using the parameters measured in [7]. The propagation e↵ects due to the refraction index are accounted for. The antenna is simulated according to the calibration measurements and a specific electronic simulation was implemented.

The comparison between simulation and the detected events is being finalized. Conclusions are di cult to draw on the small data set of radio signals. Nevertheless, the non detection at large distances will allow us to set limits on the isotropic MBR flux.

v Chapter 1

Ultra High Energy Cosmic Rays

The discovery of cosmic ray is now more than a hundred years old. It is usually attributed to Viktor Hess in 1912, who reported an increase of ionization rate in air with higher altitude during a manned balloon flight [1].

Earlier experiments on ionization in air at sea level had shown a ionization rate that was attributed to natural radioactivity. Thus, results of Hess, later confirmed by Kolhörster [2], established that a radiation was issued not from the ground but rather from the atmosphere. The study of this radiation continued further with other balloon flights and measurements under water. The conclusion remained the same, the ionization rate evolution is best explained by "cosmic ray". During the 1930s the proof was made that these particles were charged [3] and the observation of an excess of events from western direction demonstrated that most of them were positively charged [4,5]. Meanwhile, detectors had improved too, and electroscopes replaced by Geiger Müller particle counter. A breakthrough was accomplished by Bothe and Rossi, in the 30s, as they developed coincidence setup. This new technique allowed the observation of an increase of coincidences between three distant counters when a plate of lead was placed above them [6]. This was the first observation of what Rossi called a "shower" of particles. A little later in 1939, with an improved timing resolution for coincidence, Pierre Auger and collaborators were able to make coincidence between counters 300 m apart, demonstrating then the existence of extensive shower of particles in air [7]. Auger and collaborators inferred an energy of ' 10 15 eV for the particle initiating the shower. They estimated the number of particles, assumed an average energy of 10 8 eV per particle and accounted for a factor of ten in ionization losses. This very high energy led them to raise fundamental questions about the origin of cosmic ray and the mechanism that leads to such energies. These questions are expressed by Pierre Auger in the conclusions of [7]: "One of the consequence of the extension of the energy spectrum of cosmic rays up to 10 15 eV is that it is actually impossible to imagine a single process able to give to a particle such an energy". Since then, Cosmic Rays (CR) have been extensively studied. They are now defined as ionized nuclei coming from outside the solar system with an energy larger than 10 9 eV (1 GeV) and that can extend to more than 10 20 eV. At the highest energies, we will refer to as Ultra High Energy Cosmic Rays (UHECR). The di↵erential energy spectrum of cosmic ray, shown in ss started he flew a to everytor of two balloons measured ung (high ed by the together at cosmic nthesis of ch during e proved bsorbers. er of lead any expestudy the etic field. erent gerays are ome from magnetic from the ose from elopment eory. Tocollabotain altiller tubes uded that osphere. even earthat the ary cosshower' is the italersations ulated in article of y". This gh energy cosmic ray spectrum below the knee is a power law E with spectral index ↵ = 2.7. Above the knee the spectral index increases with ↵ = 0.3. Above the ankle the power law spectrum becomes flatter and similar to that before the knee. The values of the spectral indices show that below the knee the flux decreases by a factor of 50 when the energy increases by an order of magnitude. Above the knee the decrease is by a factor of 100. Because of the decrease, cosmic rays of energy above 10 14 eV are di cult to measure by direct experiments performed on balloons and satellites. The flux of such cosmic rays is about 3 particles per hour per steradian in one square meter de-Figure 1.1: Di↵erential energy spectrum of cosmic rays above 100 GeV as measured by the experiments mentioned in the upper right corner (from [8]). It is multiplied by E 2 , in gray are pointed the position of the cosmic ray knee and ankle (see text).

Knee

The energy spectrum demonstrates an almost featureless decrease with energy with a power law shape, dN/dE / E . This energy dependence indicates a non thermal phenomenon at the acceleration site. A first explanation was given by Fermi in 1949 [9]. He described a process in which cosmic rays are accelerated by "collision against moving magnetic field" in the Galaxy and gain at each interaction an amount of energy E / E. This model was extended later to di↵usive shock acceleration in astrophysical objects like Super Novae Remnant (SNR) and yields naturally to an inverse power law spectrum with a spectral index similar to the one observed. But to reach energy up the 10 20 eV one needs to find the appropriate astrophysical object likely to accelerate cosmic ray with such energy. Beyond the overall regularity of the spectrum, three main features are visible. Before 4 ⇥ 10 15 eV, the spectrum falls with an index of ' 2.7 and steepens above with ' 3.1. This change of slope, called the knee is followed at higher energy by the ankle, a flattening Ultra High Energy Cosmic Rays above 4 ⇥ 10 18 eV. At the very end of the spectrum above 3 4 ⇥ 10 19 eV, up to the years 2000, data of di↵erent experiments yielded to contradictory results: some reported a strong cut o↵ of the flux the other a spectrum falling with a constant index. This tension is now solved since the data of the most recent observatories confirm a steepening of the flux. How can these features be interpreted ? Are they related with the production process or to the source distribution or propagation e↵ects ? Because of the sharp decrease of the flux, the rate of events in an energy bin decreases by a factor 50 to 100 per decade leading to a rate of less than one particle per km 2 per century above 10 20 eV. As a consequence, cosmic rays above around 10 15 eV cannot be detected directly with satellite or balloon born detectors as at lower energy since the flux is too low to detect enough particles in a reasonable amount of time. Instead, they are detected through the shower they induce in air. Observatories covering a large surface or volume of detection are operated on earth, the atmosphere serving as a giant calorimeter. Such indirect detection necessitates a constant atmosphere monitoring and a precise understanding of interaction of ultra high energy particles with air molecules. Thus, the cosmic ray physic field embraces astrophysics to point possible sources of acceleration and evaluate the interaction of CR during their propagation in space but also high energy particle physics to study their interaction in atmosphere, and addresses challenge in detector development. We will first address the question of production and propagation of UHECR, then we will give a simple model of air shower development and deal with the main methods used to their detection. We will give in the next section a more precise insight on the Pierre Auger Observatory, its detection methods and its experimental results. The last part is a short description of the current models proposed to explain the observational data at ultra high energy.

UHECR production and propagation

Ultra High Energy Cosmic Rays

UHECR production and propagation

The question raised by the observation of UHECR is naturally how they are accelerated. Moreover, to be able to interpret the observational data one has to account for propagation e↵ects undergone by UHECR during their transport to the Earth.

Acceleration mechanism

In 1949, Fermi proposed an acceleration mechanism based on the scattering of cosmic rays on interstellar magnetized clouds. As they enter the magnetized cloud, charged particles are bent and eventually ejected away. In this process the CR energy remains unchanged in the frame of the cloud because only magnetic force are involved, but if we consider the frame in which the cloud is moving, the CR energy is changed. The gain in energy is found to be E / 2 E where = V /c the velocity of the cloud. This mechanism was attracting since it yields naturally an inverse power law energy spectrum as observed but according to the mean velocity and distribution of clouds this process is not suited to explain the cosmic ray acceleration. It was extended to what is called the di↵usive shock acceleration [10]. The acceleration is achieved by the movement of a charged particle back and forth between the upstream and the downstream region of a shock wave. For instance a supernova explosion is known to come together with such expanding shock. Particle with a Larmor radius smaller than the dimension of the shock remain in the acceleration source and gain energy at each cycle. The resulting energy gain is proportional to the velocity of the shock rather than 2 in the case of the mechanism of acceleration originally proposed by Fermi. The maximum energy reachable by a charged particle is:

E max = ZeBr s (1.1.1)
where is the speed of the shock, Ze the charge of the particle, B the ambient magnetic field and r s the shock radius. The magnetic field and the dimension of the astrophysical object are the limiting factors. Note that, in case of acceleration in medium in relativistic motion with respect to the Earth and a particle escaping in direction of the Earth, the maximum energy is increased by the Lorentz factor. For typical value of super novea of type II, the maximum energy is E max ⇠ Z ⇥ 10 14 eV [11]. More recent estimates find an energy an order of magnitude larger [12], and accounting for mechanisms of interaction between magnetic field at source and the accelerated particle can enhance this value [13], thus becoming compatible with the knee region energy.

To reach higher energies up to 10 20 eV, other astrophysical objects are proposed. They are gathered in the classic Hillas plot (Fig. 1.2, left) as a function of their magnetic field and dimension. The astrophysical objects can be potential sources if they lie above the line corresponding to the specie to accelerate above 10 20 eV. The remaining candidates are Active Galactic Nuclei (AGN) and FRII galaxies, Gamma Ray Burst (GRB) or neutron stars. A more exotic mechanism was also proposed, in this mechanism super massive particles decay producing quarks and leptons, which in turn produce ultra high energy photons, neutrinos and a small fraction of protons. These models in which no acceleration mechanism is required are called top-down models.

Ultra High Energy Cosmic Rays 1.1 UHECR production and propagation 15 ch top-down sources. ollected by HiRes and ation has been greatly rgy end of the spectrum the fraction of photons trinos have strongly ren models. On the other t iron component in the decreases by a factor 26 ndard" bottom-up cos-EeV barrier. des of investigation the even the extragalactic V has been challenged ., 2010)). In the followe necessary conditions astrophysical sites and tes. We also briefly rethe top-down models. be found in the recent 11), now in press.

sites may occur princianisms: di↵usive shock i mechanism and one electric field generated netized objects such as ce near shock waves and of charged particles on forth across the shock. hock velocities the enthe order of E ⇠ E. rge acceleration regions aves are necessary. In e energy gain reaches Lorentz factor. Such ted to the first crossing s of the di↵usive shock it naturally provides a icted index is within asurements. Depending k and on its relativistic nergy gain per crossing s to a power law index g non relativistic shock etween 2.1 and 2.4 for conditions on potential between the maximum nd the size and strength FIG. 11 Hillas plot for candidate acceleration sites, relating their size and magnetic field strength. To accelerate a given particle species above 100 EeV objects must lie above the corresponding lines.

of the magnetic field of the site:

E max = Ze ✓ B 1µG ◆ ✓ R 1kpc ◆ EeV
where represents the velocity of the accelerating shock wave or the e ciency of the accelerator 2 . We show in Fig. 11 the now famous "Hillas plot" illustrating this condition.

Looking at the Hillas diagram one sees that only a few astrophysical sources satisfy this necessary, but not sucient, condition. Among the possible candidates are neutron stars and other similar compact objects, large-scale shocks due to merging galaxies or clusters of galaxies, the core and jets of Active Galactic Nuclei (AGN), hot spots of Fanaro↵-Riley class II (FR-II) radio galaxies and processes associated with Gamma Ray Bursts (GRB).

AGN have long been considered as potential sites where energetic particle production might take place ( [START_REF] Ginzburg | The Origin of Cosmic Rays[END_REF]Hillas, 1984)). AGN jets have dimensions of the order of a fraction of a parsec with magnetic field of the order of a few Gauss ((Halzen and Zas, 1997)). These parameters could in 2 In the case of a relativistic shock the bulk Lorentz factor which cosmic rays could be accelerated [START_REF] Apel | LOPES 3D -vectorial measurements of radio emission from cosmic ray induced air showers[END_REF]. The solid line indicates (2) for protons and the dashed sources: anomalous x-ray pulsars and magnetars (AXP), neutron stars (NS), supermassive black hole galaxies (Sy) to powerful radio galaxies (RG) and blazars (BL), the central parsec (AD) of active ga and lobes (L) of powerful active galaxies, non-relativistic jets of low-power galaxies (Sy), starburst intercluster voids.

The short energy loss lengths indicate that cosmic rays with energies above a 100 Mpc sphere. Astrophysical sources within our Galaxy are disfavored. Ev stars could be thought of as accelerating particles to the highest energies obser apparent isotropic arrival direction of UHECRs to energies beyond 10 19 eV. As are no longer confined by galactic magnetic fields, it is natural to assume that th Considering diffusive shock acceleration, which is thought to accelerate cosm B in the source and the size R of the source region are related to the maximum a

E max ⇥ 10 18 eV Z s R kpc ⇥ B µG ⇥ ,
where s is the shock velocity in units of c and Z is the particle charge. This re astrophysical objects. The list of the very few viable candidate sources includes lobes of FR II galaxies [START_REF] Monasor | The MIDAS experiment: A prototype for the microwave emission of Ultra-High Energy Cosmic Rays[END_REF][START_REF] Alvarez-Muniz | The MIDAS telescope for microwave detection of ultra-high energy cosmic rays[END_REF], and gamma-ray bursts (GRBs) [START_REF] Auger Collaboration | The Pierre Auger Observatory V: Enhancements[END_REF] (for a review o Many alternative, non-acceleration scenarios -called top-down models -ha are produced in decays of super-heavy objects such as super-heavy dark defects [START_REF] Williams | UHECR 2012 -International Symposium on Future Directions in UHECR Physics[END_REF]. All of these models postulate new particle physics and predict typ energy [START_REF] Kampert | The Pierre Auger Observatory -Status and prospects[END_REF]. Finally there are propagation model scenarios in which the GZK en higher energies. Examples are a violation of Lorentz invariance [START_REF] Orfanidis | Electromagnetic Waves and Antennas[END_REF], the Z -burs with properties similar to protons [START_REF] Ardouin | An active dipole for cosmic ray radiodetection with CODALEMA[END_REF][START_REF] Charrier | Design of a low noise, wide band, active dipole antenna for a cosmic ray radiodetection experiment[END_REF]. Reviews of the different scenarios ca Measurements of the arrival direction distribution, primary mass composit solving the puzzle of UHECR sources. Given an expected angular deflection of onl in our Galaxy [START_REF] Gambetta | Study of the Attenuation of Extensive Air Showers in the Atmosphere and of the Feasibility of Measuring their Radio Signal with EASIER[END_REF] and the existence of large cosmic voids with negligible magne should finally allow cosmic-ray astronomy and reveal correlations with sou the composition of UHECRs will restrict the classes of source models. For exa top-down models. Another very important source of complementary informa i.e. gamma-rays and neutrinos, produced in UHECRs sources and during propag

Detection techniques

Shower properties

In what follows, we will introduce some general properties of extensive air measurements. Detailed presentations of this subject can be found in [93]. [8]). Right: Loss length as a function of energy for protons and nuclei (from [14]).

Propagation

Once possible sources are pointed out, one has to evaluate how the propagation of cosmic ray from their production site will a↵ect their flux on Earth. Indeed, soon after the discovery of the Cosmic Microwave Background [15] it was noticed by Greisen [16] and by Kuzmin and Zatsepin [17] that the interaction of ultra high energy protons with CMB photons exceeds the threshold of pion production:

p + ! N + ⇡ (1.1.2)
Where N can be a proton or a neutron and consequently the pion can be neutral or positively charged. Ultra high energy neutrons undergo the same type of interaction. In the Lab frame the energy in center of mass reads:

p s = q m 2 p + 2E p ✏ (1 cos ✓) (1.1.3)
with E p and ✏ the proton and photon energy and ✓ the angle of collision. In a frontal collision (cos ✓ = 1) and with a mean CMB photon energy of < ✏ >= 6.3 ⇥ 10 4 eV, the energy threshold of proton is found to be E p ' 10 20 eV. This threshold is actually lower, around 3 ⇥ 10 19 eV because of the CMB photons with energy higher than < ✏ >.

This e↵ect is referred to as the GZK e↵ect. For nuclei, the dominant process above 10 19 eV is the photo disintegration on CMB and infrared background due to giant dipole resonance [START_REF] Stecker | Photodisintegration of ultrahigh-energy cosmic rays: A New determination[END_REF]:

A + ! (A 1) + N (1.1.4)
where A is the nucleus of mass number A and N is either a proton or a neutron. The energy at which this interaction occurs depends on nuclei mass and is comparable to the GZK threshold

UHECR production and propagation

Ultra High Energy Cosmic Rays for iron nuclei.

In addition, CR lose their energy via the pair production : A + ! A + e + e + where A can be a proton or a nucleus. This interaction occurs typically around 10 18.4 eV for a proton and at higher energy for nuclei. The energy loss length for protons and nuclei are depicted in Fig. 1.2 (left). It defines the length scale on which a particle loses its energy and thus delimits the distance from which a cosmic ray can be produced and still reach the earth with the corresponding energy. Note the short length due to the GZK e↵ect constraining the sources of cosmic rays with an energy observed above 10 20 eV to be in a 100 Mpc horizon. The multiplication continues until individual pion energies drop below a critical energy n p c , where it begins to become more likely that a p ± will decay rather than interact. All p ± are then as-then develop the hadronic analogue. In all that follows, the term ''electron'' does not distinguish between e + and e À .

Electromagnetic showers

As seen in Fig. 1a, an electron radiates a single photon after traveling one splitting length Although very simplified, Heitler's model reproduces correctly three properties of electromagnetic cascades :

1) The number of particles at the maximum of the cascade development is proportional to the incoming primary cosmic ray energy :

N max = E 0 /E c (1)
2) The evolution of the depth of maximum of the shower (measured in g/cm 2 ) is logarithmic with energy:

X max = X 0 + r ln(E 0 /E c ) ( 2 )
where X 0 is the position of the start of the cascade.

3) The rate of evolution of X max with energy, the elongation rate, defined as

D 10 ⌘ dX max d log 10 E 0 = 2.3 r ( 3
)
is given by the radiation length of the medium. This elongation rate is about 85 g/cm 2 in air.

Extensive simulations of electromagnetic cascades confirm these properties although the particle number at maximum is overestimated by about a factor 2 to 3. Moreover, Heitler's model predicts a ratio of electrons to photons of 2 while simulations and direct cascade measurements in Air show a ratio of the order of 1/6th. This is in particular due to the facts that multiple photons are emitted during bremsstrahlung and that electrons lose energy much faster than photons do.

B. Extension to hadronic showers

Heitler's model can be adapted to describe hadronic showers ( [START_REF] Matthews | A Heitler model of extensive air showers[END_REF]Stanev, 2010)). In this case the relevant parameter is the hadronic interaction length I . At each step of thickness I ln 2 it is assumed that hadronic interactions produce 2N charged pions and N neutral ones. While ⇡ 0 decay immediately and feed the electromagnetic part of the shower, ⇡ + and ⇡ interact further. The hadronic cascade continues to grow, feeding the electromagnetic part at each step, until charged pions reach an energy where decay is more likely than a new interaction. A schematic of an hadronic cascade is shown in Fig. 3. The interaction length and the pion multiplicity (3N ) are energy independent in the model. The energy is equally shared by the secondary pions. For pion energy between 1 GeV and 10 TeV a charged multiplicity of 10 (N = 5) is an appropriate number.

FIG. 3 Schematic evolution of an hadronic cascade. At each step roughly 1/3rd of the energy is transferred from the hadronic cascade to the electromagnetic one.

One third of the available energy goes into the electromagnetic component while the remaining 2/3rd continues as hadrons. Therefore the longer it takes for pions to reach the critical energy E c (20 GeV in air, below which they will decay into muons), the larger will be the electromagnetic component. Consequently in long developing showers the energy of the muons from decaying pion will be smaller. In addition, because of the density profile of the atmosphere, E c is larger high above ground than at see level and deep showers will produce fewer muons.

This positive correlation introduces a link between the primary cosmic ray interaction cross section with Air and the muon content at ground. According to those principles primaries with higher cross sections will have a larger muon to electron ratio at ground.

To obtain the number of muons in the shower one simply assumes that all pions decay into muons when they reach the critical energy. N µ = (2N ) nc where n c = ln(E 0 /E c )/ ln 3N is the number of steps needed for the pions to reach E c . Introducing = ln 2N / ln 3N (0.85 for N = 5) we have:

N µ = (E 0 /E c ) (4)
Unlike the electron number, the muon multiplicity does not grow linearly with the primary energy but at a slower rate. The precise value of depends on the average pion multiplicity used. It also depends on the inelasticity of the hadronic interactions. Assuming that only half of the available energy goes into the pions at each step (rather than all of it as done above) would lead to = 0.93.

Extensive Air Showers

The detection of the highest energy CR is achieved through the observation of the cascade of particles they induce in the atmosphere. When entering the atmosphere, from the interaction of the primary CR with atoms in air, secondary particles are produced which in turn interact and achieve the process of particle production again. In this way an air shower develops in the air in competition with ionization losses undergone by the shower particles. For instance, a primary CR with an energy of E = 10 19 eV induces billions of secondary particles. After giving the basic models to describe the EAS development, we describe the main detection techniques used in the current experiments.

Model of development

We describe a simple analytical model of shower development in the case of electromagnetic cascade (induced by a electron, positron or a photon) and its extension to hadron induced shower.

Electromagnetic shower

The model was introduced by Heitler in [START_REF] Heitler | Quantum Theory of Radiation[END_REF] to describe electromagnetic cascade i.e. shower induced by photons, electrons or positrons. It assumes a fixed distance step of interaction and cross sections independent of energy. The distances, or depths, are considered as the amount of traversed matter along the particle path and they are expressed in g/cm 2 . At each step, photons produce an electron-positron pair, and electrons (or positrons) radiate half their energy on one Bremsstrahlung photon. The scheme of such development is given in Fig. 1.3 for a photon primary. The distance of interaction is then d = r ln 2 where r ' 37 g/cm 2 in air is the radiation length for Bremsstrahlung process. The development stops when particles have a critical energy E em c , at which losses in ionization dominate over the particle production. This energy is reached after n c steps when the number of particles is:

N max = 2 nc = E 0 /E em c (1.2.1)

Extensive Air Showers

Ultra High Energy Cosmic Rays with E 0 the energy of the primary particle. The number of steps to reach the maximum is then n c = ln(E 0 /E em c )/ ln 2 and its depth is given by:

X max = n c r ln(2) = r ln(E 0 /E em c ) (1.2.2)
With this simple consideration, the Heitler model points out two important behaviors of an electromagnetic cascade:

the number of particles at maximum of development, N max , is proportional to the primary energy the depth of this maximum, X max , depends logarithmically on energy More realistic simulations confirm the behavior of these parameters for electromagnetic cascade. They show however that Heitler's model overestimates the total number of particles at maximum by a factor two or three mainly because the attenuation is not accounted for, and that the ratio photon to electron is underestimated since more than one Bremsstrahlung photon is emitted by electrons at each interaction length.

Hadronic shower At ultra high energy, the CR are mainly nuclei. The previous model was extended for hadron initiated shower by Matthews in [START_REF] Matthews | A Heitler model of extensive air showers[END_REF]. In that case, it is assumed that each hadronic interaction produces a number N ch of charged pions and N ch /2 of neutral pions. The relevant interaction distance is now I ln 2 with I the hadronic interaction length. The charged pions interact with molecules of air and fuel the hadronic channel while each neutral pion decays immediately into two photons initiating electromagnetic cascades as it is depicted in Fig 1 .3 (right). The particle production ends when the decay of charged pions into muon starts to dominate. Thus, along the development of an hadronic shower, three components are present: the hadronic, the electromagnetic and the muonic one. For a primary proton of energy E 0 , after n interaction lengths, the number of charged pions is

N ⇡ = N n ch with an energy E ⇡ = E 0 /( 3 2 N ch ) n
. At a critical energy E had c , when the decay length of the charged pion becomes smaller than the interaction length in air, the hadronic channel stops to develop. The number of steps to reach this stage is given by n

c = ln(E 0 /E had c ) ln( 3 2 N ch )
. At this stage, it is assumed that all the pions decayed into muons resulting in a muon number of ln N µ = ln N ⇡ = n c ln N ch , or :

ln N µ = ln(E 0 /E had c ) ln( 3 2 N ch ) ln N ch = ln(E 0 /E had c ) with = ln N ch ln 3 2 N ch (1.2.3
)

) N µ = ✓ E 0 E had c ◆ (1.2.4)
The multiplicity N ch , the number of charged pions at each interaction, is taken in [START_REF] Matthews | A Heitler model of extensive air showers[END_REF] to be 10 from accelerator measurements. The value of the exponent is then 0.85, showing the non linearity of the number of muons with the primary energy. Concerning the electromagnetic part, the total energy taken away from it, E em , can be calculated by subtraction of muon energy, E had , from the primary energy :

E em = E 0 E had = E 0 N µ E had c ) E em E 0 = 1 ✓ E 0 E had c ◆ 1 (1.2.5)
Ultra High Energy Cosmic Rays

Extensive Air Showers

For a primary energy of E 0 = 10 14 eV the electromagnetic component takes away ' 70% of the total energy, and this value rises up to 90% for E 0 = 10 17 eV.

The depth for which the electron and photon number is maximum, is more delicate to obtain.

In principle one should sum the contributions of each electromagnetic sub-shower, however accounting only for the first interaction simplifies the treatment and keeps the main properties of X max but its absolute value will be under evaluated.

The depth of maximum is given by :

X p max = X 0 + X em max (1.2.6)
where the depth of first interaction is X 0 = I ln 2 and I the proton air interaction length. If at the first interaction, the incoming proton doesn't transfer its entire energy by just a portion K el of its kinematic energy to 1 2 N ch neutral pions, their decay yields N ch photons with an energy E 0 /(3N ch ). These photons initiate an electromagnetic cascade that reach their maximum according to Eq. 1.2.2. Then X p max writes down :

X p max = X 0 + r ln ✓ E 0 (1 K el ) 3 • N ch • E em c ◆ (1.2.7)
Now if we want to extend the problem to heavier nuclei than a proton, we can introduce the superposition approximation that states that a shower initiated by a nucleus of mass number A and an energy E 0 behave like a superposition of A showers initiated by nucleons of energy E 0 /A. In this approximation, the shower size, increasing linearly with the primary energy remains the same, but the depth of maximum becomes :

X A max = X 0 + r ln ✓ E 0 (1 K el ) 3AN ch • E em c ◆ = X p max r ln A (1.2.8)
and the number of muons :

N A µ = A( E 0 AE ⇡ c ) = A 1 N p µ (1.2.9)
The simple parameterization described above and the superposition model assumption, allow us to point out interesting features on hadronic showers: at su ciently high energy (above 10 17 eV) most of the primary energy is carried by the electromagnetic part.

the depth of shower maximum, X p max , is driven by the first hadronic interaction and the development of the first electromagnetic cascade.

X A max varies logarithmically with the mass number A of the primary.

the number of muons varies with A 1 where ' 0.85.

Nowadays, air shower description is done by means of Monte Carlo simulations. They account for much details neglected in the previous models like the energy dependence of the cross section and the inelasticity of each process. They rely on accelerator measurements but adopt di↵erent extrapolation at energies above the TeV (= 10 12 eV) scale in center of mass. We show the evolution of the number of particles as a function of the atmospheric depth for two simulated air showers induced by a proton and an iron primary at 10 19 eV in Fig. 1.4 (left).

Extensive Air Showers

Ultra High Energy Cosmic Rays Right panel: Mean depth of the shower maximum calculated with different hadronic interaction models and CONEX (from [137], modified).

If the primary particle is a nucleus, one can use the superposition model to deduce the main shower characteristics [116].

In this model, a nucleus with mass A and energy E 0 is considered as A independent nucleons with energy E h = E 0 /A. The superposition of the individual nucleon showers yields

N A max ⇤ A • E h E c = E 0 E c = N max (12) X A max ⇤ X max (E 0 /A) (13) N A µ ⇤ A • E 0 /A E dec ⇥ = A 1 • N µ . (14)
To a good approximation, while the number of charged particles at the shower maximum is independent of the primary hadron, both, the number of muons and the depth of maximum do depend on the mass of the primary particle. The heavier the shower-initiating particle the more muons are expected for a given primary energy. In addition, the superposition of A independent showers naturally explains why the shower-to-shower fluctuations are smaller for shower initiated by nuclei as compared to proton showers. Detailed shower simulations confirm the basic shower properties discussed so far. Quantitative predictions depend on the details of modeling particle production and transport [117][118][119]. Whereas em. interactions are rather well understood within perturbative QED, hadronic multiparticle production cannot be calculated within QCD from first principles. Phenomenological models have to be used to describe the final states of hadronic interactions. The parameters of these models are determined by comparing the model predictions with accelerator measurements. Reflecting the different methods for describing data, low-and high-energy interaction models are distinguished. The former ones are typically based on the picture of intermediate resonance formation and decay as well as parametrizations of data. The latter ones involve the production of color strings and their fragmentation.

For high energy interactions (E lab 100 GeV), the hadronic interaction models often used in air shower simulations are DPMJET II. 55 and III [120,121], EPOS [122,123], QGSJET 01 [124] and QGSJET II [125], as well as SIBYLL 2. 1 [116,126,127]. These models reproduce accelerator data reasonably well but are characterized by different extrapolations above a centerof-mass energy E cms ⇥ 1.8 TeV (E ⇥ 10 15 eV), leading to very different shower predictions at high energy [117,118,128,129].

The situation is different at low energy where more measurements from fixed target experiments are available. One of the main problems there is the extrapolation of measurements to the very forward phase space region close to the beam direction and the lack of measurements of pion-induced interactions with light nuclei [114]. At low energy, models based on data parameterizations and/or microscopic models such as FLUKA [130], GHEISHA [131], UrQMD [132], or TARGET [133] are used. Differences in the predictions of these models are important for the number of muons [134], in particular at large lateral distances.

In Figs. 4 and5, we illustrate some shower properties discussed only qualitatively so far by showing the results of detailed Monte Carlo simulations done with CORSIKA [135] and CONEX [136].

The longitudinal profile of a typical proton shower of 10 19 eV is shown in Fig. 4 (left). In the region of the shower maximum, less than 1% of the charged shower particles are muons. The electromagnetic component is absorbed much faster than the muonic one. where X0

36.62 g/cm 2 is the radiation length in air and em c

84 MeV is the critical energy in air at which ionization and bremsstrahlung energy losses are equal. If the total multiplicity of hadrons produced in the main interaction is N and the average hadron energy is E/N, then the shower maximum of a primary proton is

X p max p + X0 ln E 2N em c (3)
where both the hadronic interaction length and particle production multiplicity are energy dependent. The factor 2 takes into account that neutral pions decay into two photons. Furthermore, the shower maximum is expected to be influenced by the elasticity of the first interaction, ela = Elead/E, where Elead is the energy of the highest energy secondary produced in the interaction. For interactions with ela > 0.5 most of the primary energy will be transferred deeper into the atmosphere and correspondingly the shower maximum will be deeper. We are not aware of a consistent treatment of the elasticity within a Heitler model for the longitudinal development, however using air shower simulations, the dependence on the elasticity fits well to

X p max p + X0 ln ela E 2N em c . (4)
The elongation rate [START_REF] Auger Collaboration | Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter[END_REF][START_REF] Auger Collaboration | Measurement of the first harmonic modulation in the right ascension distribution of cosmic rays detected at the Pierre Auger Observatory: towards the detection of dipolar anisotropies over a wide energy range[END_REF][START_REF] Achterberg | Intergalactic propagation of uhe cosmic rays[END_REF] is a measure of the change of the shower maximum per logarithm of energy,

D = d Xmax d ln E . (5)
For protons and constant elasticity Eq. ( 4) gives

Dp = d X p max d ln E X0 (1 BN B ) (6)
where the changes in multiplicity and interaction length are given by

BN = d ln N d ln E and B = p X0 d ln p d ln E . ( 7
)
Since hadronic interaction models predict an approximately logarithmic decrease of p with energy and N E , Dp is approximately constant and therefore

X p max c + Dp ln E, (8)
with parameters c and Dp being dependent on the characteristics of hadronic interactions. Using the aforementioned (semi-)superposition assumption, one obtains

X A max = X p max (E = E/A) = c + Dp ln(E/A) (9)
and at a given energy the average shower maximum for a mixed composition with fractions fi of nuclei of mass Ai is

Xmax i fi X Ai max = X p max Dp ln A . ( 10
)
This equation explicitly demonstrates the relation of Xmax to the average logarithmic mass of the cosmic ray composition, ln A = i fi ln A.

The numerical value of Dp from air shower simulations is about 25 g/cm 2 (or about 60 g/cm 2 for the change in Xmax per decade, D p 10 = ln(10) Dp) and therefore proton and iron induced air showers are expected to di er by around Dp(ln 56 ln 1) 100 g/cm 2 . Moreover, if the hadronic cross sections and multiplicities rise with energy (and if there are no sudden changes in the elasticity as for instance suggested in [START_REF] Veron-Cetty | A catalogue of quasars and active nuclei: 12th edition[END_REF]), then Eq. ( 7) leads to Linsley's elongation rate theorem which states that the 3 Figure 1.4: Left: Number of particle for a simulated proton and iron induced air shower(from [START_REF] Risse | Properties of extensive air showers[END_REF]). Right: Depth of shower maximum as a function of the calorimetric energy for proton and iron primary. The contour lines include 90% of the simulated showers (from [START_REF] Kampert | Measurements of the Cosmic Ray Composition with Air Shower Experiments[END_REF]).

At the shower maximum, the electromagnetic part contains more particles by two orders of magnitude than the muonic part and decrease exponentially after the maximum whereas the number of muons decreases much more slowly with the traversed matter. Furthermore, it confirms the dependence of the number of muons with the primary mass. In Fig. 1.4 (right), the simulated shower maximum is shown as a function of energy for both proton and iron primary. The increase of X max with energy is approximately logarithmic as expressed in Eq. 1.2.2 and for the same energy iron induced shower reach their maximum higher in the atmosphere (at smaller X max ). The dispersion of X max is mainly driven by the fluctuations of the first interaction. The smaller dispersion for iron can be seen as a consequence of the superposition model too, since the X max for an iron induced shower is the superposition of A = 56 nucleon showers, the fluctuations on the mean are reduced by a factor nearly p A. Note that with increasing energy, the calorimetric energy, i.e. the energy transferred to the electromagnetic component, tends to the primary one and exhibits low shower to shower fluctuation above ⇠ 10 17 eV.

Detection techniques

An air shower event is characterized by a shower front crossing the atmosphere at approximately the speed of light until hitting the ground. The shower front can be composed of billions of particles and spread over an area of several km 2 . The observation of the air shower is made by collecting the particles at ground or by detecting their interactions in the atmosphere. Since the cosmic ray flux is extremely low, air shower observatories need to cover a large area or a large volume of detection. We describe here the main methods employed in the last constructed observatories.

Air shower array Following the original detection technique set up by the pioneers, air showers are generally detected by arrays of particle detectors. Their layout and the altitude of the observatory are chosen depending on the primary energy to be studied. Particle detectors of air shower arrays sample the shower front at ground and measure the lateral distribution Ultra High Energy Cosmic Rays 1.2 Extensive Air Showers of particles at one stage of the shower development. From this information, the shower core location can be retrieved, and the measurement of arrival time of particles in the triggered detectors allows the reconstruction of the arrival direction. Regarding the detector itself, if the historic ones were electroscopes or Geiger Muller counters, nowadays they are replaced by scintillators or Water Cherenkov Detectors (WCD). Scintillators, when placed on the ground, measure essentially the electromagnetic component. They can also be buried in ground so that the electromagnetic part is absorbed and only muons are detected. Scintillators were first used at Volcano Ranch [START_REF] Linsley | Extremely energetic cosmic-ray event[END_REF], then at AGASA (Akeno Giant Air Shower Array) [START_REF] Chiba | Akeno giant air shower array (AGASA) covering 100-km**2 area[END_REF] and are now the elemental detector of the surface array of Telescope Array [START_REF] Abu-Zayyad | The surface detector array of the Telescope Array experiment[END_REF]. A Water Cherenkov Detector is a tank with a reflective inner surface filled with pure water. When charged particles enter the tank, Cherenkov light is emitted in the water and, often after reflections on the tank's wall, is collected by photo-multipliers looking downward in the water. WCD were first used at Haverah Park and are now extensively used at the Pierre Auger Observatory. Deployment of WCD is more complicated than scintillators: they require pure water and are very heavy (for instance the Pierre Auger Observatory tanks are filled with 12 m 3 of water). But they are sensitive to muons, electrons and photons (via pair production in the water for the photons) and they present a non zero e↵ective area at large zenith angles making them able to detect horizontal showers. The surface detectors measure the shower development only at one stage, thus the energy of the EAS cannot be directly estimated. Indeed the energy estimation rely either on air shower simulations if these detectors are instrumented alone either on cross-calibration with detector able to measure the energy. Surface detector array can be sensitive to the primary mass if the two main components of the EAS, muonic and electromagnetic are measured separately.

Cherenkov light

The charged particles of the shower traverse the atmosphere at relativistic speed. In particular, electrons above the threshold of 21 MeV produce a Cherenkov emission beamed in the forward direction in an angle ✓ Ch ' 1.4 in air. In several experiments, like AIROBICC [26] or TUNKA [START_REF] Budnev | The tunka experiment: towards a 1-km 2 EAS Cerenkov light array in the Tunka valley[END_REF], an array of photo-multipliers pointing towards the sky measure the lateral distribution of the Cherenkov light at ground. The distribution of light decreases exponentially with distance up to ' 120 m then exhibit a break and falls steeply at larger distances. The slope within the 120 m is found to be related to the height of the shower maximum and the intensity beyond 120 m is related to the calorimetric energy. Because of the limited lateral extension of the Cherenkov light at ground, dense arrays are required. Moreover, the operation of photo-multipliers is possible only during the night reducing the statistics of events. For these two reasons, this technique is mainly used at energies below 10 17 eV.

Fluorescence light When crossing the atmosphere, the shower particles lose their energy in ionization of the molecules in air. Consequently, the excited nitrogen molecules emit photons, mainly in the UV band, between 300 and 420 nm. Contrary to Cherenkov light, the fluorescence light is emitted isotropically. The fluorescence yield (the number of photons emitted per energy deposited) depends on pressure, temperature and electron energy. Assuming a constant density and a constant energy loss of the electrons per path length, one can give a rough estimate at ground level pressure of around 4 photons per electron per meter. Recent measurement of the fluorescence yield have been conducted in accelerator and can be

Extensive Air Showers

Ultra High Energy Cosmic Rays

Fluorescent light

The charged secondary particles in EAS produce ultraviolet light through nitrogen fluorescence. Nitrogen molecules, excited by a passing shower, emit photons isotropically into several spectral bands between 300 and 420 nm. As discussed above, a much larger fraction of UV light is emitted as Cherenkov photons. But this emission is strongly beamed along the shower axis and usually considered as a background to fluorescence detection. Fluorescence photons reach the telescopes in a direct line from their source. Thus the collected image reflects exactly the development of the EM cascade (see figure 6). From the fluorescence profile it is in principle straightforward to obtain the position of the shower maximum and a calorimetric estimate of the primary energy. In practice a number of corrections must be made to account for the scattering and the absorption of the fluorescence light. Also pollution from other sources such as the Cherenkov component which can be emitted directly, or di↵used by the atmosphere into the telescope, must be carefully evaluated and accounted for. A constant monitoring of the atmosphere and of its optical quality is necessary together with a precise knowledge of the shower geometry for a careful account for those corrections. The shower geometry as viewed from a fluorescence telescope is depicted in Fig. 7. It is defined by the shower detector plane (SDP), the distance of closest approach R p , the time t 0 along the shower axis at the distance and compared to ten simulated [133] air showers for three di erent primary particle types using the hadronic interaction model Epos1.99 [START_REF] Barcikowski | Mass Composition Working Group Report at UHECR-2012[END_REF].

groups (see e.g. [150]) similar to what is done for surface detectors. In the following, however, we will concentrate on the first two moments of the X max -distribution, X max and (X max ).

For the determination of the average shower maximum, experiments bin the recorded events in energy and calculate the mean of the measured shower maxima. For this averaging not all events are used, but only those that fulfill certain quality requirements that vary from experiment to experiment, but all analyses accept only profiles for which the shower maximum had been observed within the field of view of the experiment. Without this condition, one would rely only on the rising or falling edge of the profile to determine its maximum, which was found to be to unreliable to obtain the precise location of the shower maximum. The field of view of fluorescence telescopes is typically limited to 1-30 degrees in elevation. Therefore some slant depths can only be detected with smaller eciencies than others, resulting in a distortion of the measured X max -distribution due to undersampling in the tails of the distribution [151,152]. For instance, a detector located at a height corresponding to 800 g/cm 2 vertical depth cannot detect shower maxima deeper than 800, 924 and 1600 g/cm 2 for showers with zenith angles of 0, 30 and 60 degrees respectively. On top of this acceptance bias an additional reconstruction bias may be present that can further distort the measured X max -values.

There are two ways to deal with such biases: If one is only interested in comparing the data to air shower simulations for di erent primary particles, then the biased data can be simply compared to air shower predictions that include the experimental distortions. For this purpose the full measurement process has to be simulated including the attenuation in the atmosphere, detector response and reconstruction to obtain a prediction of the observed average shower maximum, X max obs . Another possibility is to restrict the data sample to shower geometries for which the acceptance bias is small (e.g. by discarding vertical showers) and to correct the remaining reconstruction e ects to obtain an unbiased measurement of X max in the atmosphere. Whereas the former appr the latter allows the direct shower simulations even fo the time of publication. Mo independent of the detecto tance and reconstruction ca The HiRes and TA collab lish X max obs [130,132] a folded air shower simulatio were optimized to assure an ergy, but di erent for di e action models. The prelim mal cuts resulting in energ Auger collaboration quote without detector distortions tainties [153] due to the us derives X max indirectly usi the Cherenkov-LDF and h Sec. 3.2). This relation is tions and is universal with hadronic interaction model in the following, that the th and that it can be compared To allow a comparison of moreover to calculate ln A which was not used in som correct the X max obs -values by an amount which we i lished X max obs -values for values that are obtained wit X max cor 12 Figure 1.5: Left: sketch of a Fluorescence detector (from [8]). Right: Auger FD event together with simulation for di↵erent primaries (from [START_REF] Kampert | Measurements of the Cosmic Ray Composition with Air Shower Experiments[END_REF]).

found in [START_REF] Ave | Precise measurement of the absolute fluorescence yield of the 337 nm band in atmospheric gases[END_REF]. As the number of electrons in an air shower can reach several billions, the total number of photons emitted during a path length of several hundreds of meters is of the order of 10 12 . If the air shower is distant of 20 km, the expected photons flux is only ' 200 per square meter. Hence a large collection area is needed to detect distant showers and reach a su cient exposure. The idea of using fluorescence light was first raised in 1962 by Suga [START_REF] Suga | Proc. 5 th Interamerican seminar on CRs[END_REF]. After an unsuccessful try in the mid 60s by Greisen and his group, the first detection of the fluorescence light from EAS was reported in 1970 by Tanahashi and collaborators [START_REF] Hara | Observation of air showers of energies above 10 18 eV[END_REF] and the first fully functional detector, named Fly's Eyes, installed at Dugway (Utah) began to take data in 1981. Currently, the Pierre Auger Observatory and Telescope Array use this technique in complement to their particle detector array, allowing a cross calibration of the surface detector. A sketch of a fluorescence telescope is shown in Fig. 1.5 (left): the emitted light from the air shower is focussed by large area mirrors onto a camera made of photo-multipliers. The isotropic distribution of the emission makes this technique suitable to observe the shower development along the atmosphere. Since the fluorescence light is directly proportional to the energy deposit of the shower in the atmosphere, the energy deposit as a function of the atmospheric depth can be directly measured. An example of such profile is shown in Fig. 1.5 (right), together with simulations for di↵erent primaries. The longitudinal profile provides then an estimation of the primary energy and the depth of maximum development. A precise estimation of these quantities is submitted to correction due to di↵usion and absorption of light and pollution by other contributions such as Cherenkov light. The low duty cycle of about 10% is imposed by the condition of operation with clear moonless night and this is the main limitation of this technique at ultra high energy when the flux of CR is very low.

Ultra High Energy Cosmic Rays 1.3 The Pierre Auger Observatory

The Pierre Auger Observatory

The Pierre Auger Observatory is a giant cosmic ray observatory located in the western Argentina near the town Malargüe in the province of Mendoza. It was designed to study cosmic ray flux, arrival direction and composition above 10 18 eV. The Pierre Auger Observatory gathered these last years the largest statistics at ultra high energy. After giving an insight of the detector operation and its performances, we will review the latest experimental results and put them in the light of the current models.

EAS detection at the Pierre Auger Observatory

The Pierre Auger Observatory combines two complementary detection techniques: a surface detector array (SD) and fluorescence telescopes (FD).

Fluorescence detector There are in total 27 fluorescence telescopes at the Pierre Auger Observatory grouped in five sites and overlooking the surface detector array as illustrated in Fig. 1.6. Four detector stations, Coihueco, Loma Amarilla, Los Leones and Los Morados contain each six telescopes, and each telescope is equipped with a 12 m 2 mirror focusing the UV light from EAS to a 440 pixels camera (Fig. 1.7 (left)). The field of view of one telescope is 30 ⇥30 in elevation and azimuth and so that the six telescopes per station cover 180 in azimuth as depicted in Fig. 1.7 (right). A fifth station, HEAT station in Fig. 1.6, comprises 3 additional telescopes that can be tilted to higher elevation angle to study air showers at energies down to below 10 17 eV.

As the shower crosses the atmosphere, the emitted photons reach the telescope and the triggered pixels form a track in the camera. The reconstruction of the EAS is a two steps process. First, the sequence of triggered pixels fixes the plane containing the shower axis and the detector (named SDP in Fig. 1.8 (left)). Next, the timing information of the pixels t i from a direction i is used to reconstruct the shower axis in this plane, i.e. the parameters 0 , the angle between the shower axis and the horizontal line in the SDP, R p , the closest distance from the shower axis to the telescope and t 0 , the time along the shower axis at which R p is reached. It is retrieved with the equation:

t i = t 0 + R p c tan( 0 i 2 ) (1.3.1)
The reconstruction can be performed when the shower is observed only by one FD site, called monocular event, but some degeneracy can remain in the parameters 0 and R p . This degeneracy is broken in case of hybrid event, i.e. if the shower has also triggered the surface detector, or stereo event, i.e. observed in two FD sites. The geometric reconstruction is then improved. A detailed description of the detector components and the reconstruction of FD events are reported in [START_REF] Abraham | The Fluorescence Detector of the Pierre Auger Observatory[END_REF]. After the geometric reconstruction, the observed fluorescence light as a function of time is converted into an energy deposit as a function of the atmospheric depth. First, the light attenuation from the shower to the telescope is estimated, then one needs to disentangle all contributing light sources: fluorescence light, direct and scattered Cherenkov light and multiple scattered light. An example of a shower profile reconstructed with FD is shown in Fig. 1.8. The deposit energy profile is then fitted with a Gaisser-Hillas function:

N e (X) = N max ✓ X X 0 X max X 0 ◆ (Xmax X 0 )/ exp (X max X) (1.3.2)
where X max and N max are the depth and the number of particles at shower maximum, X the atmospheric depth and X 0 and two free parameters of the fit. The calorimetric energy is obtained by integration of the fitted function along the atmospheric depth. Corrections for the energy carried by neutrinos and high energy muons and not converted into calorimetric energy, the "invisible energy" is obtained now with an empirical parameterization based on hybrid events. The systematic uncertainties on the energy estimation amount to 14%, the main contributions arise from the fluorescence yield, the atmosphere monitoring, the absolute calibration of the telescopes, the reconstruction of the longitudinal profile and the invisible energy estimation. The maximum of the shower development is also retrieved from the shower longitudinal profile. The resolution on this measurement depends on the geometry of the air shower event but also on the atmospheric conditions. For instance for the mass composition studies a resolution of the order of 20 g/cm 2 is typical.

Surface detector

The surface detector is an array of 1660 stations covering 3000 km 2 of water Cherenkov tanks (one is pictured in Fig. 1.9) arranged in a triangular grid of 1.5 km spacing, its layout is illustrated in Fig. 1.6. When the shower front reaches the ground, the charged secondary particles (mainly electron, positron, photons and muons) deposit their energy and produce a Cherenkov radiation in the water. This radiation is collected by three photo-multipliers looking downward in the water. The raw data are the Flash Analog to Digital Converter (FADC) traces sampled from the Each station is equipped with a local electronics and performs the two first levels of trigger. The first one called T1 is issued if the signal in the tank crosses a threshold. The rate of T1 is approximately 100 Hz. The second level trigger T2 requires more strict conditions, it requests either a higher threshold on the amplitude of the signal or a condition in its duration (Time Over Threshold). The T2 is sent to the Central Data Acquisition System (CDAS) and if at least three nearby stations reached the same trigger level in a certain time interval, a T3 is issued. The CDAS requires then the full traces of the T2 stations and the surrounding ones with the T1 condition. From this level the data are stored in the central acquisition.

The T4 condition checks if the position of the stations and their relative trigger timing are compatible with an air shower event. Finally, T5 is a quality trigger, it insures a reliable reconstruction of the event. It requires that the event was not on the border of the array, or that no inactive station was involved in the event. The full e ciency is reached at energy above 3 ⇥ 10 18 eV [START_REF] Auger Collaboration | Trigger and aperture of the surface detector array of the Pierre Auger Observatory[END_REF].

The time delay between coincident triggered detectors is used to reconstruct the shower front and the arrival direction of the primary cosmic ray. The angular resolution is a function of zenith angle and the multiplicity of stations. It is better than 3 at 10 18 eV and better than 1 above 10 19 eV.

To estimate the energy, the lateral distribution of deposited energy in the detectors is fitted with a lateral distribution function (LDF). An example of the lateral distribution of signal in a SD event is depicted in Fig. 1.10 together with the fitted LDF. In this figure, the unit for the signal is the VEM (Vertically Equivalent Muon), it is the average charge produced by a muon penetrating vertically and centrally the tank. It is adjusted online in each tank and provide a common reference level between tanks. The deposited energy at an optimal distance from the shower axis is taken as the energy estimator. At this distance, the statistical fluctuations from particle counting and shower to shower fluctuations are minimized. It depends on the energy range and the spacing of the array and is about 1000 m in Auger's case. The lateral distribution of the signal at ground is dependent on the zenith angle. Indeed, Ultra High Energy Cosmic Rays 1.3 The Pierre Auger Observatory inclined showers are in a more advanced stage of development than vertical ones when reaching the ground and their signal is thus attenuated. When estimating the energy, this e↵ect is accounted for using an empirical method, the Constant Intensity Cut (CIC). The basis of this method is to consider the flux isotropic, i.e. in local coordinate independent of the zenith angle when integrated over a large time period. The attenuation function, CIC(✓) is computed with data to normalize the flux in such a way. To estimate the absolute energy the signal at 1000 m, S(1000) is first converted into the signal from a shower with a reference zenith angle of 38 , S 38 , according the CIC method:

S 38 = S(1000) CIC(✓) (1.3.3)
Then S 38 is converted into the shower energy using the following transformation: FIGURE 2. Compilation of cosmic ray energy spectra, with the flux multiplied by E 3 , published by Auger (combined Hybrid/SD), TA SD, Yakutsk SD, HiRes I, and HiRes II after energy-rescaling as shown in the figure has been applied. The reference spectrum is the average of those from Auger and TA. From [START_REF] Matthews | A Heitler model of extensive air showers[END_REF] where also references to the respective data sets can be found. sistent in normalization and shape after energy scaling factors, as shown in Fig. 2, are applied. Those scaling factors are within systematic uncertainties in the energy scale quoted by the experiments. This is quite remarkable and demonstrates how well the data are understood. Nevertheless, cross-checks of photometric calibrations and atmospheric corrections have been started and as a next step, common models (e.g. fluorescence yield) should be used where possible. The data in Fig. 2 clearly exhibit the ankle at ⇠ 4 • 10 18 eV and a flux suppression above ⇠ 4 • 10 19 eV. The flux suppression at the highest energies is in accordance with the long-awaited GZK-effect [5,6]. However, as discussed below, the data of the Auger observatory suggest that the maximum energy of nearby sources or the source population is seen, instead.

E = aS b 38 (1.3.4)

COSMIC RAY COMPOSITION AND INTERACTION MODELS

Obviously the energy spectra by itself, despite their high level of precision reached, do not allow one to conclude about the origin of the spectral structures and thereby about the origin of CRs in different energy regions. Additional key information is obtained from the mass composition of CRs. Unfortunately, the measurement of primary masses is the most difficult task in air shower physics as such measurements rely on comparisons of data to EAS simulations with the latter serving as reference [START_REF] Heitler | Quantum Theory of Radiation[END_REF]. EAS simulations, however, are subject to uncertainties mostly because hadronic interaction models need to be employed at energy ranges much beyond those accessible to man-made particle accel-Figure 1.12: Compilation of spectra published by Auger, Telescope Array, Yakutsk and HiRes(I and II). The rescaling in energy is indicated in the lower left corner. From [START_REF] Fukushima | Measurement of Ultra-High Energy Cosmic Rays: An Experimental Summary and Prospects[END_REF].

where coe cient a and b are given by the calibration curve using hybrid events. The independent measurement of energy of these events by the FD and SD allows the cross calibration. The absolute energy scale is given by the fluorescence measurement and has thus a systematic uncertainty for 14%.

Experimental results

Energy spectrum The compilation of energy spectra showed in Fig. 1.1 exhibit the overall regularity of the decrease of the cosmic ray flux. We examine here further the features above the knee energy. At the highest energies, above 10 17 eV, one can observe two main features. Firstly a flattening of the spectrum, the ankle, has been measured at log 10 (E ankle ) = 18.61 ± 0.01 eV in Auger data. Secondly, a clear cut-o↵ at the end of the measured spectrum is observed. A broken power law fit on Auger spectrum sets the change of index from 2.6 to 4.3 and the energy at which the flux has fallen by one half in case of extrapolation of the original power law at log 10 (E cut of f ) = 19.61 ± 0.03 eV. The deviation from a single power law was established with a statistical confidence of more than 20 . In Fig. 1.12 are illustrated the energy spectra measured by Auger, Telescope Array, Yakutsk and HiRes. After a normalization within their respective energy systematic uncertainties, the spectra agree very well together.

Mass composition

The determination of mass composition, ideally on an event by event basis or by separation of sub samples of elemental group may point more structures and constrain models. A complete review on mass composition measurements, problematic and interpretation can be found we require data from at least one SD station, we place an energy dependent cut on both the shower zenith angle and the distance of the SD station to the reconstructed core so the trigger probability of a single station at these energies is saturated for both proton and iron primaries. Finally, requiring that the shower maximum is observed means that, for some shower geometries, we could introduce a composition dependent bias in our data. This is avoided using only geometries for which we are able to observe the full range of the X max distribution. At the end 6744 events (42% of those that pass the quality cuts) remain above 10 18 eV. The systematic uncertainty in the energy reconstruction of the FD events is 22% The resolution in X max is at the level of 20 g/cm 2 over the energy range considered. This resolution is estimated with a detailed simulation of the detector and cross-checked using the difference in the reconstructed X max when one event is observed by two or more FD stations (Fig. 1).

Results and discussion

In Fig. 2 we present the updated results for X max and RMS (X max ) using 13 bins of log E = 0.1 below 10 19 eV and log E = 0.2 above. An energy dependent correction ranging from 3.5 g/cm 2 (at 10 18 eV) to 0.3 g/cm 2 (at 7.2 • 10 19 eV, the highest energy event) has been applied to the data to correct for a small bias observed face Detector (SD) has 1660 water detector stations arranged in a 1.5 km triangular grid and sensitive to the shower particles at the ground. The FD has 27 telescopes overlooking the SD, housed in 5 different stations, recording UV light emitted in the de-excitation of nitrogen molecules in the atmosphere after the passage of the charged particles of a shower. The shower geometry is reconstructed from the arrival times of the data. The number of fluorescence photons emitted is proportional to the energy deposited in the atmosphere by the shower. Using the shower geometry and correcting for the attenuation of the light between the shower and the detector, the longitudinal profile of the shower can be reconstructed. This profile is fitted to a Gaisser-Hillas function [7] to determine X max and the energy of the shower [8]. We follow the analysis already reported in [6]. We consider only showers reconstructed using FD data and that have at least a signal in one of the SD stations measured in coincidence. The geometry for these events is determined with an angular uncertainty of 0.6 [9]. The aerosol content in the atmosphere is monitored constantly during data taking [10] and only events for which a reliable measurement of the aerosol optical depth exists are considered. Also the cloud content is monitored nightly across the array and periods with excessive cloud coverage are rejected. Furthermore, we reject events with a 2 /Ndf greater than 2.5 when the profile is fitted to a Gaisser-Hillas, as this could indicate the presence of residual clouds. The total statistical uncertainty in the reconstruction of X max is calculated including the uncertainties due to the geometry reconstruction and to the atmospheric conditions. Events with uncertainties above 40 g/cm 2 are rejected. We also reject events that have an angle between the shower and the telescope smaller than 20 to account for the difficulties of reconstructing their geometry and for their high fraction of Cherenkov light. Finally, in order to reliably determine X max we require that the maximum has been actually observed within the field of view of the FD. 15979 events pass this quality selection. Another set of cuts is used to ensure that the data sample is unbiased with respect to the cosmic ray composition. Since we require data from at least one SD station, we place an energy dependent cut on both the shower zenith angle and the distance of the SD station to the reconstructed core so the trigger probability of a single station at these energies is saturated for both proton and iron primaries. Finally, requiring that the shower maximum is observed means that, for some shower geometries, we could introduce a composition dependent bias in our data. This is avoided using only geometries for which we are able to observe the full range of the X max distribution. At the end 6744 events (42% of those that pass the quality cuts) remain above 10 18 eV. The systematic uncertainty in the energy reconstruction of the FD events is 22% The resolution in X max is at the level of 20 g/cm 2 over the energy range considered. This resolution is estimated with a detailed simulation of the detector and cross-checked using the difference in the reconstructed X max when one event is observed by two or more FD stations (Fig. 1).

Results and discussion

In Fig. 2 we present the updated results for X max and RMS (X max ) using 13 bins of log E = 0.1 below 10 19 eV and log E = 0.2 above. An energy dependent correction ranging from 3.5 g/cm 2 (at 10 18 eV) to 0.3 g/cm 2 (at 7.2 • 10 19 eV, the highest energy event) has been applied to the data to correct for a small bias observed in [START_REF] Kampert | Measurements of the Cosmic Ray Composition with Air Shower Experiments[END_REF]. The model of hadronic shower presented before and especially the superposition model showed that two main observables were sensitive to the primary mass. For the same energy, a light primary penetrates deeper in the atmosphere and the number of muons at ground is smaller with respect to an heavy primary. On the experimental point of view, optical detectors, fluorescence or Cherenkov light detector, are directly sensitive to X max but are operable only around 10% of the time. Ground arrays can deduce indirectly parameters sensitive to shower development from the measurement of particles at ground and operate with a 100% duty cycle. They are however usually less precise. The distribution of the depth of maximum development for a given energy is a mass indicator through its two first moments. The evolution of < X max > as measured with the fluorescence telescopes in Auger is plotted as a function of energy in Fig. 1.13 (left) with the expected value from air shower simulations with di↵erent hadronic models for pure proton or iron primary. Auger data show a light composition around the ankle energy and indicate a trend toward heavier primary with increasing energy. It is noteworthy that two other important observatories, Telescope Array and HiRes quote a mean X max compatible with protons from 2 ⇥ 10 18 eV to around 5 ⇥ 10 19 eV. The comparison of data analysis methods, results and interpretation on mass composition studies of these current experiments can be found in [START_REF] Barcikowski | Mass Composition Working Group Report at UHECR-2012[END_REF]. The second moment of the X max distribution is complementary to the mean, especially in case of mixed composition. Indeed, from the superposition model we saw that an heavier composition would lead to smaller fluctuation of X max than a light one. But in case of mixed composition, for instance of two species, the spread of the distribution is also given by the mutual separation of < X max > that can result in larger fluctuations than if each one of them is taken separately. The measured RM S(X max ) in Auger data reported in Fig. 1.13 (right) exhibits a trend towards heavy elements above 10 18.5 eV. Other shower observables can provide information on the average composition. For instance, Auger's surface detectors are sensitive to both electromagnetic and muonic components, and the study of the time distribution of the traces allow us to extract information on the muon content. Using FADC traces of surface detector far from the core, thus dominated by muons, but to a di erent degree. For instance, the muon nummax are very sensitive to the multiplicity (as expected . ( 4) and [START_REF] Heitler | Quantum Theory of Radiation[END_REF], whereas the X max fluctuations are not. ise there is a strong dependence of X max and (X max ) not so for N µ (as suggested by -independence of n d in .

urements of the Nuclear Composition y speaking, no air shower observatory measures the composition of cosmic rays. Instead, one or more of sensitive observables from the last section can be meathe data can then be interpreted in terms of primary a comparison to air shower simulations using hadronic n models. Since di erent air shower observables react y to changes in the characteristics of hadronic interone may hope to diminish the model dependence of ass estimates by comparing the results from di erent les. section we will therefore first review measurements sition related air shower observables from particle deground and from optical detectors. The data will then ared to each other in terms of the average logarithmic ec. 3.4.

for reasons described in the previous section. These ge features can also be observed in Fig. 3. Fukui et al. [66 Khristiansen et al. [67] were the first to study the muon ber fluctuations in the knee region and they were also the concluding an enrichment by heavy nuclei above the kne ergy [START_REF] Apel | LOPES 3D -vectorial measurements of radio emission from cosmic ray induced air showers[END_REF]. Similar conclusions were drawn in [START_REF] Haungs | Air Shower Measurements with the LOPES Radio Antenna Array[END_REF] based larger data set.

In the most classical approach, electron-muon discrim tion is achieved by employing a combination of unshielde shielded scintillation detectors at ground level. Recent e ples include AGASA [START_REF] Revenu | Overview of MHz air shower radio experiments and results[END_REF], CASA-MIA [START_REF] Huege | Theory and simulations of air shower radio emission[END_REF], EAS-TOP GRAPES [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF], KASCADE [START_REF] Monasor | The MIDAS experiment: A prototype for the microwave emission of Ultra-High Energy Cosmic Rays[END_REF], KASCADE-Grande Maket-ANI [START_REF] Auger Collaboration | The Pierre Auger Observatory V: Enhancements[END_REF], GAMMA [64], and Yakutsk [START_REF] Smida | First results of the CROME experiment[END_REF]. The P Auger Observatory [START_REF] Monasor | Proc. 32nd ICRC[END_REF] operates water Cherenkov detecto 1.2 m depth which also enables limited muon identifica The electromagnetic particles (electrons, positrons, and tons) are more numerous than the muons but their mea ergy at detector level is only some 10 MeV while that o muons is about 1 GeV. The former thus produce a large ber of relatively small Cherenkov pulses whereas muons duce a small number of large pulses. This type of discrim tion technique was pioneered at the Haverah Park detector Since FADC readout was not available at that time, signal t of the detectors were photographically recorded from os muon numas expected ons are not. nd (X max ) nce of n d in easures the or more of can be meaof primary ng hadronic vables react ronic interendence of m di erent asurements particle deta will then logarithmic eir fluctualoyed techfrom EAS understood on numbers hile the raimary mass for reasons described in the previous section. These general features can also be observed in Fig. 3. Fukui et al. [START_REF] Ardouin | Radio-detection signature of high-energy cosmic rays by the CODALEMA experiment[END_REF] and Khristiansen et al. [START_REF] Falcke | Detection and imaging of atmospheric radio flashes from cosmic ray air showers[END_REF] were the first to study the muon number fluctuations in the knee region and they were also the first concluding an enrichment by heavy nuclei above the knee energy [START_REF] Apel | LOPES 3D -vectorial measurements of radio emission from cosmic ray induced air showers[END_REF]. Similar conclusions were drawn in [START_REF] Haungs | Air Shower Measurements with the LOPES Radio Antenna Array[END_REF] based on a larger data set.

In the most classical approach, electron-muon discrimination is achieved by employing a combination of unshielded and shielded scintillation detectors at ground level. Recent examples include AGASA [START_REF] Revenu | Overview of MHz air shower radio experiments and results[END_REF], CASA-MIA [START_REF] Huege | Theory and simulations of air shower radio emission[END_REF], EAS-TOP [START_REF] Werner | [END_REF], GRAPES [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF], KASCADE [START_REF] Monasor | The MIDAS experiment: A prototype for the microwave emission of Ultra-High Energy Cosmic Rays[END_REF], KASCADE-Grande [START_REF] Alvarez-Muniz | The MIDAS telescope for microwave detection of ultra-high energy cosmic rays[END_REF], Maket-ANI [START_REF] Auger Collaboration | The Pierre Auger Observatory V: Enhancements[END_REF], GAMMA [64], and Yakutsk [START_REF] Smida | First results of the CROME experiment[END_REF]. The Pierre Auger Observatory [START_REF] Monasor | Proc. 32nd ICRC[END_REF] operates water Cherenkov detectors of 1.2 m depth which also enables limited muon identification. The electromagnetic particles (electrons, positrons, and photons) are more numerous than the muons but their mean energy at detector level is only some 10 MeV while that of the muons is about 1 GeV. The former thus produce a large number of relatively small Cherenkov pulses whereas muons produce a small number of large pulses. This type of discrimination technique was pioneered at the Haverah Park detector [START_REF] Williams | UHECR 2012 -International Symposium on Future Directions in UHECR Physics[END_REF]. Since FADC readout was not available at that time, signal traces of the detectors were photographically recorded from oscilloscopes. IceTop at the South Pole [START_REF] Kampert | The Pierre Auger Observatory -Status and prospects[END_REF] uses tanks of frozen ice instead of water for obvious reasons. Sensitivity to the primary composition is achieved by measuring the dominant electromagnetic component at ground level in IceTop in coincidence with high energy muon bundles in IceCube (muon threshold about 500 GeV), originating from the first interactions in the atmosphere. Similar combinations of surface and underground detectors have been used e.g. by EAS-TOP and MACRO at the Gran Sasso [START_REF] Orfanidis | Electromagnetic Waves and Antennas[END_REF] and at the Baksan underground laboratory [START_REF] Nash | Logarithmic amplifiers explained[END_REF]. Such methods are potentially very attractive for composition 7 using QGSJETII [9,[START_REF] Chiba | Akeno giant air shower array (AGASA) covering 100-km**2 area[END_REF]. For the inelastic case, these three independent contributions are 1, 3, 5, and 4 mb, respectively. For the total cross section, they are 13, 6, 5, and 4 mb. We emphasize that the total theoretical uncertainty of converting the proton-air to a proton-proton cross section may be larger than estimated here within the Glauber model. There are other extensions of the the air-shower simulation process in a self-consistent approach.

We convert the proton-air production cross section into the total, and the inelastic, proton-proton cross section using a Glauber calculation that includes intermediate inelastic screening corrections. In this calculation, we use the correlation between the elastic slope parameter and the protonproton cross sections taken from the interaction models as a constraint. We find that the inelastic proton-proton cross section depends less on the elastic slope parameter than

FIG. 3 (color online). Correlation of elastic slope parameter,

B el , and the inelastic proton-proton cross section in the Glauber framework. The solid line indicates the parameter combinations yielding the observed proton-air production cross section, and the dotted lines are the statistical uncertainties. The hatched area corresponds to the predictions by SIBYLL, QGSJET, QGSJETII, and EPOS. See also Ref. [5].

FIG. 4 (color online). Comparison of derived inel

pp to model predictions and accelerator data [START_REF] Suga | Proc. 5 th Interamerican seminar on CRs[END_REF]. Here we also show the cross sections of two typical high-energy models, PYTHIA6 [START_REF] Auger Collaboration | The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models[END_REF] and PHOJET [START_REF] Barcikowski | Mass Composition Working Group Report at UHECR-2012[END_REF]. The inner error bars are statistical, while the outer include systematic uncertainties.

062002-7

Figure 1.14: Left: Sensitivity of < X max > with changes of cross section, elasticity and multiplicity in SYBILL hadronic model for a proton of 10 19 eV (from [START_REF] Kampert | Measurements of the Cosmic Ray Composition with Air Shower Experiments[END_REF]). Right: Proton-proton cross section deduced from the proton-air cross section measurements with Auger data [START_REF] Auger Collaboration | Measurement of the proton-air cross-section at p s = 57 TeV with the Pierre Auger Observatory[END_REF].

the Muon Production Depth (MPD) technique converts the time distribution in traces into distance of production of the muons in atmosphere. This technique yields informations on the longitudinal development of the hadronic component of the air shower [START_REF] Auger Collaboration | The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models[END_REF]. Also, as the muons are expected to travel in straight line whereas the electron to scatter in atmosphere, they populate more the early part of the FADC traces. When a non vertical shower reaches the ground, the detectors around the core sample a di↵erent "age" of the shower, the detector upstream sees a younger shower than the one downstream. The asymmetry in azimuthal angle of the rise time in the FADC traces is found to be related to shower development. By performing first this study with hybrid events (detected by both the surface detector and the fluorescence detector) one can correlate the sensitive variable with X max and then apply this method with only SD events. Note that these methods, relying on particle detector allow a larger statistics and give composition measurements above 10 19.5 eV. Surface detector based methods with Auger data yield a light composition at 10 18.5 eV and exhibit a trend to a heavier one above.

Hadronic interaction

The description of first interactions of the shower particles in atmosphere has two main goals. Firstly, the interpretation of the measurement of mass sensitive parameters is achieved thanks to the comparison with air shower simulations. The precise determination of the nuclear composition of cosmic ray requires then the correct simulation of shower development. Since most of interactions in shower development occur with low momentum transfer (soft interactions) perturbative QCD (Quantum ChromoDynamics) cannot be applied. Instead, phenomenological model are used based on measurements at accelerators and their extrapolation. Recent data from LHC (Large Hadron Collider), allow to extend the experimental knowledge to an energy of 14 ⇥ 10 12 eV in center of mass corresponding to ⇠ 10 17 eV for a fixed target experiment such as a cosmic ray interacting in atmosphere. Above these energies models rely on extrapolation. As an illustration, in Fig. 1.14 is depicted the impact of the modification of cross section (black full circle), elasticity (red open circle) of interaction and multiplicity (blue open square), on the shower < X max >. A change of a factor two in cross section can shift the < X max > by more than 50 g/cm ratio, the total exposure can be written as:

E DG (E ) = 2⇡ m X i i (E ) Z dt d✓ dD dS sin ✓ cos ✓ i (r, ✓, D, E , t) (1)
where the sum runs over the 3 neutrino flavours and the CC and NC interactions, m is the mass of a nucleon, and i is the ⌫ cross section with a nucleon. For ⌫ we have taken into account the possibility that it produces a double shower in the atmosphere triggering the array -one in the ⌫ CC interaction itself and another in the decay of the ⌧ lepton. Furthermore, we consider the possibility of a ⌫ interacting in the Andes inducing a shower through the decay products of the ⌧ lepton.

For the Earth-skimming neutrinos the procedure is described in Ref [7].

In Fig. 2 we show both the Earth-skimming and downgoing exposures for the respective search periods. Several sources of systematic uncertainties have been taken into account and their effect on the exposure evaluated.

For down-going neutrinos there is [ 30%, 10%] systematic uncertainty in the exposure due to the neutrino-induced shower simulations and the hadronic models. Another source of uncertainty comes from the neutrino cross section which is ⇠ 10% [13]. For the Earth-skimming showers the systematic uncertainties are dominated by the tau energy losses, the topography and the shower simulations [7].

Using the computed exposures and assuming a typical f (E ) = k • E 2 differential neutrino flux and a 1:1:1 flavour ratio, an upper limit on the value of k can be obtained. We use a semi-Bayesian extension [14] of the Feldman-Cousins approach [15] to include the uncertainties in the exposure. The updated single-flavour 90% C.L. limit based on Earth-skimming neutrinos is: k < energy (eV) ! Limits from other experiments are also plotted [16]. Expected fluxes are shown for cosmogenic neutrinos [17] and for a theoretical exotic model [START_REF] Stecker | Photodisintegration of ultrahigh-energy cosmic rays: A New determination[END_REF].

2.8 ⇥ 10 8 GeV cm 2 s 1 sr 1 in the energy interval 1.6 ⇥ 10 17 eV 2.0 ⇥ 10 19 eV and the updated singleflavour 90% C.L. limit based on down-going neutrinos is: k < 1.7 ⇥ 10 7 GeV cm 2 s 1 sr 1 in the energy interval 1⇥10 17 eV 1⇥10 20 eV. These results are shown in Fig. 3 including the limit in different bins of width 0.5 in log 10 E (differential limit) to show at which energies the sensitivity of the Pierre Auger Observatory peaks. The expected number of events from a cosmogenic [17] (neutrinos produced by the interaction of cosmic rays with background radiation fields) and an exotic model [START_REF] Stecker | Photodisintegration of ultrahigh-energy cosmic rays: A New determination[END_REF] (neutrinos produced due to the decay of heavy particles) are given in Table 2.

Limits to point-like sources

As we found no candidate events in the search period, we can place a limit on the UHE neutrino flux from a source at declination . A point source moves through the sky so that it is visible from the SD of the Pierre Auger Observatory with zenith angle ✓(t) which depends on the sidereal time t. For an observatory located at a latitude the relation between the zenith angle and the declination of the source is given by: cos ✓(t) = sin sin + cos cos sin( t ↵ 0 )

with = 2⇡/T , where T is the duration of one sidereal day and ↵ 0 depends on the right ascension.

The sensitivity to UHE⌫s is limited to large zenith angles so the rate of events from a point source in the sky depends strongly on its declination. The point-source exposure E PS (E , ) can be obtained in a similar way as the diffuse exposure but avoiding the integration in solid angle and taking into account that the probability of neutrino for exotic models and GZK photon. Right: Neutrino flux limit reported by Auger, IceCube Anita and Rice compared to the expected flux of cosmogenic neutrinos and produced from exotic models. (Both from [START_REF] Abraham | Astrophysical Sources of Cosmic Rays and Related Measurements with the Pierre Auger Observatory[END_REF])

that the separation between proton and iron is less than 100 g/cm 2 , the hadronic interaction parameters are crucial to interpret correctly the mass composition measurements. Furthermore, the cosmic ray flux is a unique ultra high energy beam and o↵ers the possibility to study interaction at collision energy in center of mass up to p s 50 TeV, well beyond the current accelerators possibilities. The proton-air cross section has been measured with Auger cosmic ray events [START_REF] Auger Collaboration | Measurement of the proton-air cross-section at p s = 57 TeV with the Pierre Auger Observatory[END_REF] with energy from 10 18 to 10 18.5 eV corresponding to an average energy in center of mass of 57 TeV. The study is performed at an energy where mass measurement indicate a light composition. Then the proton-air cross section is extracted from the shape of X max distribution and selecting the most deeply penetrating air showers. Proton proton cross section, shown in Fig. 1.14 can be deduced based on Glauber model [START_REF] Glauber | Cross-sections in deuterium at high-energies[END_REF] and agrees with extrapolation from accelerator measurements.

Photon and neutrinos

UHECR are known to be mainly protons or heavier nuclei. Secondary particles from interactions they undergo during their production or propagation can point to their origin. For instance, in the GZK process, charged pions decay in neutrinos, and neutral pions decay in two photons. When entering the atmosphere, photons interact inducing an electromagnetic cascade which is expected to penetrate deeper than hadron induced shower of the same energy (see section 1.2). Moreover, above 10 19 eV the LPM (Landau-Pomeranchuck-Migdal) e↵ect decreases the pair production cross section, further increasing the depth of shower maximum. So X max measurements are well suited to discriminate hadronic from electromagnetic shower. In addition, SD observables like the radius of curvature of the shower front can be used to discriminate between hadronic or photon air shower. No photon event have been observed so far by any experiments and upper limits to the flux are thus derived. Limits given by Auger data are shown in Fig. 1.15 with the flux expectation for model accounting for GZK e↵ect and more exotic models.

In the same way, GZK process or top down models are expected to produce neutrinos, but

The Pierre Auger Observatory

Ultra High Energy Cosmic Rays Author's personal copy has not escaped our notice that the directions of the five most etic events are not part of the fraction of events that correlate objects in the VCV catalog. ditional monitoring of the correlation signal with this set of nomical objects can also be found in [START_REF] Suga | Proc. 5 th Interamerican seminar on CRs[END_REF]. Further studies of orrelation exploring other parameters are currently in pro-. One conjecture often made in the literature (see e.g. 1] and references therein) is that powerful radiogalaxies are ost promising contenders for UHECR acceleration, along with a-ray bursts. The analysis of directional correlations of Rs with positions of AGNs from the VCV catalog discussed does not account for any differences among those AGNs. Thus, ical next step with respect to [6,7] would consider the AGN luminosity given in the VCV catalog as a fourth scan paramo find a threshold in radio luminosity above which the direcl correlation starts to increase. Such a scan has been rmed with a subset of the data and the signal evolution with parameters is being monitored since, similarly as presented for all AGN of the VCV. These results will be reported here. e HiRes collaboration has reported [START_REF] Mariş | Measurement of the ultra high energy cosmic ray flux using data of the Pierre Auger Observatory[END_REF] an absence of a correwith AGNs of the VCV catalog using the parameters of the r prescribed test. They found two events correlating out of a f 13 arrival directions that have been measured stereoscopi-cally above an energy which they estimated to be the same as the Auger prescribed energy threshold. The 38% correlation measured by Auger suggests that approximately five arrival directions out of 13 HiRes directions should correlate with an AGN position. The difference between 2 and 5 does not rule out a 38% correlation in the northern hemisphere that is observed by the HiRes detector. Also, it is not necessarily expected that the correlating fraction should be the same in both hemispheres. The three-dimensional AGN distribution is not uniform, and the VCV catalog itself has different level of completeness in the two hemispheres. In addition, comparison of results between the two observatories is especially challenging in this situation because the energy cut occurs where the GZK suppression has steepened the already steep cosmic ray spectrum. A small difference in the threshold energy or a difference in energy resolution can strongly affect the measurement of a correlation that exists only above the threshold.

It is worth mentioning that while the degree of correlation with the parameters of the test updated here has decreased with the accumulation of new data, a re-scan of the complete data set similar to that performed in Ref. [7] does not lead to a much more significant correlation for other values of the parameters. The largest departure from isotropic expectations in the scan actually occurs for the same energy threshold Eth = 55 EeV and maximum redshift z 6 0.018. There is a spread in the angular scales over which the correlation departs from isotropic expectations. This issue will be examined in Section 4, where we explore the correlation with other sets of nearby extragalactic objects, described by catalogs more uniform than the VCV compilation.

There is now available a more recent version of the VCV catalog [START_REF] Auger Collaboration | Trigger and aperture of the surface detector array of the Pierre Auger Observatory[END_REF]. Conclusions are similar if the arrival directions are compared to the distribution of objects in this latest version.

Examination of the arrival directions in relation to other catalogs

As noted in [6], ''the correlation that we observe with nearby AGNs from the VCV catalog cannot be used alone as a proof that AGNs are the sources. Other sources, as long as their distribution within the GZK horizon is sufficiently similar to that of the AGNs, could lead to a significant correlation between the arrival directions of cosmic rays and the AGNs positions." It is therefore appropriate to investigate the arrival directions of this data set with respect to other scenarios for cosmic ray sources in the local universe. The most likely value of the degree of correlation pdata = k/N is plotted with ots as a function of the total number of time-ordered events (excluding those iod I). The 68%, 95% and 99.7% confidence level intervals around the most value are shaded. The horizontal dashed line shows the isotropic value .21. The current estimate of the signal is 0:38

(E) = 0 + E arctan ✓ log 10 (E/EeV ) µ ◆ (4)
To report the midterm status of the prescription, the phase of the first harmonic is shown in Fig. 3. The top panel shows the phase derived with data from January 1 2004 to December 31 2010 for the larger array, that corresponds to the analysis in [5] Table 2: Mean noise in each energy interval considered in the analysis of the regular array. The analysis performed in the two first energy bins uses the E-W method, which explains why the mean noise is about two times larger than p /N.

Discussion and conclusions

We have searched for large scale patterns in the arrival directions of events recorded at the Pierre Auger Observatory. No statistically significant deviation from isotropy is revealed within the systematic uncertainties. The probabilities for the dipole amplitudes that are measured to arise by chance from an isotropic flux are of about 0.03% in the energy range from 1-2 EeV, 0.9% for 2-4 EeV and 0.1% above 8 EeV. These are interesting hints for large scale anisotropies that will be important to further scrutinise with independent data. In addition, the intriguing possibility of a smooth transition from a common phase compatible with the right ascension of the Galactic Center at energies below 1 EeV to a phase around 100 above 5 EeV will be specifically tested through a prescribed test. contrary to photons, they undergo no interaction during their propagation to Earth and the distance they can cover is only limited by adiabatic losses. All flavors of neutrino reach the Earth with an equal probability because of oscillation, and can either interact with atmosphere (down going neutrinos) or in the crust of the Earth (upgoing neutrinos). In Auger data, the signature for a neutrino event is a very inclined event produced by a young shower, i.e. developed close to the ground by contrast with inclined hadronic shower that traversed lots of matter before reaching the ground. Constraints on the topology of an air shower event are put to admit it as a neutrino candidate. For instance, the Pierre Auger Collaboration imposes that the footprint of an event on the surface detector array to have a certain ellipticity set by Monte Carlo simulations. The traces themselves are used to distinguish between young showers, with a trace waveform spread in time, and old showers whose content, mostly muonic, produce a short and sharp signal in the water Cherenkov detectors [START_REF] Auger Collaboration | Ultrahigh Energy Neutrinos at the Pierre Auger Observatory[END_REF]. Dedicated observatories like IceCube [START_REF] Abbasi | A Search for UHE Tau Neutrinos with IceCube[END_REF] or Antares [START_REF] Ageron | Performance of the First ANTARES Detector Line[END_REF], instrument respectively large volume of ice and water to obtain a large exposure. In Fig. 1.15 (right) is illustrated the neutrino flux limits quoted by Auger, IceCube [START_REF] Abbasi | Constraints on the extremely-high energy cosmic neutrino flux with the IceCube 2008-2009 data[END_REF] and Anita [START_REF] Gorham | Observational constraints on ultra-high energy cosmic neutrino flux from the second flight of the ANITA experiment[END_REF] and Rice [START_REF] Kravchenko | Event Reconstruction and Data Acquisition for the RICE Experiment at the South Pole[END_REF] experiments together with the flux expected for cosmogenic neutrinos, and exotic models.

Anisotropies

Cosmic ray anisotropy search may help at spotting either point source or region of CR production. The angular scale on which anisotropy is expected depends on the Larmor radius of the CR that can be written as:

r L = 100 1 Z E 10 20 eV ✓ B 10 9 G ◆ 1 ! [Mpc]
Calculations with random extragalactic magnetic field of magnitude of the order of nG and Ultra High Energy Cosmic Rays 1.3 The Pierre Auger Observatory coherence length of 1 Mpc, yield an angular deviation of around 2 for a proton from a 20 Mpc distance [START_REF] Achterberg | Intergalactic propagation of uhe cosmic rays[END_REF]. Such small scale of angular deviations open the possibility of tracking back sources for light composition and for sources close enough. Auger data provided a signature for a correlation between the arrival direction of events with energy above 5.7 ⇥ 10 19 eV with sources of the Veron Cetty Veron catalogue [START_REF] Veron-Cetty | A catalogue of quasars and active nuclei: 12th edition[END_REF]. In the first published result [START_REF] Auger Collaboration | Correlation of the highest-energy cosmic rays with the positions of nearby active galactic nuclei[END_REF], 20 out of 27 events were found to be within 3.1 angular distance from AGN within distances lower than 75 Mpc. This correlation has become weaker now and has stabilized at a level of (33±5)% compared to 21% for isotropic expectation. The sky map of the selected events the sources for the correlation studies are presented in the sky map Fig. 1.16 (left). At lower energy one cannot track back directly sources because of the scattering of particles on the galactic magnetic field. However, anisotropies at larger angular scales are expected if source distribution is not isotropic in the Galaxy. Moreover, if cosmic rays escape from the Galaxy with increasing energy, because of a larger Larmor radius, this may be also visible through structure in the arrival direction distribution. The level of expected anisotropy in this case is of the order of a few % for protons. Since the flux of cosmic ray observed in any direction is distorted by the coverage function of the observatory, it is critical to control accurately both the coverage function and any systematic uncertainties influencing the counting rate above a fixed energy threshold, especially when searching for anisotropies with relative amplitudes down to the % level. Detailed studies performed in Auger data can be found in [START_REF] Auger Collaboration | Constraints on the origin of cosmic rays above 10 18 eV from large scale anisotropy searches in data of the Pierre Auger Observatory[END_REF]. Upper limits of 2% at 99% confidence level on a dipole component in the equatorial plane have been derived for energies around 10 18 eV [START_REF] Auger Collaboration | Search for First Harmonic Modulation in the Right Ascension Distribution of Cosmic Rays Detected at the Pierre Auger Observatory[END_REF] and no deviation from isotropy were found in dipole or quadrupole search in both declination and right ascension. But an interesting feature was observed: right ascension of the dipole direction are smoothly aligned with energy and point toward the galactic center below 10 18 eV. In Fig. 1.16 is reported the phase of the first harmonic of the distribution of arrival directions in right ascension of cosmic rays measured in Auger. The phase at low energy corresponds to the direction of the Galactic center represented by the black horizontal line.

Models at ultra high energy

Ultra High Energy Cosmic Rays

Models at ultra high energy

Top down models were considered until the last decade as potential mechanisms to produce UHECR. Most of them have been ruled out by the limits on photons and neutrinos in particular given by Auger data.

To explain the spectral features observed on Earth and the mass composition, current models adopt a source distribution, assume a composition at the source and account for propagation e↵ects.

Around the knee region, cosmic ray are believed to be of galactic origin. They are assumed to be accelerated by the shock wave produce by Super Novae Remnants (SNR). This idea was raised by Baade and Zwicky [53] and later by Ginzburg and Syrovatskii [START_REF] Ginzburg | The Origin of Cosmic Rays[END_REF] on the argument that only 5 to 10 % of the kinetic energy of the SNR converted into cosmic ray acceleration would be enough to explain the energetic content of galactic cosmic rays. The common explanation for the knee is related to the limited acceleration in galactic sources. At ultra high energy, cosmic rays are in contrast expected to be of extragalactic origin, firstly because astrophysical sources within our Galaxy are not likely to produce them but also because arrival distribution of cosmic rays above 10 19 eV don't show the strong anisotropy that would induce close sources. The region around the ankle energy is expected to be the transition region between the Galactic and the extra galactic origin of cosmic rays. Currently three main models are proposed to explain the observational results at ultra high energy:

the ankle model In this model the ankle is assumed to be a transition from Galactic to extragalactic origin of cosmic rays [START_REF] Linsley | Proc. 8th ICRC[END_REF]. The end of the Galactic spectrum is dominated by iron composition, and an extragalactic proton component arises at the ankle energy.

The measurements of a light composition from 10 18 to 5⇥10 18 eV is in contradiction with the heavy Galactic component expected, and the trend toward heavier primaries do not support the extragalactic proton component. Moreover, in frame of this model, anisotropies are expected below the transition because of anisotropic distribution of galactic sources and the loss of confinement. Thus, the limits on the dipole structure at energies around the ankle may discard in the future this model.

the dip model This model, proposed in [START_REF] Berezinsky | Dip in UHECR spectrum as signature of proton interaction with CMB[END_REF], assumes a dominance of extragalactic protons already at E = 10 18 eV. The ankle is explained to be part of the dip created by the e + /e production by interaction of proton on CMB. The cut o↵ is a consequence of the pion photoproduction. This model is in agreement with the spectral shape observed between 10 18 and 10 19 eV. It is also more compatible with mass composition measurements, as it explains the increase of < X max > from 10 17 to 10 18 eV with the extragalactic proton component. However, it is not compatible with a heavy composition at higher energy as deduced with the Auger X max data.

the disappointing model In this model cosmic ray below the ankle are already dominated by extragalactic protons. The ankle feature is in fact the upper limit of acceleration of extragalactic proton. At higher energy, the composition is expected to be dominated by nuclei accelerated to an energy proportional to their atomic number Z. The cut o↵ of the spectrum is attributed to an exhaustion of sources. This model predicts no GZK cut-o↵ and no cosmogenic neutrinos. It was actually proposed in [START_REF] Aloisio | Ultra High Energy Cosmic Rays: The disappointing model[END_REF] to explain Auger spectrum and composition but there remains di culties to explain the ankle shape.

We saw that, at ultra high energy, results of di↵erent observatories agree on an ankle feature around 4 ⇥ 10 18 eV and a cut o↵ at the end of the spectrum. The interpretation in term of source model and propagation is not clear yet. If most of the top down models were excluded, it remains still three main scenarios. If the spectral features can be explained by these scenarios, we see that the mass composition together with anisotropy measurements can support or discard the di↵erent models. Currently, the mass measurements are performed mainly with optical measurements with a limited duty cycle. The goal of the developments presented below is to extend the mass composition measurement to a 100% duty cycle using radio technique and to do it on an event by event basis rather than with a statistical analysis done up to now . We describe in the following chapter how an extensive measurement of the composition help in a consistent understanding of the air shower measurements presented above and how the radio technique and its implementation with EASIER could reach this goal.

Chapter 2 EASIER

EASIER With EASIER, Extensive Air Shower Identification using Electron Radiometer, we intend to detect extensive air shower radio signal in a complementary way to the Pierre Auger surface detector. The radio detector is integrated with the water Cherenkov tank, and while the latter triggers at the passage of particles at ground, the former is recording the radio emission from the air shower. The measured radio profile will provide a calorimetric measurement of the electromagnetic shower and two key informations for mass discrimination: firstly the depth of shower maximum development directly related to the primary composition, secondly and more indirectly the muonic signal at ground deduced by subtraction of the electromagnetic component to the total signal recorded by the particle detector. We first describe the scientific motivation for a combined detection of particles at ground and the shower development with a large duty cycle. Then we report a status of the radio detection in the two frequency bands explored by EASIER and justify the detection principle. This will lead us to the definition of the necessary characteristics of the detector in the last section.

Scientific motivation EASIER

Scientific motivation

As stressed out in the first chapter, some fundamental questions remain open in the overall picture of UHECR. An extensive measurement of composition above 10 19 eV would be of great help for a coherent interpretation of the current results. Moreover, it would enhance our capability to address fundamental question on particle interaction and transport at the highest energies. Current methods of detection access to mass sensitive parameters on a statistical basis. On the one hand fluorescence technique allows a precise measurement of the electromagnetic cascade development. The distribution of the depth of maximum development at a given energy supplies two indicators of mass through the average and the standard deviation. However, the fluorescence light from air showers can only be detected during 10% of the time and its di↵usion in atmosphere depends largely on weather conditions imposing a constant monitoring and reducing even more the duty cycle. On the other hand, the surface detector is indirectly sensitive to mass as it samples the shower only at one stage of development. Recent studies could extract indirect observables to access the time evolution of the shower with the surface detector, for instance the time distribution of the FADC trace can be used to infer the azimuthal asymmetry of the signal rise time in the SD or the muon production depth [START_REF] Garcia-Pinto | Measurements of the longitudinal development of air showers with the Pierre Auger Observatory[END_REF] that both carry information on the longitudinal development. These observables allow to reach higher energies than FD measurements because of the SD large duty cycle. However, in both cases, the shower to shower fluctuations prevent the estimation of the primary mass on an event by event basis. A better constrain on the primary mass is obtained with the measurement of the longitudinal development together with another mass sensitive observable such as the number of muons at ground. The additional information carried by a concomitant measurement of these observables would allow an event by event mass assignment and therefor progress to be made on the following issues: mass composition and hadronic interactions A combined measurement of electromagnetic evolution and the muonic content at ground would constrain the composition of the primary based on the intuitive idea, also supported by most up to date simulation, that light primary nuclei induce deeply penetrating and muon poor showers whereas heavy ones lead to shallow and muon rich showers. Simultaneous measurement of these two anti-correlated observables will supply a separation power between light and heavy nuclei on an event by event basis. Moreover, as X max and S µ are sensitive to parameters such as cross section, multiplicity and inelasticity of the first interactions, a deviation from this anti-correlation would indicate the presence of new phenomena at the highest energies.

Cross section:

Nowadays, the study of the interaction of the cosmic ray beam with the atmosphere nuclei remains the unique way to reach collision energies above tens of TeV in center of mass. Latest published results on proton-air cross section [START_REF] Auger Collaboration | Measurement of the proton-air cross-section at p s = 57 TeV with the Pierre Auger Observatory[END_REF] reported a measurement at 57 TeV well above the LHC maximal collision energy. The performed analysis relies on the X max distribution shape, and the uncertainties that would induce a mixed composition requires stringent cuts on this distribution. The separation power provided by the simultaneous measurement of X max and S µ will improve the proton purity of EASIER 2.1 Scientific motivation the data set, while a 100% duty cycle will allow to access cross section measurement at p s = 100 TeV or more.

Neutrino and photon: If present at the highest energies, photons and neutrinos are known to be rare events. Their search requires a precise characterization of the air shower to distinguished them from nuclei induced shower. Indeed, the shower induced by a neutrino interaction in air or earth is expected to be nearly horizontal and dominantly electromagnetic. In contrast, an horizontal shower induced by a nuclei is in an old stage of development when reaching the ground, and is muon dominated. In current analysis the tagging of the "young showers" is achieved thanks to severe conditions on the signal shape. A direct measurement of the shower age would extend the angular range where a neutrino shower would be unambiguously discriminated from an hadronic one. In the same way, ultra high energy photons, whose main features are a deeply penetrating and purely electromagnetic shower, could be more e ciently distinguished from hadronic background with a measurement of electromagnetic cascade with a 100% duty cycle. In fact, photon search is now performed either with the limited hybrid data set or using SD events after selection procedure reducing sensitivity. A detection of ultra high energy photon or cosmogenic neutrino would be a clear signature of GZK e↵ect.

Anisotropies and magnetic fields. Finally, the measurement of shower development at the highest energies would allow to correlate their arrival direction with catalogues of nearby sources accounting for di↵erent mass composition. As the magnetic field deflection increases linearly with the atomic number Z, a subsample of light primary showers would enhance the power of correlation. Moreover, if acceleration mechanisms at source are rigidity dependent, with the simultaneous observation of primary mass and energy, one could determine acceleration limits as a function of mass and relate them to spectral features. Let us point out also that information on galactic and extragalactic magnetic field could be retrieved relating the angular scale of correlation with mass.

In the current configuration, the surface detector of Auger samples the total particle signal at ground. The longitudinal development is not directly measured and the muonic component at ground is mixed with the electromagnetic one. It has been stated [START_REF] Chou | An Universal Description of the Particle Flux Distributions in Extended Air Showers[END_REF] that after the shower maximum, the EAS development is the same for all showers. One can understand intuitively this behavior noticing that after the number of particles in the shower can rise up to 10 10 at the maximum development, the collective behavior can be described globally only with a few parameters like the geometry of the shower, its energy and the depth of maximum development. In experimental terms, the collected signal at ground can be parameterized with universal functions of these variables. For instance in reference [START_REF] Schmidt | Applying Extensive Air Shower Universality to Ground Detector Data[END_REF] the total signal at ground is expressed as follow :

S(E, ✓) = S em (E, ✓, < X max >) + N µ (E) • S µ (✓, < X max >) (2.1.1)
where S em and S µ are universal functions (i.e. independent of hadronic interaction models and of primary mass) of the parameter mentioned above and N µ is the normalization of the muon number at ground. Given the parameterization above and the reconstruction of an air shower by the SD, a measurement of the longitudinal development would entail the recovery [63] that the deflection of positive and negative charged particles of the shower could lead to an electric dipole and a transverse current. Firstly, particles of opposite charge emit a radiation in opposition of phase that cancels out, however if they are separed in space the phase di↵erence is shifted by a factor d/ where d is the distance of separation and the wavelength of observation. As the charge separation increases or the wavelength of observation decreases, the cancellation disappears. Secondly, from the constant deflection of the charged particles at each generation in the air shower arises a transverse current acting as a source of magnetic field. When this element of current is moving faster than the speed of light in the considered medium, a shock wave is produced and the radiation is amplified. Regardless of the mechanism, a coherent emission occurs only if the characteristic length of the shower front are small compared with the wavelength of observation. The calculation made by Kahn and Lerche with a simple model showed that the dominant process should be the transverse current. A review by Allan [64] in 1971 gives an overall picture of the radio detection at that time on the experimental point of view as well as theoretical. On the experimental side, during the 1960s several experiments detected radio pulses at frequencies ranging from a few MHz to hundreds of MHz. The radiation mechanism could be tested comparing the rate of detection with the orientation of the arrival direction with the direction of geomagnetic field. Some polarization measurement were also performed and most of the experiments agreed on a geomagnetic origin. The coherence of the emission, i.e. its dependence with the shower size is more di cult to figure out since other geometrical factors come also into play, di↵erent experiments found either almost no dependence with the number of particle N, either an incoherent emission E / N 1/2 or a coherent one E / N . Allan summarized the results obtained from the radio experiment operated at Haverah Park in the following expression of the electric field : where ↵ is the angle between arrival direction and geomagnetic field direction, ✓ the zenith angle, R the distance to shower axis. The parameter R 0 was found to be (110 ± 10) m at the frequency ⌫ = 55 MHz and with rather vertical shower ✓  35 . By measuring the ratio of the two polarizations N-S and E-W, it was proved that the dominant emission mechanism was dependent of the geomagnetic field. It is represented in Eq. 2.2.1 by the term sin ↵. The electric field is found to be proportional to energy and its lateral distribution, shown Fig. 2.1, to decrease exponentially. It was also noticed that the factor R 0 increases with the zenith angle but also as the frequency of observation is reduced. To understand qualitatively these experimental results, Allan gives an intuitive derivation of the electric field produced by an air shower and observed at ground. We first derive the electric field for a test charged particle and then we see how a more realistic situation modifies it. Based on the formula given in Feynman's lecture [START_REF] Feynman | The Feynman Lectures in Physics[END_REF], the electric field radiated by a electric charge in motion reads :

E ⌫ = 20 ✓ E p 10 17 ◆ sin ↵ cos ✓ exp ✓ R R 0 (⌫, ✓) ◆ µVm 1 MHz 1 (2.2.1) EASIER 2.

State of the art of radio detection

2.2 State of the art of radio detection EASIER E = e 4⇡✏ 0 c 2 • d 2 ✓ dt 2 (2.2.2)
where d 2 ✓ dt 2 is the angular acceleration of the charge e as it would appear to an observer where the field is evaluated. This formula stresses the importance of geometry in the electric field observed. For a test particle and a simple geometry as shown in Fig 2 .2 left, taking the refractive index into account, the time the observer in P receives the radiation emitted at t em from the source coming from the angle of observation ✓ reads:

t = t em + r c/µ = L v + r c/µ = R v tan ✓ + R (c/µ) sin ✓ (2.2.3)
where µ is the refractive index and the origin of time of emission is taken when the particle is at the same height as the observer (i.e. t em = L/v). It is clear from this equation that for an observer on the particle track and under the condition v = c/µ all the radiation emitted along the track arrives at the same time t = 0. The evolution of ✓ as a function of time retrieved from Eq. 2.2.3 is plotted in Fig 2 .2 right. In the case µv << c the bearing of ✓ is following tan ✓ / 1/t. For air shower the speed of the shower front is close to c, in that case the signal is compressed in time, the radiation from a wide range of ✓ is seen in a short time interval. One should notice the interesting behavior for a refractive index greater than 1, in this case, the radiation observed at a given time arises from two di↵erent parts of the particle track (shower development) and the second derivative of ✓ or the electric field diverges at the Cherenkov angle. The corresponding pulse shape, is shown in the same figure in the right hand plot. In this simple model, the electric field pulse is a delta function because a finite electric field reaches the observer in an infinitely small time interval.

To account for a more realistic situation, the simple model presented above has to be replaced by a vectorial summation over the shower particles individual fields. In the case of geomagnetic deflection, the changes in apparent angle are aligned with the direction of the Lorentz force and sums up arithmetically and Eq. 2.2.2 becomes :

E = 1 4⇡✏ 0 c 2 • X e • d 2 ✓ dt 2 ' 1 4⇡✏ 0 c 2 • X • d 2 [N |e|(✓ + ✓ )] dt 2 (2.2.4)
In that case, the electric field evolves with the number of particles and the angular separation of positive and negative charges as seen from the observer. In addition, in realistic condition the shower front has a physical extension caused by the lateral scattering and longitudinal lag of particles that depend on their energy distribution. Here has to come into play a realistic model of shower development. However, one can understand that the electric field pulse shape will be driven by the evolution of n • ✓ = N |e| (✓ + ✓ ) at the beginning of the shower development where the second derivative is maximum as shown in Fig 2 .3. A shower observed near the Cherenkov angle will induce a short and intense pulse and the compression in time will also increase the frequency seen by the observer. The length of the total pulse on the other side limits the low frequencies present in the electric field pulse. We can now understand qualitatively that the pulse shape and its spectral features depend not only on the shower characteristics like its energy and its depth of maximum development but also on the angle from where it is observed. The important decrease of the electric field with the distance in addition with the influence of many parameters on it, made the prospects for this technique rather pessimistic. Moreover, AY CONFERENCE ig. 6, which shows ated and even not frequencies above e LOPES dipoles ructure is related to EW) and would be S) polarization. In ossed-dipole, if une highly polarized ndencies, the radio the shower geomebeen identified are le between shower omagnetic angle"), distance from the west polarized anission for showers e is proportional to rops exponentially eases linearly with ). ely parametrized in moment valid only This would support the claims from Monte Carlo simulations [START_REF] Auger Collaboration | The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models[END_REF] that radio is a good tracer of the energy. The main reason why one suspects lower scatter in the radio measurements with respect to particle detection on the ground is the fact that radio emission in not absorbed in the atmosphere. Hence, radiation from every particle is visible on the ground -it is in that sense a bolometric measurement. Variations in the location of the shower maximum will be less dramatic compared to measurements of particles on the ground which are just a fractional tail of a quickly declining func-

30TH INTERNATIONAL COSMIC RAY CONFERENCE
An example is shown on Fig. 6, which shows that the beam shape is elongated and even not peaking towards the zenith for frequencies above the resonance frequency of the LOPES dipoles (⇠ 60 MHz). The elongated structure is related to the orientation of the dipoles (EW) and would be rotated by 90 for the other (NS) polarization. In turn this also means that the crossed-dipole, if uncalibrated, will always produce highly polarized signals.

Energy Calibration

In addition to the antenna dependencies, the radio emission will also depend on the shower geometry. The main factors that have been identified are the particle energy, E p , the angle between shower axis and geomagnetic field ("geomagnetic angle"), ↵, the zenith angle, ✓ , and the distance from the shower core, r. For an east-west polarized antenna one finds that the radio emission for showers at the same energy and distance is proportional to 1 cos ↵ (Fig. 7a), the signal drops exponentially with radius (Fig. 7b), and increases linearly with primary particle energy (Fig. 7c).

Altogether this has been nicely parametrized in Horneffer's formula [START_REF] Abraham | The Fluorescence Detector of the Pierre Auger Observatory[END_REF] (at the moment valid only for the EW polarization):

✏ est = (11 ± 1.) [(1.16 ± 0.025) cos ↵] cos ✓ exp ✓ r (236 ± 81) m ◆ ✓ E p 10 17 eV ◆ (0.95±0.04) µV m MHz (1)
We note that the exponential decay of the radio signal is also seen by the CODALEMA experiment [4].

This prescription can now be inverted to predict the energy of the incoming particle. Comparison between the energy predicted from radio with the energy estimated from KASCADE Grande, shows a scatter of 27% between the two methods for E p > 10 17 eV. This is very encouraging, given that shower-to-shower fluctuations in the KASCADE Grande estimate alone should produce a 25% scatter. Hence, the scatter in the radio measurements should be much less. This would support the claims from Monte Carlo simulations [START_REF] Auger Collaboration | The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models[END_REF] that radio is a good tracer of the energy. The main reason why one suspects lower scatter in the radio measurements with respect to particle detection on the ground is the fact that radio emission in not absorbed in the atmosphere. Hence, radiation from every particle is visible on the ground -it is in that sense a bolometric measurement. Variations in the location of the shower maximum will be less dramatic compared to measurements of particles on the ground which are just a fractional tail of a quickly declining function, whose values are quite sensitive to X max .

30TH INTERNATIONAL COSMIC RAY CONFERENCE

An example is shown on Fig. 6, which shows that the beam shape is elongated and even not peaking towards the zenith for frequencies above the resonance frequency of the LOPES dipoles (⇠ 60 MHz). The elongated structure is related to the orientation of the dipoles (EW) and would be rotated by 90 for the other (NS) polarization. In turn this also means that the crossed-dipole, if uncalibrated, will always produce highly polarized signals.

Energy Calibration

In addition to the antenna dependencies, the radio emission will also depend on the shower geometry. The main factors that have been identified are the particle energy, E p , the angle between shower axis and geomagnetic field ("geomagnetic angle"), ↵, the zenith angle, ✓ , and the distance from the shower core, r. For an east-west polarized antenna one finds that the radio emission for showers at the same energy and distance is proportional to 1 cos ↵ (Fig. 7a), the signal drops exponentially with radius (Fig. 7b), and increases linearly with primary particle energy (Fig. 7c).

Altogether this has been nicely parametrized in Horneffer's formula [START_REF] Abraham | The Fluorescence Detector of the Pierre Auger Observatory[END_REF] (at the moment valid only for the EW polarization):

✏ est = (11 ± 1.) [(1.16 ± 0.025) cos ↵] cos ✓ exp ✓ r (236 ± 81) m ◆ ✓ E p 10 17 eV ◆ (0.95±0.04) µV m MHz (1)
We note that the exponential decay of the radio signal is also seen by the CODALEMA experiment [4].

This prescription can now be inverted to predict the energy of the incoming particle. Comparison between the energy predicted from radio with the energy estimated from KASCADE Grande, shows a scatter of 27% between the two methods for E p > 10 17 eV. This is very encouraging, given that shower-to-shower fluctuations in the KASCADE Grande estimate alone should produce a 25% scatter. Hence, the scatter in the radio measurements should be much less. This would support the claims from Monte Carlo simulations [START_REF] Auger Collaboration | The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models[END_REF] that radio is a good tracer of the energy. The main reason why one suspects lower scatter in the radio measurements with respect to particle detection on the ground is the fact that radio emission in not absorbed in the atmosphere. Hence, radiation from every particle is visible on the ground -it is in that sense a bolometric measurement. Variations in the location of the shower maximum will be less dramatic compared to measurements of particles on the ground which are just a fractional tail of a quickly declining function, whose values are quite sensitive to X max . 85 Figure 2.4: Calibration results in [START_REF] Haungs | Air Shower Measurements with the LOPES Radio Antenna Array[END_REF] in LOPES. Normalized pulse height as a function of geomagnetic angle, distance to shower axis and energy. The parameters are fitted separately, the normalization is done dividing by the fits of other parameters. the development at that time of other techniques such as fluorescence detection made the development of radio detection of secondary importance. A renewed interest was raised at the beginning of years 2000 with the need for an increased aperture at ultra high energy and the progress in low noise electronics and data processing. Compared to the pioneering experiment of the 1960s, the modern experiments, like CODALEMA [START_REF] Ardouin | Radio-detection signature of high-energy cosmic rays by the CODALEMA experiment[END_REF] or LOPES [START_REF] Falcke | Detection and imaging of atmospheric radio flashes from cosmic ray air showers[END_REF][START_REF] Apel | LOPES 3D -vectorial measurements of radio emission from cosmic ray induced air showers[END_REF] operate with a larger bandwidth between the AM band and FM band. Some important progress have been made also in amplification electronics and data processing capabilities. CODALEMA has known several phases since 2003. Installed in a radio protected environment in Nancay (France) it is now composed of an array of 24 short active dipoles antenna operating in coincidence with 17 plastic scintillators. CODALEMA is also operating a stand alone array of 60 radio detectors covering 1.5 km 2 . Each detector is composed of a dual polarization butterfly antenna and a embedded electronics. LOPES (LOFAR PrototypE Station) uses also an external particle trigger from the KASCADE array. It has been operating since 2003 and in its last upgrade is composed of 30 tripole antennas, thus measuring the 3 polarizations of the radio signal. At the Pierre Auger Observatory, an

Model-data comparisons

While comparisons between di↵erent models are important and studying the reasons for deviations will be imperative to further improving the models, it is comparisons with data which matter in the end. Unfortunately, currently no data set is publicly available for the modelers to compare their models against. It would be of great use if experiments could publish a data set with all necessary details (including not only air shower parameters such as energy and angles but also the exact core positions and relative antenna locations) so that modelers

Open questions

One issue that bothered modelers over the past year was the ques the established calculations worked correctly very near the Cheren individual particle tracks. A number of contributions to these proc of the electric field pulses for a vertical 10 17 eV at the site of the Pierre Auger Observatory as simodels. The refractive index of the atmosphere was parisons n di↵erent models are important and studying the e imperative to further improving the models, it is ich matter in the end. Unfortunately, currently no e for the modelers to compare their models against. periments could publish a data set with all necessary ir shower parameters such as energy and angles but s and relative antenna locations) so that modelers

Open questions

One issue that bothered modelers over the past year was the question whether the established calculations worked correctly very near the Cherenkov angle of individual particle tracks. A number of contributions to these proceedings have 9 Recently, the contribution of the charge excess mechanism was also detected in AERA data thanks to polarization studies and in CODALEMA data measuring a shift between the core location reconstructed by particle detector and radio detector. The latest experimental results in the VHF band can be found in [START_REF] Revenu | Overview of MHz air shower radio experiments and results[END_REF].

Along with the development of experimental techniques in detectors and data analysis, progress in simulation have been performed too. The most recent algorithm uses either a "microscopic approach" applying classical electrodynamics equation to shower particles without assumption on the underlying emission mechanism, or a "macroscopic approach" where the field is calculated from features of the air shower such as current, net charge or dipole moment. A review and comparison of these recent works can be found in [START_REF] Huege | Theory and simulations of air shower radio emission[END_REF]. In general, the microscopic models agree with each other but a quantitative di↵erence is found between microscopic and macroscopic model especially close to the shower axis. shower axis and for two di↵erent models CoReas [START_REF] Huege | Theory and simulations of air shower radio emission[END_REF] and EVA [START_REF] Werner | [END_REF]. The qualitative pulse shape corresponds to the one calculated with the simple model by Allan, close to the shower axis the electric field is compressed into a short pulse and the spectrum extends at higher frequencies.

In conclusion, the early experiments showed the presence of an emission from EAS leading to a pulse in the VHF band. The most recent ones, with enhanced technologies in acquisition and data post processing, could characterize this pulse signal and compare it with complete simulations. In both cases the dominant emission process was found to be of geomagnetic origin and the lateral extension of the electric field measured to fall exponentially with the distance to shower axis because of a loss of coherence. For this reason the size of the radio arrays remained too small to be able to study the signal at the highest energy. The need of a large aperture to reach the highest energies and the characteristics of the observed signal at lower energies lead to two di↵erent options: on one side the installation of a large array able to self trigger on radio information. This path is followed by the AERA setup. It requires a dense spacing to obtain a signal large enough to trigger on and to be e cient at all angle knowing the geomagnetic e↵ect on the radio signal. Moreover, the transient noise is important in this band and is a source of spurious events therefore advanced functions of triggering are needed to select physical events. The other possibility, followed by EASIER is to equip with radio detector an existing particle detector taking advantage of the trigger it delivers. The asset of this method is to lower the required signal to noise ratio to use a radio signal, since there is no need to trigger. Nonetheless this method requires a signal su ciently intense from the air shower at large distance i.e. where the coherence is lost.

Microwave band

At higher frequencies, the spectrum of air shower emission from individual particle is expected to fall down. However, it was noticed that free electrons, products of ionization induced by the air shower, could interact with neutral molecules of air and produce continuum Molecular Bremsstrahlung Radiation (MBR). This radiation would be unpolarized and emitted isotropically, thus would be a tracker of the shower development in the atmosphere just as the fluorescence emission in the optical domain. Two experiments, one at Argonne Wakefield Accelerator (AWA) and one at the Standford Linear Accelerator Center (SLAC), described in [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF] were carried out to figure out if this emission had su cient intensity to be detected in air shower experiments. In these two experiments, whose setup is illustrated on scheme Fig 2 .6 left, a shower is induced by an electron beam in an anechoic chamber and the microwave radiation is detected by antennas. This measurement requires a great care to limit radiation from the electron beam itself. The intensity detected and averaged over 100 shots in the band 1.5 -6 GHz is shown Fig 2 .6 right, it extends out to more than 60 ns above the noise level. As the transit time of the shower in the chamber is less than 4 ns, the origin of the emission is assumed to come from the cooling of the plasma induced by the passage of the shower. The power recorded in the receivers was found to increase quadratically with the beam energy. The quantitative interpretation of the signal observed is di cult. Indeed, the emission depends on the electron velocity distribution in the plasma. On one side, a suppression of the radiation due to destructive interference in the radiation zone can lower the total emission and is velocity dependent. On the other side, several enhancements of the emission can occur

. In the limit are all unity, oh = N 2 e P 1 , ctron. Since nt power departicle. In corresponds d imaginary e total power equires a deibution funcr by considsubgroups e that the µ e that the subthe radiated he subgroup esulting paradratic in µ e power to the (14) er grows as ectrons in a h the coheriated power fact, as soon e incoherent ven modest ons can thus n expected. e correction e factor $ as e required to hese factors, in a real air vel of fullypeared to us ons, we have ure the MBR eriments we have found good evidence for microwave continuum emission with characteristics suggestive of a major departure from the standard incoherent MBR emission scenario, not an unexpected result given the variety of different non-equilibrium, non-thermal, and partially coherent processes that are possible. We detail these results here. 8

We also checked carefully whether any portion of these backgrounds could be due to radio-frequency interference, and we confirmed that this was not the case. However, we note that our conclusion regarding these backgrounds implies that they are actually stray signal, due to the unwanted beam albedo (the beam components that caused scattered bremsstrahlung due to impacts with the side-walls of the beampipe). Thus it appeared to us that the presence of microwave emission from the chamber ionization was unavoidable. To further pursue the investigation with a more tightly controlled beam, another experiment was scheduled at The Stanford Linear Accelerator Center. FIG. 6: Average microwave emission amplitude from 100 beam shots taken near shower-maximum in the 2004 SLAC T471 experiment, using a broadband antenna that was polarized along the electron beam axis, and was thus sensitive to partially coherent radiation directly from the relativistic electron shower as it transited the Faraday chamber. A strong initial pulse is seen, with rapid decay, followed by a second exponential tail with a longer decay. The noise level is in this case determined by the limited dynamic range of the oscilloscope used, rather than the thermal noise level.

SLAC T471/E165.

In the following year, a similar experiment, T471, was performed at the Stanford Linear Accelerator Center. The configuration of this experiment was largely the same as that of INCOBREMS, but additional precautions were taken against EMI and beam backgrounds, and verified in lab and beam calibration tests. This experiment was coordinated to be operated just downstream of the E165 FLASH experiment, which was used to do precise calibration of air fluorescence for the HiRes collaboration [START_REF] Mariş | Measurement of the ultra high energy cosmic ray flux using data of the Pierre Auger Observatory[END_REF]. The SLAC T471/E165 experiments also used a precisely controlled, 28 GeV electron beam which was collided with a target consisting of 90% Al 2 O 3 and 10% SiO 2 FIG. 7: A plot similar to the previous figure, but now using a crosspolarized antenna which was insensitive to radiation polarized with the electron beam. The dynamic range of the system was now improved so that the noise level is determined by thermal noise, and the detected microwave emission extends out to 60 ns or more, with an exponential decay time constant of about 7 ns. The upper and lower dashed red horizontal lines indicate the minimum detectable intensity, as given by equation 8, for the single-shot case, and the 100shot average. The diagonal dot-dash lines are the two extreme-case estimates for MBR emission: the upper case for no net collisional suppression and the lower case for maximal collisional suppression of the emission, both for the case where the electron thermalization time constant is the source of the 7 ns exponential decay observed.

to make showers with varying particle number, from 0 to 14 radiation lengths of material. In T471/E165, the 28.5 GeV electron bunches were used directly to create the showers with no intermediate conversion to photons via a bremsstrahlung radiator, as this was unnecessary given the high electron energy. Bunches with a typical charge of ⇠ 2 ⇥ 10 7 electrons were used, giving a total shower energy of typically 6 ⇥ 10 17 eV, very similar to those used at AWA.

Figure 6 shows results from measurements of the emission over the 1.5-6 GHz band, using an antenna that was co-polarized with the electron shower momentum. Here the square of the average signal voltage is plotted vs. the time after beam entry into the Faraday chamber. The transit time for the chamber is about 3.3 ns for the beam. An initial strong impulse is observed at the first causal point in time after beam entry. This impulse is found to be highly polarized with the plane of polarization aligned with the beam axis and Poynting vector, characteristic of transition and radio Cherenkov radiation. Such emission was anticipated, and is damped almost immediately due to the microwave absorber ( 30 dB per reflection even at angles of order 55 from normal incidence) that covers the interior of the Faraday chamber (the implied average time constant for quasi-exponential decay of reflec- because of a non thermal distribution of the electrons of the air shower. Based on the measured signal in beam experiment, the signal measured was scaled to air shower parameters. The expected flux density from an air shower of energy 3.36 • 10 17 eV at 10 km away from the receiver is found to be I exp = 2.77 • 10 24 W m 2 Hz 1 [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF]. In the case of a quadratic scaling with energy, the signal of an air shower above 2 EeV would be easily detectable. Even is the case of a linear scaling, it is stated that a 30 EeV air shower could be observed at ' 20 km with a radio telescope. This exciting result triggered several detector developments, starting with AMBER [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF] (Airshower Microwave Bremsstrahlung Experimental Radiometer) first installed at the University of Hawaii, it is now operated at the Pierre Auger Observatory at the Coihueco fluorescence building. The radio sensitive part is an o↵-axis parabolic dish viewed by 4 dual band (C-band 3.4-4.2 GHz and Ku-band 10.9-14.5 GHz) and dual polarized horn antenna and 12 other C-band single polarized horn antenna. AMBER uses a modified version of the surface detector trigger at the T3 level to perform a fast reconstruction of the possible air shower and retrieve the time at which the shower crossed its field of view. The corresponding radio data are recorded. The MIDAS experiment [START_REF] Monasor | The MIDAS experiment: A prototype for the microwave emission of Ultra-High Energy Cosmic Rays[END_REF][START_REF] Alvarez-Muniz | The MIDAS telescope for microwave detection of ultra-high energy cosmic rays[END_REF] (MIcrowave Detection of Air Showers) is also an imaging radio telescope. It is equipped by a 5 m parabolic dish and a 53 pixels receiver camera. MIDAS detector, first took data at the University of Chicago, and is now installed at the Pierre Auger Observatory. MIDAS group has developed a trigger based on a first level trigger on each pixel and a second level trigger searching for air shower pattern. The microwave e↵orts at the Pierre Auger Observatory are described in [START_REF] Auger Collaboration | The Pierre Auger Observatory V: Enhancements[END_REF]. Another prototype, installed at the KASCADE Grande site, named CROME [START_REF] Smida | First results of the CROME experiment[END_REF] for Cosmic Ray Observation via Microwave Emission, is also a radio telescope working in the C-band. In parallel, two beam experiments were setup to confirm and characterize the emission observed in SLAC experiment: MAYBE (Microwave Air Yield Beam Experiment) [START_REF] Monasor | Proc. 32nd ICRC[END_REF] at Argonne National Laboratory uses a electron beam below the Cherenkov threshold to prevent Cherenkov radiation from the beam, and AMY (Air Microwave Yield) at the beam test facility of the National Laboratory of Frascati which uses as an electron beam a LINAC, similar to the EASIER 2.3 EASIER Detector one used in SLAC experiment. For the moment, the results were not confirmed, particularly the quadratic scaling with energy was not observed with MAYBE [START_REF] Williams | UHECR 2012 -International Symposium on Future Directions in UHECR Physics[END_REF]. The emission in microwave band observed in SLAC had an intensity that once scaled to air shower can be detectable. The underlying process is not yet fully understood and the spectral features of this emission are not measured. The confirmation of an isotropic emission would lead to the development of a new technique of EAS observation. However, recent beam experiment didn't reach the same conclusion as the first ones. The uncertain value of flux coming from air shower and its dependence with energy makes a coincident detection crucial to determine the characteristics of this emission. In this scope the principle of EASIER is well suited. Firstly the combined detection with the SD lowers the signal to noise ratio needed to claim a detection. Secondly, as EASIER observes the shower from the ground, if the emission is not completely isotropic but beamed in the forward direction of the shower, it remains detectable. The key parameter is once again the maximum distance at which a radio signal can be detected.

EASIER Detector

We saw the assets of a combined detection on the physics point of view as it lead to a multicomponent information on the shower, but also on the technical side because it permit to avoid triggering issues. We present here the general requirements of the EASIER detector led by its integration in the surface detector unit of Auger.

Auger SD unit

The EASIER radio system is integrated into the surface detector units of the Pierre Auger Observatory. Integration represents a clear asset but sets also constraints in terms of mechanical integration, electromagnetic compatibility and acquisition. The SD station, pictured in Fig. 2.7, is a cylindrical tank made of polyethylene plastic with a base of 3.6 m diameter and a height of 1.55 m. Inside, a liner is filled with 12 tons of purified water (of resistivity 5-15 M⌦cm). The Cherenkov light produced at the passage of particles in the water is collected by three 9 inches PMTs (Photonis XP1805). The PMT base has two outputs, one from the anode (low gain channel) and the other one from an amplifier connected to the last dynode (high gain channel). The overall gain ratio between the two outputs is around 32 and they are both transmitted to the acquisition electronics. The electronics, located under a metallic dome on top of the tank, is composed of a Unified Board (UB) which is a motherboard with CPU and memory that performs all the logics between the Front End, the time tagging and the communication unit. PC operating at The local electronics perform the local triggering, and transmit the data trough the communication antenna to the closest FD stations which in turn transmits them to the central acquisition. The SD station is powered by a 24 V battery charged by two solar panels. The power supply of the station is controlled by a specific electronic board, the Tank Power Control board, (TPCB).

Mechanics

The EASIER mechanics has to fit into the components already on the tank. The top of the tank presents little flat surface area. The EASIER mechanical installation will have to take advantage of this surface or to be installed on the side of the tank. white di↵usive Tyvec r liner and is detected by three 9" XP1805 Photonis photomultiplier tubes (PMTs). The PMT signals from the last dynode and the anode are continuously sampled at 40 MHz by six 10-bit FADCs, yielding a dynamic signal range in total of 15 bits. The digitised data are stored in ring bu↵er memories and processed by a programmable logic device (FPGA) to implement various trigger conditions [12,13]. Two solar panels, combined with bu↵er batteries, provide the electric power for the local electronics, for the GPS clock, used for absolute timing, and for the bi-directional radio communication. Recorded signals are transferred to the Central Data Acquisition System (CDAS) only in cases where a shower trigger has been detected in 3 ad- the cables: when a SD event occurs, the current in the cable may radiate for instance if a connection is not well shielded. the electronics: the processor of the UB operates at 100 MHz and the Flash ADC sample at a frequency of 40 MHz. Note that the electronics boards are enclosed in a metallic shielding (cf Fig. 2.8 (right)) and lay under a metallic dome. the SD antenna: the communication link is operated at around 900 MHz.

Moreover, the sensitive part of EASIER will be an antenna, and if it is placed at a distance of the order of the wavelength of observation from the surrounding objects, the latter are likely to modify the shape of the radiation pattern.

Acquisition and data

The acquisition is performed by the Front End board (FE). The six inputs acquire the negative signal from the anode and the dynode of the three PMTs. The FE input connection is a coaxial SMA female. It is followed by an input Bessel low pass filter with a cut-o↵ frequency of 20 MHz. An inverter mounting performs an amplification by a factor -1/2 before entering the sampling stage. Strictly speaking the acquisition is achieved by 10 bits FADC with a sampling rate of 40 MHz. Their input dynamic, [0 -1 ]V, sets the dynamic range of the Front End input to [-2 -0 ]V. EASIER signal will replace the anode signal of one PMT. It will have to fit into this dynamic range. Moreover, the sampling frequency prevents us from recording directly the radio high frequency signal therefore the RF signal will be first transformed in its envelope. When an SD event has reached the trigger level T3, the six traces of the PMTs are stored in the central acquisition. The EASIER trace will replace one of them and thus have the same characteristics: 768 time bins of 25 ns and digitized on 1024 ADC counts. Moreover, a stream of monitoring data of the tank is recorded every 6 minutes. Useful variables such as the temperature, the power consumption and baseline value will be a great asset to check the good integration and operation of EASIER system.

EASIER system

The general scheme of the EASIER detector is sketched on Fig 2 .9. The radio signal is detected by an antenna in one polarization, amplified and filtered, then a power detector integrates the power in the selected bandwidth and provides its envelope. A linear transformation will follow so that the final output matches the front end input range of the SD acquisition electronics. The radio signal will use one of the FADC channel originally assigned to a PMT low gain output and the power will be supplied by the Auger SD battery. This setup is adjustable for di↵erent frequency bands with few changes and has been applied in the VHF band MHz and the C-band [3.4 -4.2 ]GHz. We describe here the common concerns for the two di↵erent frequency bands, the specific issues will be developed in dedicated chapters.

Antenna The antenna is the sensitive part of the EASIER detector, we list here the main parameters we will focus on to build the prototype and characterize it.

Field of view

The nominal goal is to observe the shower profile of the highest energy air showers (E 10 19 eV) from a distance of 1 km. The depth of maximum shower development at these energies is measured to be ' 750 g/cm 2 [START_REF] Auger Collaboration | The Pierre Auger Observatory II: Studies of Cosmic Ray Composition and Hadronic Interaction models[END_REF] i.e. ⇠ 2.6 km for a vertical air shower. As the Pierre Auger Observatory site is at an altitude of around 1400 m, the angle required is thus Viewing the earth as a flat disk overestimates the required angle ∆θ B for earth coverage.

Looking down from a satellite at a height r, the angle between the vertical and the tangent to the earth's surface is given by sin θ = R/(r + R), which gives for r = 36,000 km, θ = 8.

GmM ⊕ r 2 = mω 2 r = m 2π T 2 r ⇒ r = GM ⊕ T 2 4π 2 1/3
The distance r is measured from the Earth's center. The corresponding height from the surface of the Earth is h = r -R.

Effective Area

When an antenna is operating as a receiving antenna, it extracts a certain amount of power from an incident electromagnetic wave. As shown in Fig. 15.3.1, an incident wave coming from a far distance may be thought of as a uniform plane wave being intercepted by the antenna. The incident electric field sets up currents on the antenna. Such currents may be represented by a Thévenin-equivalent generator, which delivers power to any connected receiving load impedance.

The induced currents also re-radiate an electric field (referred to as the scattered field), which interferes with the incident field causing a shadow region behind the antenna, as shown in Fig. 15.3.1. around 40 . So the half power beam width defined as the angle such that the gain of the antenna is a half of the maximum, has to be of the order of 80 .

E↵ective area or e↵ective length

A receiving antenna extracts an amount of power from an incident flux. The power intercepted can be related to the incident flux introducing an e↵ective area or an e↵ective length when the conversion from electric field to voltage is considered.

P out = A ef f • F in and V out = L ef f • E in (2.3.1)
The e↵ective area or length is dependent on the angle of reception and on the frequency. The scheme in Fig. 2.10 (right) illustrates the fact that only a part of the incident flux is collected by the antenna. The e↵ective area or length are crucial quantities to recover the incident signal. For a lossless antenna, it is related to the gain G of the antenna through:

G(✓, ) = 4⇡A ef f (✓, ) 2 (2.3.2)
where is the wavelength.

EASIER 2.3 EASIER Detector

Analog Dialogue 33-3 (1999) amp. Because log amps are generally ac-coupled, you should do this by connecting the inputs to ground through coupling capacitors.

Solving the problem of noise pickup generally requires some kind of filtering. This is also achieved indirectly by using a matching network at the input. A narrow-band matching Now take a look at the figure on the right. This shows what will happen if the frequency of the input signal is lo than the corner frequency of the output filter. As migh expected, the full wave rectified signal appears unfiltere the output. However this situation can easily be improve adding additional low-pass filtering at the output. Filter The filtering is crucial in EASIER setup. As the signal is integrated over the whole band and no o✏ine filtering can be performed, it is necessary to select a clean band. Some radio frequency band are known to be used for telecommunication. For instance FM band and AM band are used for radio broadcast. But other contribution from local emitter can also pollute the band and require first a survey to determine their frequency.

Part Number

Amplifier The amplitude at the output of the antenna is expected to be very low. An amplification is needed to recover a signal that can be processed by usual electronic device.

The crucial parameter of an amplifier is the noise the amplification can add to the signal. It is quantified by the ratio of input and output signal to noise ratio called the noise figure: F sys = SN R out /SN R in . If the electronics system is composed of several stages, the total noise figure is the sum of the noise figures of each stage weighted by the previous gains :

F sys = F 1 + F 2 1 G 1 + F 3 1 G 1 • G 2 + ... + F n 1 G 1 • G 2 ...G n 1 (2.3.3)
This equation states that provided that the gain of the first amplifier is large enough, the noise of the following stages is negligible.

Power detection

The acquisition of EASIER is performed by the Auger SD FADC with a sampling rate of 40 MHz. The reception band is either the VHF band or the microwave one so the RF signal needs to be transformed in its envelope that can be sampled at lower frequency. This operation is performed by a logarithmic amplifier [START_REF] Nash | Logarithmic amplifiers explained[END_REF]. The output of this device is a voltage proportional to the logarithm of the input power. A typical response of a logarithmic amplifier to a sine wave input is represented on

P 1 P 2 VPD PdBm V PD2 V PD1 VEB VPD V EB2 = 0V V EB1 = -2V P 2 P 1 V PD2 V PD1 Power detector EASIER board Front End VFE [V] 0V -2V
Figure 2.12: Scheme of operation of the di↵erent part of EASIER electronics chain. From an initial power dynamic range [P 1 P 2 ] to the input of the front end.

EASIER board

The final output of the EASIER detector has to fit into the Auger SD front end. The voltage input range is [-2 ; 0 ]V. The signal from the power detector has to be adapted to adjust the input power dynamic range ([P 1 -P 2 ] in Fig. 2.12) and the baseline level to this input voltage range as indicated in Fig. 2.12. The output of the power detector V P D is:

V P D = a • P dBm + b [V ] (2.3.4)
An electronics board is designed to perform a linear transformation so that its output, V EB , is:

output of the EASIER Board:

V EB = c • V P D + d = a • c • P dBm + c • b + d [V ] (2.3.5)
The gain c is set such that the input power dynamic range is P dBm = 2 a•c• . The o↵set d is chosen to place the baseline between [0 ; -2 ]V. The last stage of EASIER acquisition chain is actually the Auger front end electronics. It is composed of a 20 MHz low pass filter, an amplifier with a gain G = 0.5 and 10 bits ADC sampling at 40 MHz. The transformation performed by the Auger front end are: output of the Front End amplifier:

V ADC = 0.5 • V EB [V ] (2.3.6) output of the ADC : ADC = V ADC • 1023 [ADC counts] (2.3.7)
At the end, the trace in ADC counts is proportional to the logarithm of the input power.

Power supply board

The power supply is provided by the tank power supply, an electronic board is designed to share the power between the di↵erent active parts of EASIER electronics.

As the nominal power delivered by the solar panel is 10 W, and the tank elements like PMT and electronics use only 7.5 W, our goal was to design a system consuming less than 2 W.

Chapter 3

VHF band

Early experiments have already detected radio signal emitted from air shower in the VHF frequency band [64]. More recent setups with improved electronic and data processing facilities have been studying the origin and characteristics of this signal [START_REF] Revenu | Overview of MHz air shower radio experiments and results[END_REF]. Because of the low extension of the radio signal, it has always necessitated a dense array of detectors, and has never been exploited on very large areas. The principle of EASIER in the VHF band is to take advantage on both the new development in radio detection and the facilities of the Pierre Auger Observatory to study the radio signal emitted by air shower with energy above 10 18 eV. By using the trigger of surface detector and focusing on the ultra high energies, we hope to detect a radio emission that could extend at larger distances than previously measured.

We present in this chapter, the assembling of the EASIER setup in the VHF band, then its installation at the Pierre Auger site. In a third part we describe the resulting data: the detection of radio event and an analysis of their characteristics.

Detector

The VHF band is well utilized in communication and most of the electronics devices include electronic clocks at these frequencies. Moreover, at low frequency (⌫  30 MHz) the background noise can be modulated by atmospheric e↵ects. As an illustration we show in the digram 3.1 the di↵erent noise contributions between 1 and 100 MHz. In principle, in a radio quiet environment, the limiting noise comes from the galactic thermal emission. Also, it is clear from this figure that in urban condition, with a noise three orders of magnitude larger than in radio quiet condition, no complete test can be performed easily in real conditions for instance in Paris. Test in Faraday cage can be done however, given that the characteristic wavelength in VHF band is of the order of a few meters, the size of the cage must be of this order of magnitude to performe reliable test. We relied on the sensor developments performed by the CODALEMA experiment [START_REF] Ardouin | An active dipole for cosmic ray radiodetection with CODALEMA[END_REF]. The CODALEMA collaboration developed an active antenna for the purpose of radio detection of air showers. This setup was installed in a radio protected site in Nancay (France) and later at the Pierre Auger Observatory site. It has proven to have an excellent e ciency in the configuration set up by CODALEMA. In the case of EASIER, the setup will be di↵erent from the original one because of the constraints imposed by its integration with the Water Cherenkov detector. We will have to face two specific concerns related to the installation of the sensor on the tank: the SD electronics placed on the tank is likely to radiate noise and impair the sensitivity.

as the wavelengths considered are of the order of a few meters, the power pattern can be influenced by surrounding objects. In particular, the amount of water in the SD tank, and solar panels or communication antenna placed on the tank.

Our setup is composed of a fat dipole antenna and a preamplifier both developed for the CODALEMA experiment, followed by an adaptation level specific to EASIER. To fulfill the noise and bandwidth constraints, an ASIC amplifier was designed at SUBATECH. The chip is based on three fully differential amplifiers. The input amplifier is low noise with a gain of 45 and a capacitive input impedance of 10 pF. The gain of the middle amplifier is programmable from 3 to 6.9. The power output amplifier is designed to drive a 100 O load. Because a low noise is required from the lowest frequencies and the antenna impedance is inversely proportional to frequency, a MOS transistor was chosen due to its absence of current noise. The flicker noise is reduced choosing a P channel whereas the thermal noise is lowered by sizing a wide PMOS transistor. A measurement of the ASIC input noise density is shown in Fig. 3. The middle range gain of the amplifier board is 34 dB with a high cut-off frequency of 240 MHz and a low cut-off adjustable above 10 kHz. The input dynamics is 24 mV and the consumption is 1 4 W. and a good sensitivity on the whole spectrum [3].

The active antenna concept

A simplified electrical model of a dipole antenna is a voltage source V a in serial with the antenna impedance Z a , composed of a capacitance C a , an inductance L a and a radiation resistance R rad . For frequencies well below resonance (up to 1/5 of the resonance frequency f 0 ), Z a becomes equivalent to a capacitance due to a drop of the radiation resistance when the frequency decreases. Two options are possible to create the active dipole antenna: if the antenna is loaded by a preamplifier whose input impedance is a capacitance C in (high input impedance), then a capacitive attenuator is obtained (see Fig. 1); if the antenna is loaded by a capacitive feedback preamplifier (low input impedance), then the transfer function is given by the ratio of the antenna capacitance on the feedback one. In both cases, the relationship between the voltage induced on the antenna V a and the preamplifier output voltage V out becomes independent of the frequency. The first solution was implemented. In this scheme, the larger the antenna capacitance, the smaller the capacitive attenuation. One way to increase the antenna capacitance without decreasing f 0 is Antenna and Amplifier The combination of the antenna and the LNA constitute an active antenna meaning that the amplifier impedance is adapted to compensate the loss of the antenna at frequencies far from the resonance resulting in a wide band of reception. The antenna is a dipole made of two aluminum blades of 0.6 m each and 0.1 m wide, they are separated by a gap of 0.01 m . The drawings of the radiator are shown in Fig. 3.1 (right). The simulated power pattern of the dipole is shown Fig. 3.2 (left), it exhibits a half power beam width of 90 and 120 respectively in the E-plane (defined as the plane containing the electric field vector (in our case the dipole direction) and the antenna boresight) and the H-plane (defined as the plane containing the magnetic field vector (orthogonal to the dipole direction) and the antenna boresight). This field of view characteristics are well suited for the EASIER purposes. The pattern is simulated for a dipole placed horizontally at 1.2 m above a perfect conducting ground. The pattern is given by the geometry of the antenna but it is also shapped by interferences of waves reflected by the ground. The pattern is thus expected to change if the detected wavelength is comparable to the distance from the dipole to the ground or if the conductivity characteristics of the ground change. The main purpose of the active antenna choice is to obtain an approximately flat response with the frequency. The electronic equivalent circuit of the antenna and amplifier system is depicted in Fig. 3.2 (right). In that scheme, the antenna is represented by a voltage generator and a series circuit R rad , L a , C a . The e↵ective length, defined as the ratio of the voltage at the output of the antenna with the incoming electric field depends on the gain pattern of the antenna and the radiation resistance as:

L ef f = c ⌫ r R rad (⌫)G(✓, , ⌫) 120⇡ 2 (3.1.1)
Then, the transfer function of the amplifier is given by:

H(⌫) = Z in (⌫) Z in (⌫) + Z a (⌫) (3.1.2)
The product of the e↵ective length and the transfer function determines the factor between the incoming electric field and the voltage at the output of the LNA. The input impedance of the amplifier is mainly capacitive, so to obtain a transfer function independent of the frequency, the terms in Eq. 3.1.2 need to evolve the same way with frequency, i.e. the antenna impedance has to be mainly capacitive too. This characteristic is obtained by means of the important width of the dipole's blades with respect to dipole wires for instance. Moreover, according

Detector

VHF band

to Z a is connected to the di↵erential input. This ASIC is mounted on a small printed board with a balun output transformer allowing to drive a 50 ⌦ load through a coaxial cable. The V out /V a ratio of this preamplifier board (Fig. 2) is 30 dB with a 10 pF dummy antenna capacitance, and the -3 dB bandwidth is ranging from 80 kHz to 230 MHz. With the measured values of Z a , it exhibits a maximum value of 34.7 dB at 113 MHz due to the antenna resonance. Two external feedback resistors connect the di↵erential outputs to the di↵erential inputs to bias the preamplifier. Moreover, thanks to C in , they act as an active first order high pass filter whose cut o↵ frequency can be easily adjusted from 10 kHz to more than 1 MHz.

The active antenna sensitivity

Two noise sources should be considered to evaluate the antenna sensitivity: the preamplifier electronic noise v 2 amp which is mainly dominated by the first transistor stage, and the noise resulting from the sky background temperature T sky . It to Eq. 3.1.2, the higher the capacitance, the higher the transfer function. This justifies the choice of a fat dipole with respect to a usual dipole made of conductor wires. The amplifier was especially designed for the purposes of cosmic ray detection, with a constraint of low noise, wide bandwidth and fast response [START_REF] Charrier | Design of a low noise, wide band, active dipole antenna for a cosmic ray radiodetection experiment[END_REF]. It is composed of three di↵erential amplification stages (in di↵erential mode, i.e. not referenced to the electrical ground). It is then followed by a "balun" (BALanced UNbalanced) to make the signal asymmetric, i.e. referenced to the electrical ground. The measurement of the amplifier gain is shown in Fig. 3.3, it was performed replacing the antenna impedance by a capacitance (solid line). Then an independent measurement of the antenna impedance allow to calculate the actual gain calculated from the combination of the antenna and the LNA (shown in dotted line Fig. 3.3). The overall gain is 30 dB and is flat from 200 kHz to 100 MHz for the amplifier alone. When the antenna impedance is taken into account, the gain increases near the antenna resonance frequency at ⌫ 0 ' 113 MHz. In the design of the LNA, a special care was taken to keep a low noise level. Noise measurements were performed once again replacing the antenna by an equivalent capacitance of 10 pF, the noise induced by the LNA is found to be less than 1 nV/ p Hz ' 1500 K for frequencies larger than 10 MHz, thus lower than the galactic noise. The power consumption is 0.25 W and it can be supplied by a voltage from 6 to 12 V. This setup was first used in CODALEMA in Nancay and later at the Pierre Auger Observatory in the framework of the Radio Auger project. So the noise background condition was already tested and we can then estimate the background noise expected with the spectrum presented in Fig. 3.4. The EASIER setup imposes us to select a clean band. This band, in red in Fig. 3.4, is between 30 and 80 MHz. The noise density in this band after amplification by the LNA is lower than -125 dBm/Hz. EASIER board As described in chapter 2, the EASIER electronics has to fulfill three main functions: select a clean band, transform the high frequency signal into its power envelope and adapt it to fit the input dynamic range of the SD front end. The physics requirements for the board are imposed by the background noise level, the amplification factor of the LNA and the expected signal from air showers. To establish the electronic requirements we first choose a limited frequency range: the chosen frequency band is filtered with a pass band filter from 30 to 80 MHz. In this band the spectrum after amplification shows a noise density of -127 dBm/Hz, which, once integrated over the frequency VHF band

Detector

in the 5-30 MHz range, the sky noise floor is clearly greater than the preamplifier noise. The atmospheric noise seems to dominate below 5 MHz whereas the galactic noise is the greatest above 30 MHz. The v 2 sky /v 2 amp ratio characterises the active antenna sensitivity: 0 dB at 50 MHz and 4.5 dB at 100 MHz. At 100 MHz, with a preamplifier gain of 34 dB (Fig. 2) and an output electronic noise of -131.7 dBm/Hz (Fig. 3), a galactic noise of -161.2 dBm/Hz at the preamplifier input can be deduced. With R rad = 51.3 ⌦, T sky = 1340K is calculated. The same calculation at 50 MHz, where R rad = 5.3 ⌦ gives T sky = 9480K. These two temperature estimations agree fairly well with the known values [4]. One should note that those noises could be used as a calibration method for the CODALEMA experiment.

Conclusion

This active antenna gives good results for its purpose. Since June 2005, a cross shape array of 16 antennas has been installed and is currently under operation at the Nançay radio-observatory. A new ASIC design with an up-to-date technology is under work from which an electronic noise improvement of 3 dB is expected. This radio frequency signal has to be adapted to fit into the Auger FADC with the wanted dynamic range. To do so, an electronic board was designed, its main functions are summarized in Fig. 3.5. The first amplification stage, by amplifying the signal from the low noise amplifier (LNA) set the size of the dynamic range. The following filters select the clean bandwidth. Then, the power detector Analog Device AD8310 [85] was chosen because it is suited for VHF frequencies and the background noise level is well in its dynamic range. Its calibration curve taken from the constructor's data sheet is given Fig. 3.6 (left). With its nominal configuration , its slope is S = 24 mV/dB and 80 dB of dynamic range are covered at output voltages from 0.5 to 2.5 V. We decided to set the background noise level at 1/4 of the final dynamic range and to allow ' 30 dB (a factor 1000) for the signal from air showers. This value sets the requirements for the electronic board: an input power of -50 dBm results in -0.5 V at the output of the EASIER board and the slope is set to 20 dB/V. The last amplification stage sets an o↵set to place the background signal at V bkg = 0.5V , corresponding to one fourth of the front end input. The calibration curves in Fig. 3.6 (right) measured at several frequencies represent the output voltage of the EASIER board as a function of the input power. The e↵ect of the filter is clearly seen and in the middle of the band, at 50 MHz, the dynamic range extends from -60 to -20 dBm on the range of 2 V as expected. The calibration relation is :

P dBm = 20 • V EB 60 (3.1.3)
with V EB 2 [-2 ; 0]. Or in ADC counts:

P dBm = 3.9 ⇥ 10 2 • ADC 60 (3.1.4)
with ADC 2 [0 ; 1024] A power supply board was also implemented to feed the LNA and the active component of the EASIER board.

Complete setup

In a first version of the setup, a metallic box containing the LNA, the power supply board and the EASIER board, was placed just above the dipole. In fact, the metallic box created a parasitic capacitance with the dipole and the signal was highly attenuated [START_REF] Gambetta | Study of the Attenuation of Extensive Air Showers in the Atmosphere and of the Feasibility of Measuring their Radio Signal with EASIER[END_REF]. In the definitive version the metallic box is replaced by a plastic one containing uniquely the LNA placed above the dipole and one metallic box containing the two other electronic boards. A scheme of the complete setup is shown in Fig. 3.5 (right) or in Fig. 3.9 once installed on site. All the boards were tested and calibrated, and the response of the complete detector was tested only qualitatively because of noise conditions. Seven complete setups with radiator, LNA and EASIER board were shipped to Argentina at the end of year 2010.

Installation

In February 2011, we proceeded to the installation of seven prototypes at the Pierre Auger Observatory. The shipped material was first assembled on site. The mechanic assembling to integrate the antenna with the tank was chosen with the help of the local mechanics. The dipole is placed on top of a 3 m plastic pole with a plastic screw (cf Fig. 3.7), the LNA directly connected to the blades of the dipole (cf Fig. 3.5 right) is just above them in a plastic box. Two cables are connected to the LNA box, one to feed the power supply to the amplifier, the other one is conducting the signal output of the LNA to the EASIER board.

Tests and modifications As it was mentioned before, the frequency band from 1 to 200 MHz is very noisy, especially in city environment. The setup could not be tested completely in Paris for this reason. Once we assembled a complete setup, we tested it near the assembly building of the Observatory campus which is in the town of Malargüe. As the noise background level was still orders of magnitude higher than expected in the Pampa, we made some tests in a container serving as a Faraday cage. The first test we performed revealed an important resonance at the resonance frequency of the antenna (see Fig. 3.8).

In principle, this frequency is filtered however the LNA has an upper limit input power to operate nominally. The resonance was suspected to arise from radiation of elements of the setup such as connection or cables. To attenuate this spurious ray, we brought two main improvements :

we soldered directly the signal cable to LNA board (in the original setup the LNA was connected to the electronic boxes with two cables, one from the LNA to the plastic box and a second one from the plastic box to the electronic box, thus with an additional connection)

we shielded the cables transporting the RF signal with flexible metallic pipe.

Installation

VHF band

[MHz] ν We decided to test the whole setup about ten kilometers away from the city. The resulting spectra were almost free from any peaks in the chosen bandwidth and the background noise level was approximately the one expected i.e. ' 125 dBm/Hz. These results made us confident in the possibility to install finally the setups in the field.

First installation

We installed the first setup on the tank Vieira (LsId: 433) on the 1 st of March 2011 . The final setup once installed is shown in Fig. 3.9. The spectrum recorded during the installation shown in Fig. 3.10 in red, as expected, an almost flat noise background between 30 and 80 MHz of density around 125 dBm/Hz (or -85 dBm/10kHz).

On figure (3.10 left) is also represented in black a spectrum recorded when a computer was on the tank showing once more the necessity to get rid of any noise source to perform reliable tests. The zoom of the spectrum in Fig. 3.10 (lower panel) shows first that two peaks at 67.5 and 80 MHz of amplitude around 10 dB above the noise remain in the selected band, they will pollute the data. Second at each side of the selected band important peaks are present, therefore if the filter slope is not steep enough they may still bring a contribution in the integrated signal.

The six other detectors were installed in the following week. The date of activation for the seven installed setups are reported in Table 3.1 and their locations are depicted on the map Fig. 3.11.

All the dipoles were placed with an East West polarization. This is justified by the expected emission mechanism, the geomagnetic e↵ect. Soon after the installation we had the confirmation of the proper functioning of the detector as a clear event was detected in the radio channel just a few days after its installation.

Data Analysis

The seven VHF setups installed in March 2011 operated until November 2011 when they were decommissioned. During this period, not all the recorded data are exploitable. We present first a selection of the data set, then the method of selection of radio events and finally we discuss the origin of these detected radio events. Monitoring data allow us to follow the behavior of EASIER detectors over an important time period. One can see in Fig. 3.12 the evolution of the baseline as a function of time during five months of operation. For the stations 384, 385, 422 and 431, the baseline increases by steps appearing at the same moment for the four of them. Such simultaneous behavior can be explained by RFIs that were not present at the time of the installation and appeared in the area of these antennas. The three others don't show a peculiar behavior for the first months. However, every antenna seem to have su↵ered of the local winter (months of June to September) when some failure appear. Indeed, the antennas were decommissioned in November 2011 and some of them were broken lying on the ground. We suspect a too important wind load of the dipole to be the cause of the failure of the antennas. We should also precise that just before the installation many soldering were redone and some of them may have also broken. In particular, two 5 m cables are soldered directly on the LNA, one supplying the power for its functioning, the other to transport the RF signal and the weight of these cables may have broken the solderings. In this analysis, the time period considered starts from the installation date and ends the 19 production. During this period 970 events have a reconstructed energy and at least one of 7 stations, on which a VHF EASIER antenna is installed, has triggered. The resulting data set is composed of 1748 available traces for radio signal search. Despite the di culties, during the period of good operation of the antennas, we recorded a total of 36 unambiguous radio events, we further detail the procedure of event selection below.

Data set

Event selection

Even if the radio environment is quiet in the Pampa, some radio traces can show some clear episodic perturbation when the baseline and its fluctuations are much larger than usual. Some malfunctions, like a brutal increase of the baseline can be detected thanks to the monitoring data in Fig. 3.12. A further look at the radio traces bring more detail on the origin of these malfunctions. We show for instance two traces in Fig. 3.13 with a specific behavior. The trace in the upper panel exhibits peaks at regular time intervals. The origin of these peaks is likely to come from the EASIER electronics itself and appears constantly in the data of the detector 432. The trace in lower panel of Fig. 3.13 exhibits a strong modulation. This may be due to a close intermittent emitter. The event selection criteria we present are chosen to exclude this kind of trace and to select potential radio pulses correlated with EAS. The event selection is performed in four steps:

For each available trace, the distribution of amplitude in ADC counts is fitted with a Gaussian distribution and the mean and the standard deviation are extracted.

a cut is applied to keep traces with a mean 2 [100 , 800] ADC counts and the standard

Data Analysis

VHF band

deviation 2 [0 , 150]ADC count. This insure a good estimation of the mean and remove trace with too large fluctuations. 5% of the traces are rejected by this cut.

the maximum of the trace is required to be within ± 4 times bins around the arrival time of the particles in the tank.

the amplitude of the maximum is required to be more than 250 ADC counts above the baseline corresponding to a power around a factor of ten above the background noise. Table 3.2 reports the cut e ciency on the radio traces. We show an example of event for which a signal was found in three antennas in Fig. 3.14 shown together with a PMT signal to indicate the start time of the particle arrival. The radio events show a characteristic pulse shape of a few time bins long, i.e. no more than 200 ns. The characteristics of the air shower that led to the selected radio events are shown in the histograms in Fig. 3.15 in red compared to the distribution of the events detected by the SD. Events from a few 10 17 eV up to more than 3 ⇥ 10 19 eV were detected in radio. The distances to shower axis are concentrated in the lower values under few hundreds of meters. The arrival direction leading to radio event don't follow the distribution of the air shower detected by the SD array. Indeed it exhibit an excess of detection for EAS events with a large zenith angle and a southern direction. This e↵ect is explained in the next paragraphs.

Origin of the observed events

We discuss in this paragraph on the origin of the radio events selected above. We present first a study performed in [START_REF] Thiery | Influence des cuves du detecteur de surface de l Observatoire Pierre Auger sur les antennes MHz d EASIER[END_REF] that eliminates the possibility that the radio event originate from the tank noise in the VHF band. We discuss then the possible origin mechanism that give rise to the events and their arrival direction distribution.

Noise from the tank It was pointed out in introduction of this chapter that the good functioning of the EASIER setup is subjected to its integration to the SD tanks and the non influence of the latter on the former. As a matter of fact, one of the main concern was that the radiation emitted by the SD electronics, the PMTs or the cable conducting the PMT signal could be detected by the EASIER antenna and lead to spurious events. A study was performed making use of the LED (Light Emitting Diode) system originally utilized for the calibration of the PMT of the water Cherenkov tank. The LED system simulates the Cherenkov light of the particles in the water tank and causes a fake event. We can thus estimate the noise induced only by the tank elements on the antenna. However, the LED cable itself was found to emit noise detected by the EASIER antenna. The method to cancel it is to record separately the noise induce by both the tank elements and the LED and then by switching o↵ the PMT high voltage, record the noise induced solely by the LED system. The noise induced by the tank is obtained by subtraction. Moreover, we can vary the intensity of the light emitted by the LED to check if there is any correlation between the PMT charge and the radio signal. In real events, the intensity of light in the tank depends on the shower energy and the distance from the tank to the shower core. The results are reported in Fig. 3.16 for 5 antennas. The Y-axis represents the amplitude of the maximum radio signal in units of baseline, i.e. the signal to noise ratio (SNR), in this case, it is in fact the di↵erence of SNR when the PMTs were on and when they were o↵. A fixed number of 5 was added first to prevent from negative signal to noise ratio and be able to plot it in log scale. The X-axis represent the light in the tank and is expressed in V EMcharge which is the integral of the signal in the PMTs. Except for important value of LED intensities, corresponding to cosmic ray event very close to the station, the noise induced by the tank is compatible with zero. The radio signals induced by air shower events presented before are shown in the same figure. All of them are above the noise induced by the tank at the corresponding particle signal proving that the signals observed are not spurious.

Anisotropy of detection e ciency

The distributions shown in Fig. 3.15 point to an excess of radio events detected from inclined shower and coming from southern direction. It is more evident on the plot in polar coordinate in Fig. 3.17 (left), where the red dots represent the radio event and the black open circles air shower events selected but without radio event. This excess is consistent with two expected e↵ects, one is related to the emission mechanism and the other to the detection setup. Another e↵ect has to be accounted for to explain the excess in Fig. 3.17 (left). It is related to the pattern of the antenna which is modified due to its position with respect to the tank. The dipole response in presence of the water tank has been simulated with the Ansoft's 3D electromagnetic simulation software HFSS [89]. The antenna gain patterns at three frequencies, 30, 50 and 70 MHz are shown in Fig. 3.18. If at 30 MHz the pattern is regular and looks like the expected one, at higher frequency the pattern become highly anisotropic and a lobe pointing in the southern direction (negative y in Fig. 3.18) participate to excess of detection in this direction. The voltage at the output of the antenna, V out is related to the electric field via :

VHF band 3.3 Data Analysis

V out = L ef f • k Ẽk • cos (3.3.1)
where cos is the polarization vector of the incoming electric field, and the e↵ective length

L ef f / p G(✓, , ⌫).
The excess of detection can be explained by the combined e↵ect of the geomagnetic field and the anisotropic gain pattern. The amplitude of this combined e↵ect is shown in Fig. 3.18 (bottom panel) and matches qualitatively the results presented in Fig. 3.17 (left).

Lateral distribution of the radio signal

The important parameter for the study of the UHECR is the maximum distance of detection. It determines the minimum spacing needed for an array of detectors. G(✓,,⌫) and the transformation factor induced by the EASIER electronics which depends also of the frequency (cf Fig. 3.6). The overall calibration relation, from the electric field to the voltage is not known precisely enough, so the amplitude is calculated relatively to the baseline of the trace and is reported in arbitrary units. One can notice a bulk of events decreasing exponentially with the distance. The exponential decrease is consistent with Allan's formula in Eq. 2.2.1 and later results from CODALEMA or LOPES experiments and suggest a coherent process. The characteristic distance of the exponential decrease is found to be approximately 200 m. One can also notice also four outliers (in red in Fig. 3.19) with an amplitude of a factor ten above the bulk of events. One possible explanation for these large amplitudes is the amplification of the radio signal during stormy conditions, but no for the moment we haven't drawn any conclusion on these events. 3.4 Outcome of the first prototype and further developments VHF band

Outcome of the first prototype and further developments

First setup We constructed and installed an array of seven radio detectors at the Pierre Auger Observatory operating in coincidence with the surface detector. The detection of cosmic rays in coincidence with the Auger SD tank was proven to be possible and e cient. However, this first prototype had several deficiencies. Firstly some electronic connections were found to be fragile. Secondly, the wind load of the antenna was found to be too important for the conditions at the Pierre Auger site. Thirdly, the position of the antenna on the tank influenced the power pattern preventing us from deriving a reliable absolute calibration of the complete detector, and making the e ciency of detection anisotropic. We also realized the di culties in instrumenting this frequency band. The noise conditions even in the Argentinian pampa are evolving and emitters in the selected band can appear after the deployment. Despite these issues, EASIER detectors in this band managed to detect 36 radio events. Their characteristics are consistent with the detection by other experiments of a beamed emission dominated by a geomagnetic e↵ect. However, with this first prototype, we couldn't succeed in the detection of vertical events at distances larger than 200 m. Two main paths are being investigated: first the analysis method presented may be improved with a more thorough data processing. An analysis and a filtering of the noise would allow to lower the detection threshold. Secondly we developed a new prototype taking advantage of the experience we gained.

second setup The second setup was developed in order to respond to the requirements set by the first setup experience. The overall setup remained unchanged, but some improvements were brought. We followed the evolution of CODALEMA in the sensor part. The antenna is still an active antenna but is now a butterfly antenna in reference to its shape (see Fig. 3.20). Its design was chosen to optimize its sensitivity between 30 and 80 MHz [START_REF] Charrier | Antenna development for astroparticle and radioastronomy experiments[END_REF]. The comparison of the e↵ective length of the fat dipole and the butterfly antenna is shown in Fig. ?? (left).

The LNA remained the same but the cable transporting the RF signal is now shielded to avoid its radiation and amplification (one of the problem we had during the first installation). As noticed in the spectrum taken during the installation of the first setup, the initial selected band (30 and 80 MHz) was too wide and peaks were present into this band. The filtering was improved by ordering a filter designed specifically for our purposes. The specifications for the filter design were a steep cut of the frequencies below 30 MHz and above 60 MHz. A loss of 40 dB is reached at 3 MHz out of the selected band.

A special care was also taken to insure no electronic noise arises from the EASIER electronic itself and the two electronic boards (the power supply board and the EASIER board) are now separated to ensure that no radiated noise from the first can interfere with the second. The picture in Fig 3.20 (right) shows the two electronic boxes. They are connected with a cable equipped with ferrite to filter any low frequency modulation from the power supply board to the EASIER board. Five detectors were installed in March 2013, the position of the antenna on the tank was chosen to keep symmetric lobes according to simulation results including the water tank and the solar panels . The antenna is now placed at the center of the tank at 1.5 m above the water. Up to now, on the five antennas installed, only two are operating correctly. The failure of the others are under investigation. With this second prototype our goal is to be sensitive to a possible isotropic emission Chapter 4

Detector developments and sensitivity in microwave band

In the microwave band two setups were installed at the Pierre Auger Observatory surface detector. The first one, a prototype hexagon was deployed in April 2011 and the second one, an extension to 61 detectors, in April 2012.

We describe here first the di↵erent steps we followed in the detector development. From the noise survey carried at the very beginning of the project to the installation of the first setup and then its extension. We detail then the calibration of the detector electronics performed both in laboratory and on site and extract an absolute calibration of the system. In a third part of this chapter, we give the important parameters to estimate the performance of the detector and describe the e↵orts we made to measure them.

Detector developments

Detector developments and sensitivity in microwave band

Detector developments Noise survey

A noise survey was carried out to estimate the noise pollution in the microwave band at the Auger site. The survey was achieved with an ultra wide band [2 -18 ]GHz spiral antenna circularly polarized, and two cascaded low noise amplifiers AM48 L4003 of 38 dB of gain each, a nominal bandwidth of [4 -8 ]GHz and a noise figure of 2 dB. We performed the survey where the first prototype is planned to be installed, i.e. in front of the Los Leones FD building. In Fig 4 .1 are illustrated the spectra recorded on the roof of the FD building Los Leones (left), and on the tank Vieira (right) which is situated close to Los Leones. Two peaks between 7.5 and 7.8 GHz from the FD communication are present near Los Leones and disappear if the antenna is placed far enough from the FD building. From the spectra, the frequency band [3 -9 ]GHz exhibits no peaks when the antenna is placed in the array. In this large band, the C-band (3.4-4.2 GHz) is an interesting choice. This band was originally chosen for satellite broadcast because of the good propagation of in atmosphere at these wavelengths. Therefore, this band is adapted for us for physical reasons, and in addition the antenna and the amplifier are already developed for commercial purposes and can be found really inexpensive. This band is chosen for the first setup of EASIER.

Setup components

Overview of the setup A scheme of the complete setup is presented in Fig. 4.2. In the scheme, the blue blocks represent the EASIER components, whereas the pink ones are Auger SD components. The red connections feature the radio signal lines and the dashed line the power supply circuit. The setup is largely composed of commercial equipments assembled together.

The antenna we chose is a TV satellite antenna, it is already equipped with a high gain amplification. On the same line is carried the power supply for the amplification and the output signal.

the bias Tee split the radio signal and the power supply voltage.

LNB ~60dB

Bias Tee the high pass filter is added to get rid of any low frequency modulation the power detector integrates the RF signal in its power envelope.

the adaptation board accommodates the right dynamic range to fit into the Auger acquisition.

the power supply board derives a part of the Auger surface detector power and feeds it to the active element of EASIER.

Antenna The antenna chosen for the first setup is a Golden Interstar GI-301SC. These commercial products embed also the amplifier, they are composed of a feed horn antenna and of a Low Noise Block. A picture of the LNBF used for the first setup is shown Fig. 4.3 (left). The receiving part is the metallic cylinder, a wave guide, it is used to collect the electromagnetic waves from the free space. The dimensions of the cylinder set the frequency band. The radiator itself is placed at the bottom of the waveguide an is a quarter wave monopole antenna. The signal collected is fed to the LNB. It is first amplified by a large factor,

Adaptation board

The adaptation board is designed to transform the signal at the output of the power detector so that it fits the front end input range and covers the required dynamic range. As the variations of the mean noise power and the expected signal are uncertain, it was chosen to cover 20 dB in power and we foresaw an adjustable voltage o↵set. The main functionalities of the EASIER board are an amplification with a fixed gain and the addition of an adjustable voltage o↵set controlled by a variable resistance. The electronic circuit is shown Fig. 4.5. The gain is set by the ratio R3/R2 = 8.2, the o↵set is taken from a stable voltage (M8) and is modified with the adjustable resistor P01. The sum of the amplified signal and the o↵set are then divided by a voltage divider

V out = (R coax /(R4 + R coax )) • V in . As the output impedance is R coax = 50 ⌦ = R 4
, the signal is divided by 2 and the final amplification factor is -4.1.

Power supply board

The power supply board is designed to distribute the power from the SD TPCB (Tank Power Control Board) to the active elements of EASIER. The voltage Detector developments and sensitivity in microwave band 4.1 Detector developments plastic pipe with one side driven in the ground and the antenna attached at the other side with the main lobe pointing to the zenith. Before the installation in the fields we tested the operation of the detector at several stages of the electronics chain: recorded a spectrum with a spectrum analyzer at the output of the antenna measured the voltage after the power detector, and after the adaptation board with a portable oscilloscope recorded FADC traces after the whole acquisition chain, i.e. when the detector is in place and connected to the SD electronics EASIER detectors operate in slave mode with respect to the SD station and thus traces are recorded only when a T3 trigger is issued. The T3 trigger are issued only a few times per day because it requires a coincidence between three SD detectors. To be able to test the complete chain of detection during the installation, without waiting for the data production, a dedicated software was developed. It is a modified version of the local trigger that is uploaded in the control board of the SD station and records the FADC traces when a T2 (a local trigger with a 20 Hz rate) is issued. The first step in the installation is to test the integration of the mechanical and electronic setup with the tank. We performed this first test on the tank Jamie next to the assembly building in Malargüe. We detected strong pulses with a power larger than 10 dB above the noise level shown in Fig. 4.7 (left) with a large rate. To understand the origin of these pulses we made several measurements: we supplied the electronics with a fixed power supply (and not the power supply board): we still observed some pulses.

[GHz] ν 2.
) The pulses don't arise from a radiation of the power supply.

We disconnected the antenna : the signal was then really di↵erent but we still observed some pulses.

) The pulses may arise from a bad ground isolation, i.e. if a transient signal is captured by the metallic part of a circuit element like the power detector, and if this part is not well linked to the ground, then a signal can appear.

Detector developments

Detector developments and sensitivity in microwave band we recorded spectra of the antenna inside the assembly building that exhibits lots of peaks at various frequencies (cf. ) the noise in the environment of the assembly building is important and transient pulses may come from electronic devices emitting at these frequencies, or communication link.

We decided to link the electrical ground of the power detector to the ground of the power supply board. We also tapped the electronics elements to the box with conductor tape to insure a continuity of ground. With this shielding, the pulses remained frequent. We concluded that their origin can be caused by transient noise from the human activity. We have decided to test if in the pampa the noise would disappear with the first complete installation.

We prepared eight sets ready to install (seven to be installed and one spare). The first installation in the fields was carried out the 15 th of April on the tank Paloma. The process for the installation is in four steps:

1. mechanics installation: the plastic pole with the antenna at its top is driven into the ground and tied to the tank. The electronic box is placed on the SD electronic box. 2. spectrum acquisition: we recorded spectra with the spectrum analyser on peak mode to check if the place is noiseless. The superposition of spectra in Fig. 4.9 do not show the peaks as it was observed in the previous tests.

3. noise level measurement: the noise level is measured after the power detector to have an absolute reference of the noise.

4. o↵set adjustment: the voltage after the EASIER board is measured and the o↵set is adjusted to -1 V the middle of the input dynamic range of SD FADC. . check of the complete installation: FADC traces are recorded on the UB in order to have a final calibration between the noise level and the mean level in ADC counts.

In the next three days, the other six antennas were installed following the same process. The spectra taken of each antenna at the installation in RMS mode are shown in Fig. 4.9.

First data

Monitoring The first setup has been running in a stable way up to now for more than two years. In the first months a specific trigger, recording random data every 10 or 20 minutes, was set to be able to check the trace itself rather than just the mean parameters supplied by the SD monitoring. A typical radio trace of background noise is represented in ADC counts First GHz signal observed On the 30th of June 2011 at 3:17 o'clock an air shower with an energy of (13.9 ± 1.3) EeV and a zenith angle of (29.7 ±0.3) degrees has triggered the surface detector. The impact point on ground, (easting, northing) = (465012 ± 42, 6077615 ± 50) m, is well contained within the GHz hexagon. Los Leones was shut down at the time of this event, due to strong wind. The footprint on the array and the reconstructed lateral distribution function are illustrated in Fig. 4.12. Nene was the station closest to the shower axis at a distance of (136 ± 40) m.The uncertainty on the distance of the stations to the shower axis gives a large uncertainty on the estimation of the expected GHz signal. The recorded traces for Nene from the low gain of the PMTs together with the recorded GHz signal are illustrated in Fig. 4.12. There is a clear time coincidence between the GHz signal and the signal produced by the air-shower particles. The GHz signal is up to two bins in advance of the PMT signal, corresponding to a time advance of 25 to 50 ns. The radio signal is very likely from the air shower origin and not a noise coming from the tank for two main reasons:

the radio signal appears before the signal of particle in the FADC trace. The GHz signal is up to two bins in advance of the PMT signal, corresponding to a time delay of 25 to 50 ns. The transit time of a single photo-electron in a EMI9350 8" tubes (slightly smaller than SD ones) is 70 ns with a dispersion of about 7 ns [93]. We expect a larger delay in the Auger PMTs. We measured the response time of the mini-circuit power detector to be about 35 ns. Assuming that the amplifier chains and cables introduce roughly the same time delay in both systems we obtain an expected time delay of the PMT pulse w.r.t. the GHz pulse of at least 35 ns.

we checked on other SD events that the particle signal was not related to the radio signal. The amount of light in the water Cherenkov detectors and thus the intensity in the PMT and the cable that follow can be excluded as an origin of the microwave signal observed.

Detector developments and sensitivity in microwave band

Detector developments x [km]

-20 -18 -16 -14 -12 -10 -8 -6 y [km] - The recorded signal is the first detection of an air shower emission in the C-band. The interpretation on the origin of the emission is di cult because the distance from the antenna to the shower axis is small. The observed pulse could arise from an isotropic signal enhanced by time compression or from a coherent signal as observed in the VHF band. For a more detailed discussion, see chapter 5. To confirm this detection, and to characterize the signal observed, we decided to extend the EASIER GHz array to 61 units. The system being mainly of commercial origin, and rather inexpensive, the assembling of 60 more units was made in less than six months.

EASIER61

The extension of the EASIER array was carried out around one year after the first installation, in April 2012. 54 new detectors were installed with an improved mechanical integration. The first seven detectors remained unchanged apart from change in the attachment to the tank. The times of deployment are given in Appendix B.

Setup In the EASIER61 setup, just a few changes with respect to the first hexagon configuration have been made and we will describe them next. The antenna, a commercial TV satellite LNBF, has the same design but the model is now a WS international ESX241. The power detector underwent an important change. The commercial version of the ZX 47-50 is a power detector with a capacitor at its output. This capacitor is meant to filter the noise at the output of the logarithmic amplifier but makes the power detection less sensitive to short pulses due to a longer rise time. We decided to remove this capacitor on new detectors. The signal electronic board was not changed at all and the power supply board was slightly modified. All the electronic items are now integrated in a metallic box (cf Fig. 4.14), the RF chain, the power detector and the electronic boards. 60 boxes were prepared at LPSC (Grenoble) and checks and calibration were made at LPNHE (Paris).

Location The completed hexagon of 61 detectors covers now an area of 193.5 km 2 . This is the largest radio array in the C-band. In After the installation of a few detectors, we realized that the radio baseline was dependent on the voltage supplied by the SD batteries. The EASIER design did not include a voltage regulator on the power supply board. The SD battery voltage, which is the source of power for EASIER, has daily variations as well as seasonal ones because of the modulation of the power delivered by the solar panels. It can vary from ' 23 V to 30 V. When the voltage at the input of the power supply board varies from the nominal value of 24 V, the -8 V output varies and since the o↵set added to the radio baseline is directly related to this voltage (cf Fig. 4.5) the radio baseline was strongly dependent on the changes of battery voltage. The resulting variation on the radio baseline can lead to saturation of the FADC and to a reduction of the dynamic range available for the microwave signal. We had to find a fast solution and with material available in Argentina. To circumvent this problem, we added a 24 V regulator in each box. This device insures an output voltage of 24 V if the input voltage is larger than V th = 24 + V drop out . The chosen model is LM7824 with a drop out voltage of approximately 1.5 V. This was the model with the smallest V drop out available near Malargüe. An example of the measured regulated voltage is shown Fig. 4.16 (left) and the radio baseline as a function of the input voltage in the same figure (right). The regulated voltage is slightly di↵erent from 24 V and is stable above 26 V while still depending on the battery voltage below. This variation will be corrected for in the calibration procedure.

Electronics calibration

In this section, I will describe the measurements performed in the laboratory in order to calibrate and understand the detector response.

Power detector

The power detector transforms the RF signal into a DC voltage and thus is one of the most important element in the electronic chain. The data-sheet of the power detector Minicircuit ZX47-50 supplied by the constructor shows that the characteristic function is dependent on the signal input frequency as shown in Fig. 4.4 (right) and thus we measured in a first step its response as a function of the frequency. The calibration curves are given for input sine wave at frequencies from 10 to 8000 MHz in steps of 1 GHz. EASIER antenna output is between 950 and 1750 MHz and is approximately a white noise with a flat spectrum. We characterized the power detector in the frequency range of EASIER with the setup shown in Fig. 4.17. First the signal generated is a sine wave at di↵erent frequencies and amplitudes, the signal is split with a power splitter Minicircuit ZFRSC-42 [94] before the power detector and one part, the RF signal, is acquired by the oscilloscope the other is fed to the power detector and then recorded. The oscilloscope is a Lecroy sampling at 5 GHz with a resolution of 8 bits. The RF power is computed on a 50 ⌦ impedance, P RF = V 2 RM S /50. The RF power and the voltage output of the power detector are averaged over the trace of 2 µs. The Then the sine wave signal is replaced by the output of a LNBF, followed by an adjustable attenuator. By this mean, we can characterize the response of the power detector to the same type of noise as in real condition. The calibration curves of one power detector for the noise input are represented by the black triangles in Fig. 4.18 . The calibration curve for an input sine wave at 1 GHz and for a noise waveform input can be described by: sine at 1 GHz: V PD = 0.0244 • P dBm + 0.789 V (4.2.1) noise waveform: V PD = 0.0234

• P dBm + 0.877 V (4.2.2)
The slope is slightly di↵erent and the intercept di↵ers by about 100 mV. The calibration of the rest of the electronics was mainly performed with sine waveform, whereas the physical signal detected by the antenna is a noise waveform. We will account for the di↵erent calibration curves in the next paragraph.

Power detector + EASIER board

The output of the electronic chain of EASIER is a linear function of the logarithm of the input power. Thus to characterize this transformation we measured the slope defined in Eq. 2.3.5 and the o↵set that sets an absolute scale. The slope of the EASIER board is set with the electronics board gain and was measured in laboratory with sine wave input. The o↵set is adjustable and was first set in laboratory and then shifted during the installation to accomodate the baseline to the right level in the input dynamic range of Auger electronics. First setup All the power detectors of the first setup were tested. A calibration curve is given in Fig. 4.19 at three di↵erent frequencies: 950, 1350, 1750 MHz. The mean fitted slope of the eight tested power detectors (seven installed + one spare) at the same three frequencies is found to be S PD = 0.0245 V/dB. One complete set of electronics was calibrated, the calibration curve of the power detector and the EASIER board are shown in Fig. 4.19. The voltage o↵set is set so that the output of the EASIER board is -1 V for an input power of -30 dBm at 1350 MHz. Taking the Eq. 4.2.1 we can then retrieve the transformation of the EASIER board: at 1 GHz and P in = -30 dBm, V PD = 1.521 V and V EB = -1 V (4.2.3) then the calibration formula for the EASIER board only is:

V EB = 4.1 • V PD + 5.23 V (4.2.4)
If the input signal is a noise waveform, then V P D is computed with Eq. 4.2.2. During the installation, the voltage o↵set was shifted in order to place the noise level at the center of the dynamic range (cf. section 4.1). To obtain a final calibration we have to account for this shift. The absolute power at the output of the antenna is measured with the power detector and calculated with the calibration curve Eq. 4.2.2 for a noise waveform. Then after the shift of the baseline at the center of the dynamic range of the SD FADC, we recorded FADC traces that give us the level of the baseline in ADC counts. The measured power detector voltage, the deduced power and the final level of the baseline are given in Table 4.1.

Accounting for the Auger Front End electronics, i.e. a gain of 1/2 and a sampling in a 10 bits FADC, the relation between ADC and input power is :

#ADC = 0. Second setup The calibration of the second setup is more complicated because it depends on the voltage supplied by the battery of the SD. We saw in section 4.1 that the baseline of EASIER electronics is dependent of this voltage. A correct description of the baseline has to account the time dependence of the battery voltage. We first describe the calibration we performed in laboratory and then we explain how we recover the power out of the final trace. The electronics box integrates the whole chain, so its input is suited to the impedance of the LNBF output, a F connector on 75 ⌦ impedance. In addition, in the same coaxial cable, the DC voltage to supply the LNBF is also transmitted. The signal generator used to perform the calibration has an output impedance of 50 ⌦ and can be damaged by the DC voltage transmitted through the cable. Thus, we connected an impedance adapter between the signal generator and the box, and to cut the DC component a cable with a capacitor was used. The loss induced by these additional stages is taken into account in the following calibration. The purpose of the calibration is to check the slope of the EASIER and to set the o↵set voltage to make correspond the input power to the wanted output voltage. For each box we set the o↵set voltage so that the middle of the Auger dynamic range (V EB = 1 V) corresponds to an input power of -28 dBm, at a frequency of 1 GHz. We measured the output voltage for three di↵erent input powers: -18 dBm, -30 dBm and -38 dBm. The calibration curves of the 61 boxes are shown in Fig. 4.20 (left). The distribution of the measured slopes is shown in Fig. 4.20 (right), the average slope is found to be S = (0.101 ± 0.001)V/dB. The final calibration of the second setup di↵ers from the first setup, Eq. 4.2.4, only by the o↵set voltage:

V EB = 4. To recover the original output of the EASIER board, we need to add a correction that will depend on the input supplied voltage :

if V input > V th : V corr+ = S • (V reg 24V ) if V input < V th : V corr = V corr+ + S • (V input V th )
The response as a function of input supplied voltage was measured for each electronic set.

A table with the parameters V th , V reg and S is reported in Appendix B. In addition, the o↵set set in laboratory calibration was shifted by V shift = 600 mV. So at the end the relation between ADC counts and radio power is :

#ADC = 511.5

✓ ADC V ◆ • V 0 EB = 511.5 • (V EB + V corr ) (4.2.9)
where V EB is the voltage calibrated in laboratory (cf Eq. 4.2.8) and V corr = V corr+ (or V corr )+ V shift . To summarize, to transform the number of ADC counts into a power trace we use equations 4.2.2, 4.2.8 and 4.2.9:

P dBm = #ADC 511.5 ⇥ 0.096 1.44 V + V corr 0.096 . (4.2.10)
This power is the result of the background noise amplified first by the antenna gain, then by the LNB gain and attenuated by the adapter 75-50⌦. In order to obtain the power received by the antenna, the LNBF gain has to be accounted for. We do not have a complete characterization of the di↵erent LNBFs. As the gain of these detectors can vary by a few dB we will mainly use an estimation of the power relatively to the power of the baseline P BL .

The measured power is then:

P measured [dBm] = P BL [dBm] + #ADC 511.5 • 0.096 (4.2.11)
Detector developments and sensitivity in microwave band

Detector Sensitivity

The factor one half is needed because the black body intensity contains all the polarizations whereas the antenna selects just one. Using the relation between the e↵ective area and the gain (A e↵ = Gc 2 4⇡⌫ 2 ) and the property of the gain for a loss less antenna:

Z ⇡ ✓=0 Z 2⇡ =0 G(✓, ) • sin(✓)d✓d = Z ⇡ ✓=0 Z 2⇡ =0 G max • g(✓, ) • sin(✓)d✓d = 4⇡ (4.3.6)
where g(✓, ) is the gain relative to the maximum gain of the antenna, we can express the antenna temperature:

T ant = 1 ⌦ Z ⇡ ✓=0 Z 2⇡ =0 T B (✓, ) • g(✓, ) • sin(✓)d✓d (4.3.7) with ⌦ = R ⇡ ✓=0 R 2⇡ =0 g(✓, )
• sin(✓)d✓d The total power received by the antenna is then:

P ant = k B T ant ⌫ (4.3.8)
Because the brightness temperature of the ground is large, back-lobes have to be well controlled to keep the antenna temperature as low as possible.

Electronics temperature Another contribution of noise arises from the amplification electronics. If the spectral power of noise added by the electronics is N a , the gain of the device G and the bandwidth ⌫, one can define the electronics noise temperature as :

T e = N a k B G ⌫ (4.3.9)
As noted in the chapter 2, if the gain of the first stage of amplification is large enough, the temperature of the following stages can be neglected.

Minimal flux detectable

To estimate finally the minimum flux detectable by our system we compute the flux F signal required to equate the noise fluctuations:

P signal = F signal • A e↵ (✓, ) • G LNB • ⌫ = < P noise > p ⌧ • ⌫ = k B • T sys • G LNB • ⌫ p ⌧ • ⌫ (4.3.10)
then

F signal = k B • T sys A e↵ (✓, ) • p ⌧ • ⌫ (4.3.11)
with T sys = T ant + T e (4.3.12)

The two main parameters we need to estimate are the e↵ective area and the system temperature. We present now a set of measurements performed on this purpose.

Sensitivity measurements

Power pattern and e↵ective area

The power pattern provides the relative gain, g, of the antenna as a function of the angle. If the antenna is sensitive to very large zenith angle ✓, thus detecting the thermal noise from the ground, the antenna temperature is increased significantly. Also the e↵ective area A e↵ (✓, ) is directly linked to the power pattern through Eq. 2. The maximum gain of the antenna can be calculated using relation 4.3.6. We find for frequencies from 3.4 to 4.2 GHz a mean gain of G max = 8.75 dB. From the maximum gain the angular e↵ective area is calculated as follows:

A ef f (✓, ) = 2 • G max • g(✓, ) 4⇡ (4.

Noise temperature measurements

Noise temperature measurement of a Device Under Test (DUT) are usually performed using the Y-factor method [96]. This method is based on the measurement of the response of a DUT to two known noise power references. Their comparison allows us to retrieve the noise added by the DUT. The Y-factor is the ratio P hot P cold , where hot and cold refer to higher and lower noise power input. The temperature added by the DUT is then:

Y = P hot P cold = T hot + T DUT T cold + T DUT ) T DUT = T hot Y • T cold Y 1 (4.3.14)
This method is particularly suited for electronic devices with no loss between the noise source and the DUT. In case of losses of a factor ↵ between the source of noise and the DUT, Eq. 4.3.14 becomes :

T DUT = ↵ • T hot Y • T cold Y 1 (4.3.15)
Following this method, several measurements were undertaken.

Spectrum comparison

We apply the Y-factor method to measure the noise induced by the amplification part of the LNBF. The two noise references are thermal noise received by the antenna when looking either at object at room temperature (T hot ) either looking at the sky (T cold ). The measurement of hot temperature is performed recording a spectrum when the antenna points toward a microwave absorber. This material absorbs the radiation around it and reemits it as a thermal emission at its physical temperature. Based on Eq. 4.3.7, the antenna temperature when the brightness temperature T B is constant over the antenna pattern yields to an antenna temperature of T B . Then T hot = 300 K. The measurement of the low temperature was performed during the installation in the fields. We recorded a spectrum with the antenna in its definitive position, i.e. pointing toward the sky. T cold is computed with Eq. 4. profile taken from reference [START_REF] Otoshi | Noise Temperature Theory and Applications for Deep Space Communications Antenna Systems[END_REF] is a parameterization at a frequency ⌫ = 2.295 GHz, close to the one we operate and represented in red in Fig. 4.23 (right). After integration over the solid angle at frequencies from 3.4 to 4.2 GHz, the mean temperature is found to be T cold = 7.5 K. The comparison of the spectra at hot and cold temperature, shown in Fig. 4.23 is a measure of Y-factor. We considered a lossless antenna, however, because of the polarization mismatch between the unpolarized thermal noise and the linear antenna we used Eq. 4.3.15 with ↵ = 0.5.

For instance, we show in Fig. 4.24 the temperature for one antenna in the lower panel. The gain is deduced from the total power and the temperature, it is illustrated in the upper panel. This measurement was performed for 28 of the 54 ESX241 antennas installed (second setup).

Detector developments and sensitivity in microwave band The distribution of temperature and gain in Fig. 4.25 show a mean temperature of LNB of 23±2 K and a mean gain of 58±1 dB. The total noise temperature, the sum of the antenna temperature and the LNB temperature is then T sys = 30 K for the antenna ESX241.

KIT measurements As mentioned before, other experiments with the same goal as EASIER and using the same type of equipment have been operating. Among them, CROME is an experiment in Karlsruhe at the KASCADE Grande site. They developed a dedicated setup to measure the LNB noise temperature [START_REF] Engel | [END_REF]. It is also based on the Y-factor method, but the LNBF are pointing into a cryostat filled with absorber on its inner sides. The hot reference temperature is obtained when the absorber is at room temperature and the cold temperature when the cryostat is filled with Liquid Nitrogen (LN2). The CROME collaboration measured the noise temperature of LNBF GI301SC and ESX241. For the LNBF GI301SC, the temperature measured was really unstable and they found a mean temperature of 91 K but ranging from 40 K to 180 K. ESX241 LNBF were more stable and a LNB temperature of around 25 K was found and is compatible with the 23 K found with room/sky spectrum comparison presented before.

LNB noise measurements with a noise meter A third method to measure the noise temperature of the LNB was performed. The amplification stage of the LNBF ESX241 installed for EASIER61 exists without the feed horn. The LNB DMX211 is only the electronics part and a waveguide as shown in Fig. 4.26 (left). To measure the noise temperature of this part we had available a spectrum analyzer with a noise meter function (Agilent PXA N9030A) and a coaxial noise source (Agilent N4002A). The spectrum analyzer switches automatically on and o↵ the noise source in order to feed the DUT with P hot and P cold . To connect the coaxial noise source to the LNB we used an adapter from a coaxial line to a waveguide. The setup is shown in Fig. 4.26 (right). The resulting noise temperature and the gain as a function of frequency are shown in Fig. 4.27. The mean noise temperature is found to be 201 ± 30 K, i.e. a factor of 10 larger than the one found with the other methods. The reason of this discrepancy is not understood. However the gain is also much lower than the announced one and that measured with other methods. As a matter of fact, the gain of the LNB alone (not taking into account the antenna gain) is expected to be around 60 dB. It is a factor 10 larger the second. This signal is attenuated by 12 dB and emitted by a spiral antenna circularly polarized whose pattern is known from data sheet at 3 and 4 GHz (see Fig. 4.29). The power emitted by the source is:

P emitted = ( P (⌫) | {z } oscillator 12 dB | {z } attenuator + G spi (✓) | {z } spiral antenna gain ) dBm ± ✏ spi ± ✏ V CO
.The function P (⌫) retrieved from the oscillator data sheet is shown in Fig. 4.29 and has a systematic uncertainty of ✏ V CO = 1 dB. The gain of the spiral antenna, G spi , is taken as the average gain at 3 and 4 GHz, its dependence in zenith angle is approximated by a quadratic polynomial. An uncertainty ✏ spi = 0.73 dB, taken as the standard deviation of the di↵erence between curves and the average, is added to the emitted power. Knowing the distance between the octocopter and the receiving antenna, R, the incoming flux at the receiver becomes: where calib = 0.25 dB for ADC < 210 and calib = 0.1 dB for ADC > 210.

F = 1 4⇡R

Data analysis

The data set is composed of two di↵erent runs corresponding to two di↵erent parameter scans: a vertical scan in distance and frequency (Run 1), a scan in frequency at di↵erent zenith angle (Run 2).

Data selection

The octocopter flew at several distances from the receiving antenna and covered a span of 300 MHz, thus covering di↵erent values of gain of the antenna. Given that the noise is at around 450 ADC counts, the dynamic range for the signal is less than 9 dB. Thus for some distances and frequencies, the received flux was larger than the dynamic range of the receiver leading to saturated traces. We define a trace as saturated if more than 10% of the 768 bins are out of the ADC range and for each distance for run 1 (100 m, 150 m, 200 m) or zenith angle for run 2, we select the range of frequency for which there is no saturated trace. For run From ADC counts to signal power During the calibration a sine signal from the source is added to the noise always present produced by the environment (sky + ground) and the electronics. To extract from the traces the contribution from the source, we will first estimate the noise from traces when the octocopter is not emitting and then we will use the relation 4.3.18 to estimate the signal to noise ratio.

Noise power

The noise power is calculated averaging over 7 traces recorded when the octocopter was not emitting and amounts to < ADC noise >= 452.6 ± 1.3ADC where the uncertainty is the dispersion of the mean over the 7 traces recorded. Using the calibration for the noise waveform, this gives :

P noise = 25.6 dBm ± 0.1 dB (4.3.19)
Where an uncertainty of 0.1 dB is added on the power estimation to account for the uncertainty on the electronic calibration.

Sine power To obtain the sine power coming from the source, we average the trace in ADC counts, and then we estimate the parameter A dB with relation 4.3.18:

| ADC| = | < ADC > < ADC > noise | = 4.1 • 511.5 • | V P D |
The linear signal to noise ratio is given by : SN R lin = 10

Results

The observed power is the sum of the noise and the signal sent by the source :

P obs = P signal + P noise = P emitted 4⇡R 2 • A e↵ (✓, ⌫) • G LNB (⌫) + k B • Z ⌫ G LNB (⌫) • T sys (⌫) d⌫. (4.3.22)
where A e↵ is the e↵ective area of the antenna, G LNB is the gain of the amplifier, and T sys the system temperature defined before. The octocopter measurements can provide us the first part of Eq 4.3.22, while the second part can be extracted by the frequency spectrum in Run 1: distance scan The 3 distances that covered the octocopter during run 1 allow us to test the distance dependency and check the consistency of the method to extract the signal. Figure 4.34 shows the signal power observed as a function of distance at di↵erent frequencies. The plain curves are fits of power law k 1 /R k During Run 1 we scanned the frequency range of 300 MHz at di↵erent distances, at a zenith angle close to 0. The signal power recorded is highly dependent on frequency, around a factor 10 in the range explored (see Fig 4.33). This behavior is the combined e↵ect of the frequency dependency of the e↵ective area, the LNB gain and the power emitted by the source.

Once corrected with the expected flux at the receiver (Fig 4 .35), we can extract the product

A e↵ (✓ = 0, ⌫)•G LNB (⌫) = P sine F ⌘ G tot (
⌫) which is the global factor to transform the incoming flux for a zenithal angle ' 0 into a recorded power. The uncertainties on G tot come from the measurement itself and has a additional systematic uncertainty from the flux emitted. In the range of frequency scanned, G tot (⌫) can be fitted by an exponential function. The mean G tot is retrieved out of the integration of the fitted function over the frequency range : The errors on the fit coe cients are propagated on the mean. We obtain:

< G tot > ⌫ = 1 ⌫ Z 3.
< G tot > ⌫ = 2499 ± 285(stat) ± 1225(sys) (4.3.24)
Inferred sensitivity The estimate of the sensitivity is given as the constant flux density, f , required over a frequency band to give an output equal to the noise in this band. We estimate the noise in the band scanned with the octocopter, [ The flux density that yield a power equivalent to the noise in this band is found to be :

f = 4.02 • 10 19 ± 11% ± 49% [W m 2 Hz 1 ] (4.3.27)
For comparison, the sun flux density is around 100 times lower than this value. Furthermore, the flux density estimated in [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF] for an air shower of 3.36 • 10 17 eV at 10 km is 2.8 ⇥ 10 24 W m 2 Hz 1 . A rough estimate for an air shower of 3 ⇥ 10 19 eV at 500 m yields to a flux of ⇠ 10 19 W m 2 Hz 1 accounting for a linear scaling of the flux with energy or a factor 100 larger in case of a quadratic scaling. The flux sensitivity can also be converted in noise temperature according the following equation:

T sys = f • A ef f 2k B (4.3.28)
Detector developments and sensitivity in microwave band

Detector Sensitivity

[degree] θ where the factor two comes from the polarization mismatch between the circularly polarized source and the linearly polarized receiver. We find a system temperature of T sys ' 51 K. This result is consistent with the noise temperature found before with other methods.

Run 2 : Angular scan During Run 2 we scanned in zenith angle. We can then reconstruct the power pattern of the receiving antenna. We determine the relative gain with respect to the gain at the zenith by dividing the factor G tot (✓, ⌫) by the fitted function of G tot (✓ = 0, ⌫). In Fig 4 .36 it is illustrated the dependency on zenith angle of the e↵ective area for 4 ranges in frequency. The black dots represent the measurements and the colored plain circles the mean in angle bins. The error bars are the dispersion in the bin. From 3.75 GHz to 3.95 GHz the gain is rather constant until 30 -40 degrees, and the -3 dB opening angle is around 50 degrees. This number is in good agreement with pattern measurements. At lower frequency between 3.65 GHz and 3.75 GHz the gain seems to fall faster with the elevation angle and does not match the measurements. But a large uncertainty of 2 dB, given the spread of the points is present.

Outlook on the octocopter measurements

The set of measurements done with the octocopter allowed us to test and calibrate the whole acquisition chain of the EASIER detector. Two di↵erent sets of data, Run1 with a source at fixed angle (✓ = 0) and variable distances and Run2 at di↵erent zenith angles allowed us to scan various parameters. The product of the e↵ective area times the LNB gain at ✓ = 0 was measured in the band 3.65 -3.95 GHz. The comparison of this parameter at di↵erent angles

Detector Sensitivity

Detector developments and sensitivity in microwave band showed an opening angle at -3 dB of around 50 degrees for most of the frequencies scanned in agreement with antenna simulation. The equivalent flux of noise at ✓ = 0 was determined to be 4.02 • 10 19 W/m 2 /Hz with an uncertainty of 11% and a systematic error of 49%. The uncertainties of these measurements are large due to the limited knowledge on the flux emitted by the source. These measurements could be improved by scanning the whole frequency band of the receiver or emitting in a wide spectrum a noise signal. The described method can be a complete method of an on site calibration and could give a precise measurement of the system sensitivity at di↵erent angle with such improvements.

Chapter 5

Data analysis in microwave band

In the microwave band, EASIER is an array of 61 radio detectors. Seven have been taking data since April 2011, and 54 since April 2012. Its purpose is the observation of the isotropic radiation from air showers produced by Molecular Bremsstrahlung Radiation (MBR). The MBR has been observed in one beam experiment in SLAC in 2008 but the observation in EAS experiments has not been established.

In the previous chapter we reported the characteristics of the EASIER detectors, in particular their ability to detect the MBR emission if the parameters observed in beam are scaled to EAS. However, in this frequency range, other types of emission are likely to be detected. Indeed, the mechanism responsible for the detection of air shower in the VHF band, namely a geomagnetic e↵ect on the shower particles and a charge separation could extend at microwave frequencies.

Emission mechanisms in the microwave band

Data analysis in microwave band

Emission mechanisms in the microwave band

Molecular Bremsstrahlung The R&D for experiments measuring EAS in the microwave band were triggered by the results of a test beam experiment in SLAC. These measurements reported the detection in the frequency band [1.5 -6 ]GHz of a continuum emission produced by the plasma induced by the passage of a shower in an anechoic chamber. A maximum flux of F ref = 4 ⇥ 10 16 W /m 2 /Hz was observed at a distance d = 0.5 m, from the showers produced by an electron beam of 2.8⇥10 10 eV. Knowing the beam current, the energy of the equivalent shower is estimated to E ref = 3.36 ⇥ 10 17 eV. Then to compute the corresponding flux for an air shower one introduces the following relation:

F (t) = F ref • • ⇢ ⇢ 0 • ✓ d R(t) ◆ 2 • ✓ N (t) N ref ◆ ↵ (5.1.1)
where ⇢ and ⇢ 0 are the density of air at the point of emission and at see level where the beam test was performed. The expected emission is also scaled by the number of particles N (t) in an air shower with respect to the number of particles at the maximum development of an EAS with the energy E ref .

In the beam experiment, the scaling of the flux was observed to increase quadratically with the beam energy, which is proportional to the number of particles. This was explained by a possible coherent e↵ect in the plasma emission. This coherence is represented by the parameter ↵. A value of ↵ = 2 is expected in case of a full coherence of the emission and ↵ = 1 if the emission is non coherent. is the ratio of the distances over which the emission occurs in the anechoic chamber of the beam experiment and in air shower, it is taken as = 4.62 in [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF].

Coherent radiation It was recently pointed out that the mechanism responsible for air shower radiation in the VHF band is likely to extend to higher frequencies [START_REF] Huege | Simulating radio emission from air showers with CoREAS[END_REF]. The mechanism of coherent emission of shower particles due to the geomagnetic e↵ect and a charge excess was first studied and expected in the VHF band because the shower front thickness, of the order of 1 m, corresponds to frequencies below 300 MHz. But recent simulation show that the flux produced by this emission can be important at short distance from the shower axis up to the observation band of EASIER. The two components (North-South and East-West) of the simulated electric field produced by an air shower with an energy of 10 17 eV is shown in Fig. 5.1. The di↵erence of amplitude between the two components is due to the geomagnetic e↵ect. The order of magnitude of the flux from this emission is found to be of the order of tens of µV/m/MHz at 100 m from the shower axis. An electric field spectral density of 0.1 µV/m/MHz represents a power flux of 1.3 ⇥ 10 10 W/m 2 once integrated on the bandwidth of EASIER. By comparison, a rough estimate of the MBR flux with equation 5.1.1 yields a power flux around 3 orders of magnitude lower.

The MBR is expected to be produced by the low energy electrons of the plasma induced by the shower front. Thus it is expected to be emitted isotropically. In contrast, a coherent emission produced by the relativistic particles of the shower produces a radiation pattern beamed in the forward direction and is expected to be dominant at short distance from the shower axis, and decrease with distance much rapidly than a isotropic emission as shown in Fig. 5.1. In addition, the MBR is expected to be unpolarized whereas the emission produced

Event search

Data analysis in microwave band

Event search

We select the Auger data until June 2013. On this data set, we apply the usual quality cut insuring a good reconstruction of the SD event: we ask that the tank with the highest particle signal is surrounded by six active tanks at the moment of the event. In addition we select the events with zenith angle smaller than 60 and events tagged as lightning are also removed. We apply also a selection on the radio trace. We reject the station if the radio trace has saturated bins, caused by the dependence of the baseline with the supply voltage (see chapter 4). The total number of traces available is 72465, out of which 28787 are from EAS above E = 10 18 eV and 842 above E = 10 19 eV. The raw radio trace in ADC counts is in logarithmic scale because of the power detector operation. We transformed it first in absolute power in dBm unit according to Eq. 4.2.6, it is then exponentiated to retrieve the microwave power in Watt. As the gain from one antenna to the other is di↵erent and is not known with precision we cannot obtain an absolute power scale. To compare the data of all the antennas, we transform the absolute power trace into a trace relative to its mean and its standard deviation. For each point we calculate the relative power:

P rel = P abs mean standard deviation (5.2.1)
The trace obtained is thus centered around zero and normalized with the fluctuations of the trace.

Event search The shape, the arrival time and the amplitude of the expected radio signal depend on the position of the antenna with respect to the shower axis. At short distances from the core we expect short pulses approximately in coincidence with the particle arrival time. Fig. 5.2 (left) represents the maximum of each radio trace as a function of the time di↵erence between the start time of the particle signal and the radio maximum time. Three points emerge from the bulk of events1 . They have a maximum of more than ten times the trace fluctuations and are located in the trace one or two bins (25 to 50 ns) before the start time of the particle signal. These three events are also visible in Fig. 5.2 (right) well beyond the distribution of the other maxima. The characteristics of these three events are gathered in Table . 5.1 and their radio traces in ADC counts and after linearization are shown in Fig. 5.3, 5.4 and 5.5. For these three events the distance from the antenna to the shower axis is less than 300 m and the antenna is oriented in the East West polarization direction. Two events have an energy larger than 10 On the origin of the radio signals The surface detector electronics does not operate at microwave frequencies. However, other processes inducing pulse in the radio trace can be imagined. For instance the acceleration of electrons in the phototubes of the surface detector or the current draw associated in cables which occur at the event time. We checked if the radio signals observed are likely to be spurious by comparing the radio maximum signal with the particle signal in VEM in Fig. 5.6. If the radio signal were produced by the tank at the moment of the event, we would expect a correlation between the radio maximum and the particle signal. Fig. 5.6 show no correlation, excluding the tank elements as a source of spurious events. If the signals observed seem to originate from air shower, the mechanism producing the emission is still unknown. The events characteristics, a short distance from the antenna to shower axis, and short pulse favors a beamed emission. Moreover, the East-West orientation of the antenna that detected the radio signals points to a geomagnetic origin. However, the statistics gathered up to now doesn't allow us to draw firm conclusion. Events 12046376 and 20830870 have an energy above 10 19 eV, thus we expect them to produce MBR with a su cient intensity to be detected. Event 21050180, on the other hand, is a much lower energy event and the radio pulse is of the same order of magnitude than the two others. Moreover, the distribution in Fig. 5.2 is not continuous. The three events are largely above the bulk of events. This could indicate that for these three events, we reached a specific regime. For instance, the coherent emission is known to be maximum at the Cherenkov angle around the shower axis like in the VHF band. And in case of an isotropic emission the radio pulse is also greatly enhanced at the Cherenkov angle simply because, depending on the geometric configuration, the emission of di↵erent parts of the shower are detected at the same time. the speed c/n, where n is the refractive index of air, whereas the shower front is assumed to traverse the atmosphere at the speed of light. Because of the delay thus induced and depending on the shower geometry, di↵erent parts of the shower can be detected at the same time, enhancing the signal in amplitude and compressing it in time. To account for this propagation e↵ect, the time of propagation from the emission point to the antenna is calculated at each height of the shower development. For two consecutive steps we compute ⌧ up and ⌧ down , as indicated on the sketch in Fig. 5.9 (left) with :

Microwave signal simulation

Data analysis in microwave band

⌧ up = 1 c sin ↵up R hup hantenna n(h 0 ) dh 0 and ⌧ down = 1 c sin ↵ down R h down hantenna n(h 0 ) dh 0
The time compression is defined as the ratio of the di↵erence ⌧ = |⌧ up (⌧ step + ⌧ down )| with the step time along the shower ⌧ step = L step /c, where L step is 10 m. In the simple case of a vertical shower with a refractive index of n = 1, all the emitted radiation along the shower is detected at the same time for an observer underneath the shower. For an air index di↵erent from n = 1, the radiation along the shower sum up and give rise to a compression in time of the signal received, at a certain angle. The Cherenkov angle depends on the refractive air index as : cos(✓ Ch ) = 1/n. We take a realistic air index decreasing exponentially with the height. The refractivity defined as N = 10 6 (n-1) is parameterized as follow:

N = 285 • exp( h/5.992 ⇥ 10 3 ) + 25 (5.3.2)
The resulting air index is shown in Fig. 5.9 (right). To illustrate this phenomenon we show in Fig. 5.10 the time compression for di↵erent refractive air index as a function of the angle between the emission point and the receiver, called ✓ shower in Fig. 5.9 (left).

For the simulations, the lateral distribution of the particle in the shower front is not taken into account and the emission is simulated as a moving point like source. We mentioned in chapter 2 that under this simplification, the time compression can, in principle, lead to an infinite signal thus non physical. However, because of the finite sampling of the shower in height steps, the signal enhancement cannot be infinite but it is very dependent of the shower sampling when the angle between the emission point and the antenna reaches the Cherenkov angle. The time compression is then overestimated and the resulting trace can be strongly peaked. As an illustration of this e↵ect, we show in Fig. 5.11 the flux as a function of time for simulated vertical showers at a distance of 300 m (left) and 1000 m (right). The Cherenkov peak can be clearly noticed at 300 m. For su ciently large distances, the Cherenkov angle is not observed.

Antenna simulation From the simulated profile, we obtain the flux at the detector and the shape of the signal after the propagation in air. To simulate the antenna in the setup we transform the incoming flux into a power through the e↵ective area A e↵ (✓, ). In addition, the antenna adds a noise component corresponding to the system temperature T sys .

Microwave signal simulation

Data analysis in microwave band

[degree] The relation between the incoming flux and the power at the output of the antenna before the LNB amplification is simply:

P S (t) = F (t) • A e↵ (✓, ) • ⌫ (5.3.3)
Where we take bandwidth ⌫ = 0.8 GHz. The e↵ective area is taken from the measurements described in chapter 4 at the middle frequency of the range of observation, i.e. at 3.8 GHz. The e↵ective area is assumed to be invariant in azimuth. At the zenith, A ef f (✓ = 0) = 3.8 ⇥ 10 3 m 2 and its dependence in zenith angle is represented in Fig. 5.12 (left). The high frequency trace is amplified by the LNB gain, but the signal and the noise are amplified with the same factor G LN B . This part is just a multiplication by a factor G LNB . The power detection is an important part in the setup since the signal is strongly modified at this stage. The high frequency trace is transformed in its power envelope in logarithmic scale. The mean response to a steady signal was already studied in chapter 4 in the electronics calibration section and we present here a method to reproduce the time response of the power detector.

Two power detectors Minicircuit ZX47-50 were tested in laboratory. One of them is equipped with a filtering capacitor like the ones installed in the seven first prototypes, and one has this capacitor removed like the 54 other detectors. We recorded at the same time the high frequency trace at the output of the antenna and the same signal processed by the power detector in the condition illustrated in Fig. 5.14 (left). To produce microwave pulses with time length of the order of a few tens of nanoseconds, we used an electronic lighter. The spark produced was found to emit such short pulse. We show for instance the response of the power detector to a short pulse in Fig. 5.14 (right). Our goal is to reproduce the power detector curve in the bottom part from the high frequency trace shown in the upper part. We found that the power detector response is well reproduced when performing the three following steps:

1. transform the high frequency trace in dBm units 2. convolve the dBm trace with an exponential function: 3. transform the convoluted trace in a voltage according the power detector calibration curve.

P sim = (P dBm ⇤ f )(t) = Z +1 1 P dBm (u) • f (t u) • ✓(u) du (5.3.8)
Step 1 is done by taking for each point: P dBm = 10 • log 10 (P watt /10 3 ). An example of high frequency trace and the resulting dBm trace are shown in the upper panel and the middle left panel of Fig. 5.15. The convolution done in step 2 is done with an exponential function of 500 ns length and sampled with a period of 0.2 ns. The average of the convoluted trace is :

< (P dBm ⇤ f )(t) >=< P dBm > • Z +1 0 f (t) dt (5.3.9)
The convolution function is normalized so that the mean of the convolved trace is the mean of the trace in dBm.

Step 3 is performed using the calibration curve of the power detector to transform the dBm trace into a voltage trace. The calibration of these two power detectors gives the following transformation:

V sim = k 0.023 • P sim (5.3.10)
In order to match the simulated trace and the real one, we tuned several parameters. We let free the intercept k in Eq. 5. exponential function f . To estimate the best suited parameters, we minimize the square of the di↵erence between simulated and real points (↵

2 = P i (V sim [i] V real [i]) 2
). We performed the minimization in two parts of the trace. The part before the pulse (noise part) and the part around the pulse. For the power detector with capacitor we find that an o↵set k = 0.76V and time delay of 19 time bins (3.8 ns) minimize ↵ 2 in the two regions (noisy and pulse).

Then for these parameters, the integration time that minimize ↵ 2 is found to be 39 ns for the noise part and 31 ns for the pulse part as shown in Fig. 5.16. We take the average of these two values, ⌧ capa = 35 ns, as the power detector time constant. An example of superposition of simulated and real traces is shown in Fig. 5.17 with their di↵erence in bottom panel. For the power detector without capacitor, the o↵set is found to be k = 0.74, the time delay of 21 time bins, and an integration time ⌧ = 5 ns is found in both parts (noisy and pulse). On the 20 traces that we recorded and simulated, the distribution of their di↵erence (in Fig. 5. [START_REF] Matthews | A Heitler model of extensive air showers[END_REF] show a bias on the mean smaller than 2 mV for the power detector with capacitor ( 3 mV without) and the standard deviation around 10 mV (and 22 mV without), i.e. less than 0.5 dB (or 1 dB without).

The EASIER board is simulated multiplying by a factor 4.1 the voltage at the output of the power detector and adding an o↵set voltage. The front end simulation accounts for the low pass filtering at a frequency of 20 MHz and the amplifier gain of -0.5. The simulated trace is then sampled in time (each 25ns) and in amplitude (in 1024 bins). Note that the value of the o↵set k in equation Eq. 5.3.10 and the o↵set added by the EASIER board are not important as long as we consider traces relative to the mean. To estimate the validity of the electronics simulations, we performed a complete simulation of a shower with an energy of 3 ⇥ 10 19 eV accounting for di↵erent system temperatures. We compare the signal to noise ratio before and after the electronics processing. The traces represented in Fig. 5.20 and are in good agreement in signal shape and in the value of signal to noise ratio. The relative di↵erence between the maximum before the electronics simulation and after is plotted in Fig. 5.21 as function of the original signal to noise ratio. It shows that the maximum after the electronics simulation is larger than the initial one. This is expected since the electronics simulation add fluctuations and we take always the positive ones when searching for the maximum. We apply the simulation described above to the observed events in order to estimate if these detections can be attributed to an isotropic emission as measured in the SLAC experiment.

Microwave signal simulation

Data analysis in microwave band

For each of the three events we simulated 10 showers of proton primary and 10 showers of iron primary. We compare then the maximum of traces and the time width above half of the maximum of simulated pulse and the real ones. In Fig. 5.22, it is illustrated the superposition of the 10 simulated traces with the real event signal to noise ratio for the three radio events detected. Quantitative results are presented in Table 5.2 for proton primary and in Table 5 This first comparison between the simulated events and their corresponding real trace show a compatibility in terms of amplitude for the event 12036476 but discrepancy in terms of time length. The two other events show a maximum for (F ref , ↵ = 1) lower than the one observed. For the full coherence case, i.e. ↵ = 2, simulations yield a signal to noise ratio too large for the events 12036476 and 20830870, but still unsu cient to explain the event 21050180.

Limits on an isotropic emission

The detection of events only at short distances from the shower axis favors a beamed emission as dominant emission process. The comparisons with simulations in the previous section The reference flux observed in the beam experiment is also depicted with the dashed blue line. This reference flux is excluded for ↵ 1.2. The limits found with MIDAS detector are represented with the red line. The limits found with EASIER are comparable for ↵ close to 1 and exclude a wider range of flux at ↵ 1.3.

Discussion on the limits on MBR

The limits presented above constrain the parameters the MBR emission F ref and ↵. The simulations presented include the microwave signal simulation, its propagation and the main detector e↵ects. The results quoted here are found under the assumptions exposed in section 5.3. The number of events may be overestimated mainly because of the following reasons:

the time compression may be overestimated because the lateral extension of the shower front is not accounted for.

there remains some uncertainties on the system temperature measurements, they may be larger than the one assumed in the simulations.

The limits found are in agreement with the results of other experiments aiming at the MBR detection from EAS (like AMBER, MIDAS, CROME) or in laboratory (AMY and MAYBE). AMBER is a telescope like experiment instrumented with feed horns antenna in C-band 2.3⇥10 16 W/m 2 /Hz to 4.6⇥10 15 W/m 2 /Hz (cf. Eq. 1) for the MIDAS configuration operating at the University of Chicago campus. For each pair of {↵, I f,ref }, events are simulated in discrete bins of primary energies between log 10 E = 17.65 and log 10 E = 20.05 in logarithmic steps of 0.1, sampled from an isotropic distribution. For each energy bin, the simulation is run until 4000 SLTs or 4 ⇥ 10 6 simulated EAS are reached, whichever occurs first. The result is then weighted with the UHECR energy spectrum of [14] to produce a realistic energy spectrum of simulated SLT events. The selection criteria (1) to (6) were applied to the simulated samples, and corresponding number of expected events were derived. For example, for a fully coherent emission (↵ = 2) and a reference power flux I f,ref = I 0 f,ref , we expect, in our 61 days of livetime, greater than 15 EAS candidate events above 2 ⇥ 10 18 eV passing all our search criteria. This is excluded at a greater than 5 level by our null detection result. To cover the full space of {↵, I f,ref }, we used a linear surface interpolation of the grid of simulated samples. The shaded gray region in Fig. 3 is excluded with greater than 95% confidence. We exclude the reference power flux I 0 f,ref as measured by [1], indicated by the solid horizontal line in Fig. 3, over a large range of partial coherence emission hypotheses. An incoherent emission for that reference power flux is not yet excluded by our measurement.

VI. CONCLUSIONS

We reported the results of a search for microwave emission from UHECRs with the MIDAS experiment. No candidate events were found in the 61 days of live time of the measurement, resulting in the strongest limits to date on the power flux and coherence of EAS microwave emission. In particular, we rule out fully quadratic scaling at the power flux value measured by Gorham et al. [1]. This result has implications on the prospects for the microwave detection of UHECRs, indicating a higher detection energy threshold (or the need for a larger antenna) than the one so far considered. Notice that our limits apply to any microwave emission mechanism producing isotropic radiation that can be detected from the side of EAS at large distances, as in the fluorescence detection technique. The time response of the MIDAS electronics and the event search strategy is not optimized for detection of very fast signals that may come from a beamed emission along the shower axis, as potentially observed in preliminary reports of EASIER [7] and CROME [8].

Measurements will continue, with the MIDAS detector being deployed at the Pierre Auger Observatory in Malargüe, Argentina. Operating the MIDAS experiment in coincidence with the Auger Observatory will provide a much greater sensitivity to EAS events over the search reported here, eliminating the need for severe topological and timing cuts on candidate events. In addition, eV, and the parameter characterizes the possible coherence of the emission. The shaded area is excluded with greater than 95% confidence. The horizontal line indicates the reference power flux suggested by laboratory measurements [1]. The projected 95% CL sensitivity after collection of one year of coincident operation data of the MIDAS detector at the Pierre Auger Observatory is represented by the dashed line.

the rural environment of the site is significantly more radio quiet than the urban environment of the University of Chicago campus, increasing overall detector livetime. The projected 95% CL sensitivity after one year of data is collected at the Pierre Auger Observatory is shown as a dashed line in Fig. 3, indicating that exclusion of incoherent emission over a large range of reference fluxes will be achieved. We would like to thank Peter Gorham, Antoine The CROME detector, is composed of a parabolic dish with feed horns at the focus. Unlike MIDAS or AMBER, the dish is oriented towards the zenith thus this setup is sensitive to radiation beamed in forward direction from vertical showers. It is installed at the KASCADE site and operates in coincidence with its air shower surface detector. The CROME collaboration has reported the detection of 30 radio events in the C-band in coincidence with shower of reconstructed energy above 3 ⇥ 10 16 eV [START_REF] Smida | Observation of Polarised Microwave Emission from Cosmic Ray Air Showers[END_REF]. Fig. 5.26 (left) shows two detected events. An interesting feature is the distribution of the shower cores shown in Fig. 5.26 (right) that led to radio events. The events are represented with square and the simulated electric field with CoREAS code for a vertical iron shower of 10 17 eV. This simulation code accounts for both the geomagnetic and the charge excess e↵ect. The shower cores position forms a ring structure with a radius of around 100 m as expected in the simulation. The detected pulses shape and the characteristics of the detected showers indicate a coherent emission beamed around the shower axis. Two beam tests were conducted in order to confirm the results of the SLAC experiment and to characterize further this emission. AMY experiment uses an electron beam accelerated by the same type of linac (Linear particle Event selection -We have analysed all reconstructed events passing the KASCADE-Grande quality cuts measured up to August 10, 2012. From these events, we selected the showers crossing the field of view of at least one CROME receiver (approximately 5.5 showers above 3 ⇥ 10 16 eV per day) for which a cone of half-width of 2°w as assumed.

The expected arrival time of the microwave signal from each air shower was calculated using the reconstructed air shower geometry, accounting for the altitude-dependent refractive index and the measured signal propagation times in the detectors. The typical uncertainty of the signal arrival time due to measurement, reconstruction, and simulation uncertainties is about 50 ns. The strength of a signal in the estimated time window is quantified relative to the mean noise level of each 20 µs trace.

Selecting events with a pulse amplitude of more than 8 dB above the mean trace voltage and energy above 3 ⇥ 10 16 eV we have found 35 showers with a microwave signal. Two of those showers produced a signal above the threshold level in two microwave receivers with the predicted time ordering. The expected number of noise signals above 8 dB is estimated from data by repeating the analysis for shifted time windows and it is found to be 7.1 ± 1.6.

A signal with an amplitude of more than 10 dB, corresponding to more than 5 significance for the observed baseline fluctuations within a 50 ns time window, was 3 measured for 8 events. For the given time interval no noise signal of the same strength is expected.

The time traces of microwave signals measured for two air showers are shown in Fig. 1. The top panel shows the largest signal, 17.7 dB above the noise level, measured with the CROME experiment. The energy of the shower was 2.5 ⇥ 10 17 eV with a zenith angle of 5.6°and a core distance of 120 m to the antenna. A shower measured in two receivers of two di↵erent antennas (stereo event) is shown in the bottom panel. The shower parameters are: 3.7 ⇥ 10 16 eV, zenith angle 3.7°and core distance 110 m. Very good agreement is found between the measured and calculated time di↵erences for the signals in the two independent antennas in the case of the stereo event.

Properties of the microwave signal -The duration of the microwave signals is about 10 ns. Based on the shower geometry and field of view of the corresponding receivers it can be concluded that most of the signals were emitted from altitudes close to the expected maximum of shower development (typically 4 km above the ground). In Fig. 2, the distribution of the viewing angle (the angle between the shower axis and the boresight of the receiver) is shown for events passing the shower selection criteria. The red line indicates the distribution of the viewing angle for receivers with a signal above 8 dB and the black line for all other receivers. One can clearly notice a lack of events in the signal distribution at viewing angles larger than 4°. With a receiver field of view of ⇠ 2°t he observed angles are compatible with the Cherenkov angle in air (⇠ 1°).

In addition, the core position of events with microwave signal form a ring structure at a distance of 70-150 m around the antennas (cf. Fig. 3). All these features favour an emission mechanism with properties similar to Cherenkov radiation as the dominant source of the observed GHz signals.

Interpretation -For a comparison of the measured events with predictions for the radio signal expected due to the geomagnetic and Askaryan emission mechanisms we improve the purity of the event sample. By considering only events with a viewing angle less than 4°( cf. Fig. 2) we obtain 30 showers (two of which were observed with two receivers) for an expected number of 1.2 ± 0.5 noise signals. For these events, the positions at which the GHz signal is detected relative to the shower core are given in Fig. 3. By applying the end-point formalism [START_REF] Suga | Proc. 5 th Interamerican seminar on CRs[END_REF], CoREAS [8] allows the simulation of the radio emission associated with acceleration of charged particles in extensive air showers (i.e. including signals due to both the geomagnetic and Askaryan e↵ects). At GHz frequencies, the predicted electromagnetic pulses form a Cherenkov-like cone in the forward direction. The electric field has its highest amplitude on a ring at a distance of 100 ± 20 m. accelerator) than in SLAC experiment. The AMY instrument itself is a large anechoic chamber (4 m ⇥ 2 m ⇥ 2 m) equipped with antennas on its sides. When the electron beam interacts with targets placed before the chamber, a shower of particles is produced and the microwave signal is recorded by the antennas. The microwave signal recorded was found to be dominated by the Cherenkov emission of particles in particular at the LINAC frequencies. The data analysis of AMY data is underway, and a thorough filtering of the LINAC frequencies will allow the AMY collaboration to set limits on an isotropic emission. MAYBE experiment utilize an electron beam produced by a Van Der Graa↵ generator. The energy of the electrons produced is lower than the Cherenkov threshold, thus the measurements are free from strong signal from the beam itself. The results of the runs already conducted are still being analyzed but the first measurements published confirmed the observation of a continuum emission in a large bandwidth from 1 to 15 GHz [START_REF] Williams | UHECR 2012 -International Symposium on Future Directions in UHECR Physics[END_REF]. However, the dependence of the flux observed with the beam energy is found linear (cf Fig. 5.27) contrary to the results found in [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF]. In addition, the absolute reference flux is found significantly lower.

The detection of air showers with EASIER in both bands showed the possibility and the assets of a coincident operation. However, the characteristics of the observed radio pulses and the short distance of detection, point to an emission mechanism beamed around the shower axis, instead of isotropic. In the perspective of the original purpose of EASIER, the observation of the shower longitudinal profile at energy larger than 10 19 eV, the only observation of these type of emission entail two main drawbacks. First, the short distances of detection prevent from instrumenting a large area, mandatory to be able to detect with su cient statistic the low flux at ultra high energy. Second, the short length of the pulse makes it hard to extract the information on the longitudinal profile. The work done during this thesis provides radio data on cosmic rays at the highest energies in two frequency bands. It will serve as a basis to improve further both the detector, to lower the sensitivity, and the analysis, to perform a deeper event search and reach better limits.

This chapter will focus on the fundamental theory of how a spectrum analyzer works. While today's technology makes it possible to replace many analog circuits with modern digital implementations, it is very useful to understand classic spectrum analyzer architecture as a starting point in our discussion. In later chapters, we will look at the capabilities and advantages that digital circuitry brings to spectrum analysis. Chapter 3 will discuss digital architectures used in modern spectrum analyzers.

Figure 2-1 is a simplified block diagram of a superheterodyne spectrum analyzer. Heterodyne means to mix; that is, to translate frequency. And super refers to super-audio frequencies, or frequencies above the audio range. Referring to the block diagram in Figure 2-1, we see that an input signal passes through an attenuator, then through a low-pass filter (later we shall see why the filter is here) to a mixer, where it mixes with a signal from the local oscillator (LO). Because the mixer is a non-linear device, its output includes not only the two original signals, but also their harmonics and the sums and differences of the original frequencies and their harmonics. If any of the mixed signals falls within the passband of the intermediate-frequency (IF) filter, it is further processed (amplified and perhaps compressed on a logarithmic scale). It is essentially rectified by the envelope detector, digitized, and displayed. A ramp generator creates the horizontal movement across the display from left to right. The ramp also tunes the LO so that its frequency change is in proportion to the ramp voltage.

If you are familiar with superheterodyne AM radios, the type that receive ordinary AM broadcast signals, you will note a strong similarity between them and the block diagram of Figure 2-1. The differences are that the output of a spectrum analyzer is a display instead of a speaker, and the local oscillator is tuned electronically rather than by a front-panel knob.

Spectrum analyzer

The spectrum analyzer measures the power as a function of the frequency.

The block diagram of a super heterodyne spectrum analyzer operation is represented in Fig. 1. To determine the power at a given frequency f sig it mixes the input signal with a local oscillator signal with an adjustable frequency f LO . The result of the mixing yields a signal with all the harmonic frequencies but the two most important are at the sum and the di↵erence of f sig and f LO . The power is measured at the di↵erence, the Intermediate Frequency (IF), by a n envelope detector in a frequency band defined by the IF filter in Fig. 1. A video filter is applied after these operation to smooth the frequency trace.

The main option to choose before doing a spectrum measurement are: the bandwidth.

the resolution, driven by the IF filter or Resolution Bandwidth (RBW).

the display of the result.

The choice of the bandwidth is clear, and depends on the measurement.

The resolution is the ability on the spectrum analyzer to separate two input sine signal into distinct response. A choice of a small RBW is right to distinguish close peaks.

The result can be displayed in di↵erent way depending on the information that one wants to stress. The bandwidth displayed is divided in frequency windows. In each of these window, the measurement displayed is defined by the mode of detection:

the peak mode: displays the highest power in the window the sample mode: displays the instantaneous level at the center of the window.

the RMS mode: displays the average power in the window.

We used the portable spectrum analyzer Anritsu MS2723. Its main characteristics are a large bandwidth from 9 kHz to 13 GHz and a noise level lower than 140 dBm/Hz over the bandwidth. The measurement of the response of a device to two di↵erent noise power input allow to deduce the noise induced by the device itself.

A noise meter is an apparatus made for this purpose, it is essentially a spectrum analyzer but in addition it controls a calibrated noise source. The measurement is made when the source is on (large noise power) and compared with the measurement when the source is o↵. The setup for this measure is illustrated in Fig. 2. A first phase is needed to calibrate the system, it allow to account for the loss inserted by cables for instance. Then the Device Under Test (DUT) is inserted and the measurement performed.

The noise meter we used is an Agilent PXAN9030A and the noise source Agilent N4002A.

III

Fig 1 . 1 ,

 11 reports measurements of the flux by several experiments over almost 10 decades in energy.

FIG. 1

 1 FIG. 1 Di erential energy spectrum of cosmic rays of energy above 10 11 eV multiplied by E 2 . The positions of the cosmic rays knee and ankle are indicated with gray arrows. The experiments that contribute data to this graph are shown. The equivalent laboratory energy of the Large Hadron Collider is also shown.

sFig. 3 .

 3 Fig. 3. Left panel: Energy loss lengths of protons and nuclei calculated for a redshift z = 0 [66]. R

Figure 1 . 2 :

 12 Figure 1.2: Left: Hillas plot collecting the source candidate as a function of the dimensions and magnetic field characteristic of the source. (taken from[8]). Right: Loss length as a function of energy for protons and nuclei (from[14]).

Fig. 1 .

 1 Fig. 1. Schematic views of (a) an electromagnetic cascade and (b) a hadronic shower. In the hadron shower, dashed lines indicate neutral pions which do not re-interact, but quickly decay, yielding electromagnetic subshowers (not shown). Not all pion lines are shown after the n = 2 level. Neither diagram is to scale.

Figure 1 . 3 :

 13 Figure 1.3: Sketch of the development of a simplified electromagnetic cascade (left) and hadronic cascade (right). Respectively taken from [19] and [8].

Figure 1 :

 1 Figure 1: Air shower simulation of the shower maximum vs. calorimetric energy. Contour lines illustrate the regions which include 90 % of the showers and the inset shows a detailed view at 10 20 eV.

FIG. 6

 6 FIG. 6 Sketch of the detection principles of a fluorescence detector. The fluorescence light emitted by the air shower is collected on a large mirror and focussed onto a camera composed of photo-multipliers (Auger collaboration).

FIG. 7

 7 FIG. 7 Geometry of the detection of an air shower by a fluorescence telescope, from (Kuempel et al., 2008).

Figure 9 :

 9 photon proton iron

Figure 10 :

 10 Figure 10: Elongation rates obtai of HiRes, Yakutsk, TA and Auger results with 2 /Ndf < 2 are sho obtained for HiRes, Yakutsk and average for all four experiments.

Figure 1 . 6 :

 16 Figure 1.6: Layout of the Pierre Auger Observatory surface detector array (dots), and the five fluorescence detectors, the lines indicate the field of view of each telescope. The central campus outside of the array is located in the town of Malargüe.

1. 3 Figure 2 . 9 :

 329 Figure 2.9: Setup of the fluorescence de

Figure 1 . 7 :

 17 Figure 1.7: Left: Scheme of one FD telescope (from[START_REF] Abraham | The Fluorescence Detector of the Pierre Auger Observatory[END_REF]). Right: Picture of Los Leones FD station, with next to it the telecommunication tour. (from[START_REF] Mariş | Measurement of the ultra high energy cosmic ray flux using data of the Pierre Auger Observatory[END_REF]).

Figure 9 .Figure 1 . 8 :

 918 Figure 9. Time vs angle correlation for the hybrid event shown also in Figs. 6(b) and 7; the fit parameters are also given in the figure.

1. 3 Figure 1 . 9 :

 319 Figure 1.9: Surface detector unit in the pampa amarilla.

Figure 1 .Figure 1 . 11 :

 1111 Figure 1.10: Left: Footprint of a SD event. The color code represent the arrival time (early tanks are yellow, late ones are red). Right: Lateral distribution of the signal at ground fitted with a LDF function. The red square is the signal at 1000 m, the energy estimator.

Figure 2 :

 2 Figure 2: X max (top panel) and RMS (X max ) (bottom panel) as a function of the energy. Data (points) are shown with the predictions for proton and iron for several hadronic interaction models. The number of events in each bin is indicated. Systematic uncertainties are indicated as a band.

Figure 1 :

 1 Figure1: The resolution of X max obtained using events recorded simultaneously from two FD stations, compared to a detailed Monte Carlo simulation.

Figure 2 :

 2 Figure 2: X max (top panel) and RMS (X max ) (bottom panel) as a function of the energy. Data (points) are shown with the predictions for proton and iron for several hadronic interaction models. The number of events in each bin is indicated. Systematic uncertainties are indicated as a band.

Figure 1 . 13 :

 113 Figure 1.13: Left: Mean X max (Left) and RM S(X max ) (right) measured with fluorescence detector in Auger data as a function of energy. The lines represent the expectation from simulation with several hadronic models and case of pure proton or iron. Systematic uncertainties are indicated with the gray bands. (from [35]).

  shower observables on characteristics of hadronic interactions as a function of a change in model characteristics growing logarithm t Tevatron energies to the quoted values on the x-axis at 10 19 eV (proton showers at 10 19.5 eV, adapted from[START_REF] Ginzburg | The Origin of Cosmic Rays[END_REF]).

  as a function of a change in model characteristics growing logarithmically s at 10 19 eV (proton showers at 10 19.5 eV, adapted from[START_REF] Ginzburg | The Origin of Cosmic Rays[END_REF]).

Figure 2 :

 2 Figure 2: Exposure of the surface detector of the Pierre Auger Observatory for Earth-skimming neutrino initiated showers (3.5 yr of full Auger) and for down-going neutrino initiated showers for all the considered channels as a function of neutrino energy (2 yr of full Auger).

Figure 3 :

 3 Figure 3: Differential and integrated upper limits (90% C.L.) from the Pierre Auger Observatory for a diffuse flux of down-going ⌫ (2 yr of full Auger) and Earth-skimming ⌫ (3.5 yr of full Auger).Limits from other experiments are also plotted[16]. Expected fluxes are shown for cosmogenic neutrinos[17] and for a theoretical exotic model[START_REF] Stecker | Photodisintegration of ultrahigh-energy cosmic rays: A New determination[END_REF].

23 Figure 1 . 15 :

 23115 Figure 1.15: Left: Photon flux limit measured estimated with Auger data together with expected flux for exotic models and GZK photon. Right: Neutrino flux limit reported by Auger, IceCube Anita and Rice compared to the expected flux of cosmogenic neutrinos and produced from exotic models. (Both from [39])

  The 69 arrival directions of CRs with energy E P 55 EeV detected by the Pierre Auger Observatory up to 31 December 2009 are plotted as black dots in an Aitoffer projection of the sky in galactic coordinates. The solid line represents the border of the field of view of the Southern Observatory for zenith angles smaller than 60°. ircles of radius 3.1°are centred at the positions of the 318 AGNs in the VCV catalog that lie within 75 Mpc and that are within the field of view of the Observatory. blue indicates larger relative exposure. The exposure-weighted fraction of the sky covered by the blue circles is 21%. (For interpretation of the references to colour in ure legend, the reader is referred to the web version of this article.)Total number of events (excluding exploratory scan)

  and from September 12 2007 to April 11 2011 for the infill. The bottom panel is derived with data since June 25 2011 up to December 31, 2012. At this stage, the values as derived from the analysis applied to the infill array are still affected by large uncertainties. On the other hand, the overall behavior of the points as derived from the analysis applied to the regular array shows good agreement with equation 4, using the same parameters as the ones derived with data prior to 2011. The final result of the prescription is expected for 2015, once the required exposure is reached. E[EeV] mean noise 0.25 -0

Figure 3 :

 3 Figure 3: Phase of the first harmonic as a function of energy. The top panel shows the phase calculated using data from January 1 2004 to December 31 2010 for the larger array, and from September 12 2007 to April 11 2011 for the infill. The bottom panel shows the phase derived with data since June 25 2011 up to December 31 2012. The continuous lineshown in both plots corresponds to the value =263 , that comes from a fit to the phase measured by the infill of the first period, and the dashed line is the fit performed in[5], defined by eq. 4.

Figure 1 .

 1 Figure 1.16: Left: Sky map (in Aito↵-Hammer projection of the sky in galactic coordinates) of events above 55 ⇥ 10 19 eV (black dots) with the sources reported in the Veron-Cetty Veron catalogue (blue dots), the shades of blue represent the relative exposure of the Pierre Auger Observatory in the corresponding direction. (from [46]). Right: Phase of the first harmonic of the development in Rayleigh analysis of the right ascension of events as a function of energy. (from [47])

Figure 2 .

 2 Figure 2.1: from [64]

EASIER 2 . 2

 22 State of the art of radio detection

Figure 2 . 3 :

 23 Figure 2.3: Left : Vertical air shower. due to lateral dispersion and longitudinal lag of the shower particle the observer sees radiation from the di↵erent part of the shower at the same time. Right: Evolution of the quantity responsible for the electric field at ground. The kink at t = 0 is smoothed out due to a realistic shower development. The corresponding pulse don't show anymore a function shape.

Fig. 7 .

 7 Fig. 7. Calibration results of LOPES showing the normalized radio voltage vs. air shower parameters where the other parameters have been divided out. Each point represents the average and spread of all events in that bin. Panels a-c are from top to bottom.

Fig. 7 .

 7 Fig. 7. Calibration results of LOPES showing the normalized radio voltage vs. air shower parameters where the other parameters have been divided out. Each point represents the average and spread of all events in that bin. Panels a-c are from top to bottom.

Fig. 7 .

 7 Fig. 7. Calibration results of LOPES showing the normalized radio voltage vs. air shower parameters where the other parameters have been divided out. Each point represents the average and spread of all events in that bin. Panels a-c are from top to bottom.

2. 2

 2 State of the art of radio detection EASIER

Figure 3 :

 3 Figure 3: West-component of the electric field pulses for a vertical 10 17 eV proton-induced air shower at the site of the Pierre Auger Observatory as simulated with the indicated models. The refractive index of the atmosphere was set to unity.

Figure 4 :

 4 Figure 4: Absolute amplitudes of the frequency spectra for a vert proton-induced air shower at the site of the Pierre Auger Observa ulated with the indicated models. The refractive index of the atm set to unity.

Figure 4 :

 4 Figure 4: Absolute amplitudes of the frequency spectra for a vertical 10 17 eV proton-induced air shower at the site of the Pierre Auger Observatory as simulated with the indicated models. The refractive index of the atmosphere was set to unity.

Figure 2 . 5 :

 25 Figure2.5: Electric pulses and spectra for a proton induced vertical shower of 10 17 eV at di↵erent distances and for a two di↵erent models CoReas and EVA (in[START_REF] Huege | Theory and simulations of air shower radio emission[END_REF]).

2 . 2

 22 Fig 2.5 illustrates simulations of the electric field pulse and spectrum at di↵erent distance from the EASIER State of the art of radio detection

FIG. 3 :FIG. 4 :

 34 FIG. 3: Schematic of AWA INCOBREMS (top) and SLAC T471 (bottom) experiments, which used electron beams to shower in eitherTungsten or alumina targets to produce ionization inside an anechoic Faraday chamber, observed by internal antennas.

Figure 2 . 6 :

 26 Figure 2.6: Left: setup of AWA and SLAC experiments. Right: Intensity of microwave signal detected after the passage of showers.

Figure 1 .

 1 Figure 1. Photograph of a typical water tank in the Pampa Amarilla. The main components are indicated.

Figure 2

 2 Figure 2. L locations of are the loca of their tel the part of thermore, a Coihueco si

Figure 2 . 7 :

 27 Figure 2.7: Surface detector unit and its di↵erent elements. (from [80]).

• 8 Figure 2 . 2 . 49 :Figure 0 60 :

 8224960 Figure 2.2.49 : Unified Board picture 2.2.3.5.3. Memory Mapping : • DRAM 32 MBytes : from 0 • Flash 8 MBytes : from FF800000 • Slow Control :

Figure 0 61 :

 61 Figure 0 61: Electronics weather enclosure.

Figure 2 . 8 :

 28 Figure 2.8: Left: Picture of the Unified Board of SD local electronics. Right: Auger SD electronics elements as installed on site, enclosed in a metallic shielding. At the left hand side: the communication module, at the center: the UB, at the right hand side: the TPCB.

Figure 2 . 9 :

 29 Figure 2.9: Left : functional scheme of EASIER

Example 15 . 2 . 4 :

 1524 68 o . The subtended angle will be then ∆θ B = 2θ = 0.303 rad = 17.36 o . It follows that the required antenna gain should be G = 16/∆θ 2 B = 174.22 = 22.41 dB. The flat-disk approximation is more accurate for smaller areas on the earth's surface that lie directly under the satellite.⊓ The radial distance of a geosynchronous orbit can be calculated by equating centripetal and gravitational accelerations, and requiring that the angular velocity of the satellite corresponds to the period of 1 day, that is, ω = 2π/T, where T = 24 hr = 86 400 sec. Let m be the mass of the satellite and M ⊕ the mass of the earth (see Appendix A):

  For the more precise value of R = 6378 km, the calculated values are: r = 42 237 km = 26 399 mi h = 35 860 km = 22 414 mi

Fig. 15 . 3 . 1

 1531 Fig. 15.3.1 Effective area of an antenna.

Figure 2 . 10 :

 210 Figure2.10: Left: Scheme of the half power beam width. Right: Scheme of the e↵ective area and length of an antenna. (both scheme are taken from[START_REF] Orfanidis | Electromagnetic Waves and Antennas[END_REF]).

Figure 2 . 11 :

 211 Figure 2.11: Left: Typical response of a power detector to a sine waveform pulse. Right: Typical characteristic curve of a power detector.

Fig 2 .

 2 11 (left) and a typical characteristic is shown in Fig.2.11 (right). Remark on units We will widely use the decibel units: the dB to compare two powers: X[dB] = 10 log 10 ( P 1 P 0 ) the dBm unit is a power in dB with P 0 = 10 3 W att 2.3 EASIER Detector EASIER P [dBm]

3. 1 Figure 3 . 1 :

 131 Figure 3.1: Left: Contributions of noise background in noise temperature for natural source (galaxy and atmosphere) and human source. Right: Fat dipole industrial design.

  the direct and ground reflected waves. Nevertheless the 100 MHz zenith gain is still one half of the 1 MHz one.

Fig. 4

 4 Fig. 4 shows the frequency spectra measured in the range 1-150 MHz. The bottom plot corresponds to the analyser noise, the middle one shows the amplifier noise and the top one exhibits the performances of the whole device when detecting the sky. Since 2005, eight such dipoles have been used in the CODALEMA experiment.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .

 1234 Fig. 1. Filtered transients induced by a cosmic ray detected in coincidences by three dipoles of CODALEMA (voltage in V vs. time in ms). Oscillating structures seen on the edges are artifacts due to the numerical offline filtering.

Figure 1 :

 1 Figure 1: Electrical equivalent model of the active antenna.

Figure 3 . 2 :

 32 Figure 3.2: Left: Normalized gain of the fat dipole in E-plane and H-plane (from [83]). Right: Electronic equivalent circuit of the active antenna. (from [84]).

Figure 2 :

 2 Figure 2: Preamplifier gain measurements (V out /V a ): the solid line is the measured gain replacing Z a by a 10pF dummy antenna capacitance, whereas the dotted line is the gain calculated by taking into account the measured values of Z a .

Figure 3 . 3 :

 33 Figure 3.3: Transfer function of the set antenna + amplifier (from [84])

Figure 3 :

 3 Figure 3: Noise density measured with (solid line) the active antenna and a spectrum analyser at Malargue (Argentina) and without (dotted line) the antenna radiator.

Figure 3 . 4 :Figure 3 . 5 :

 3435 Figure 3.4: Spectrum recorded at Malargüe. The shaded area represents the clean frequency band operable for EASIER. The dashed line is a spectrum taken replacing the antenna by a dummy impedance, it is then the amplifier noise.

Figure 3 .Figure 4 .Figure 5 .Figure 6 .INPUTFigure 7 .Figure 8 .Figure 3 . 6 :

 34567836 Figure 3. RSSI Output vs. Input Level, 100 MHz Sine Input at TA = -40°C, +25°C, and +85°C, Single-Ended Input

  Tube PVC (Plastiflex) plomberie de 3m section 50mm Tête de mat en PVC rigide collée sur le tube Sur l'antenne Bouchon de plastique se vissant sur la tête de mat percé au centre pour le passage de la vis de montage sur le radiateur Vis en nylon (type cuvette de toilette) Boite plastique arge (pour collage antenne) Montage du mat Tube PVC (Plastiflex) plomberie de 3m section 50mm Tête de mat en PVC rigide collée sur l Sur l'antenne Bouchon de plastique se vissant sur la de mat percé au centre pour le passag de la vis de montage sur le radiateur

Figure 3 . 7 :

 37 Figure 3.7: Elements of mechanical assembly of the dipole and the mast.

20 Figure 3 . 8 :

 2038 Figure 3.8: Spectrum recorded in a container showing the resonance peak just above 110 MHz.

Figure 3 . 11 : 55 3

 31155 Figure 3.11: Location of the VHF hexagon centered on Vieira tank

Figure 3 . 12 :

 312 Figure 3.12: Baseline as a function of time over the time of operation of the VHF setup.

Figure 3 . 13 :

 313 Figure 3.13: Example of rejected traces. Up: regular peaks on the station 432. Down: Important fluctuations of the radio trace.

Figure 3 . 14 :

 314 Figure 3.14: Example of a threefold event (Id: 11748502). In grey is represented the trace of one PMT and in red the radio trace in adc counts.

Figure 3 . 15 :Figure V. 1 -

 3151 Figure 3.15: Distribution of the energy, distance of station to shower axis, zenith angle, azimuth angle of the air shower event selected. The distributions in red represent the characteristics of the radio events.

Figure 3 . 16 :

 316 Figure 3.16: Di↵erence of SNR induced by the tank when LED and PMTs are on and when PMT are o↵. The stars represent the signal to noise ration induced by air shower radio events

Figure 3 .

 3 Figure 3.17: Left: Arrival direction of radio events recorded compared to the air shower event non associated with radio events. Right: Intensity of the geomagnetic e↵ect ([ṽ ⇥ B k Bk ] EW ) as a function of the arrival direction

Figure 3 . 18 :

 318 Figure 3.18: Dipole antenna pattern simulated with HFSS in realistic condition at 30 (left), 50 (middle) and 70 MHz (right)

Figure 3 . 19 :

 319 Figure 3.19: Lateral distribution of the electric field as a function of the distance from antenna to the shower axis. The electric field is normalized with the shower energy and the projection on the antenna polarization direction of the vector ṽ ⇥ B.

Figure 4 . 1 :

 41 Figure 4.1: Noise survey. Left : spectrum taken a the FD building Los Leones. Right : Spectrum taken on the tank Vieira.

Figure 4 . 2 :

 42 Figure 4.2: Scheme of the complete detector microwave band

4. 1 Figure 4 . 3 :

 143 Figure 4.3: Left: Picture of LNBF GI 301SC with its scalar ring and radome. Right: Spectra of the 7 first antenna installed. The Y axis is the power integrated on 100 kHz band. The red dashed lines set the boundaries of the nominal bandwidth.

Figure 4 . 4 :Figure 4 . 5 :

 4445 Figure 4.4: Left: picture of the power detector. Right: supplied calibration curve from 10 MHz to 8 GHz (from [92]).

Figure 4 . 7 :

 47 Figure 4.7: Left: Pulse observed after the power detector next to the assembly building. Right: superposition of spectra taken inside the assembly building. The spectra were taken with the spectrum analyser on the peak mode option (cf Appendix A).

Fig 4 . 7 (

 47 right)).

Figure 4 . 8 :

 48 Figure 4.8: Left: antenna integrated with the SD tanks. Right: EASIER electronics box on top of the SD electronics.

Figure 4 . 9 :Figure 4 . 10 :

 49410 Figure 4.9: Left: Superposition of spectra recorded during the installation (here on Paloma tank).The spectrum analyser option is peak mode. No peaks are detected compared to the spectra taken at the assembly building (cf. 4.7). Right: Spectra during the installation of the seven prototypes. The spectra analyser option is RM S mode

Fig 4 .

 4 10 and the variation of the baseline during one week is shown inFig 4.11 (left). The daily modulation is of the order of 100 ADC or 2 dB and it is not completely understood.

Figure 4 . 11 :

 411 Figure 4.11: Left: variation of the baseline in ADC counts over one week for station Nene. Right: the baseline as a function of SD electronic temperature

Figure 4 .

 4 Figure 4.12: (left) Footprint on the array. The ellipse surrounds the GHz hexagon. (right) Lateral distribution function.

Figure 4 . 13 :

 413 Figure 4.13: FADC traces from the anodes of the PMT 1 and PMT 2 together with the GHz trace.

4. 1

 1 Detector developmentsDetector developments and sensitivity in microwave band

Figure 4 .

 4 Figure 4.14: Left: electronic box of the 2 nd GHz setup. The output of the LNBF is P in , the voltage V out is the radio signal transform by the electronic chain : 1: Bias tee; 2: 75-50⌦ adapter; 3: high pass filter; 4: power detector Minicircuit ZX 47-50; 5: power supply board; 6: EASIER board. Right: Picture of the mechanical installation of EASIER antenna for the second setup

  Fig 4.15 (left) it is illustrated the location of the radio array at the Pierre Auger Observatory. Regarding the polarization of the antenna, the array has 33 antennas oriented to have a North-South polarization, and 28 East-West. Their layout is illustrated in Fig 4.15 (right).

Figure 4 . 15 :

 415 Figure 4.15: EASIER GHz arrays. Left : EASIER GHz arrays into the Auger array, in blue the first setup installed in 2011, in green the extension completed in 2012. The field of view of the other microwave detection prototypes (MIDAS and AMBER) are also displayed Right : polarization distribution of the complete array

Fig 4 .

 4 14 (right)), and the EASIER antenna is held by a bracelet . This simplification allowed us to install the 54 detectors in 5 days with two teams of two persons.

Figure 4 .

 4 Figure 4.16: Left : Regulated voltage as a function of supplied voltage. Right: Output of the EASIER board as an function of supplied voltage.

Figure 4 . 17 :

 417 Figure 4.17: Setup for the calibration of the power detector.

4. 2

 2 Electronics calibrationDetector developments and sensitivity in microwave bandInput Power[dBm]

Figure 4 . 18 :

 418 Figure 4.18: Calibration curves for sine waves and noise.

Figure 4 . 19 :

 419 Figure 4.19: Left: Calibration curve of one power detector at three frequencies. Right: Calibration curve of the set power detector and EASIER board. The horizontal red lines shows the dynamic range determined by the Auger SD electronics.

Figure 4 . 20 :

 420 Figure 4.20: Right: Calibration curves of the 61 prepared boxes. Left: Distribution of the slopes

Figure 4 . 21 :

 421 Figure 4.21: Measured relative gain. Upper panel: Pattern of the antenna ESX241 with an attached scalar ring and a radome. Lower panel: Di↵erence of gain of the pattern shown in upper panel with the one of an antenna without scalar ring or radome.

3 . 2 .

 32 The normalized gain of the antenna ESX241 was measured in an anechoic chamber at the IMEP (Institut de Microelectronique Electromagnetisme et Photonique) at Grenoble. The pattern was measured for the antenna with the scalar ring and the radome (shown in Fig.4.21 in the upper panel) and without scalar ring or radome. The di↵erence of these two measurement is shown in the lower panel of Fig.4.21. The opening angle is widened and the backlobes reduced by up to 25 dB.

3 . 13 )

 313 The e↵ective area are represented in linear scale in Fig.4.22.

Figure 4 . 22 :

 422 Figure 4.22: Calculated e↵ective area at frequency from 3.4 GHz to 4.2 GHz.

Figure 4 . 23 :Figure 4 . 24 :

 423424 Figure 4.23: Left: Superposition of two spectra recorded at T hot and T cold (see text). Right: Profile of brightness temperature at 2.295 GHz. The normalized gain of the antenna at 3.8 GHz is superimposed.

Figure 4 . 25 :

 425 Figure 4.25: Distribution of temperature (left) and gain (right) of 28 LNBF (ESX241)

Figure 4 . 26 :

 426 Figure 4.26: Left: picture of the LNB DMX211. Right: setup for the noise measurements

Figure 4 . 27 :Figure 4 . 29 :

 427429 Figure 4.27: Measured gain and temperature of the LNB DMX211 using a noise figure meter.

Figure 4 . 31 :

 431 Figure 4.31: Calibration of the parameter A dB with a second order polynomials. The lower plot shows the residuals of the fit.

Figure 4 . 32 :

 432 Figure 4.32: Frequency and distance of selected traces (in red) and rejected (in blue) for the 2 runs

10 A

 10 dB SN R lin (4.3.21)4.3 Detector SensitivityDetector developments and sensitivity in microwave bandWe can finally extract the sine part of the signal with the following relation:P sine = P noise .SN R linearThe uncertainties are dominated by the contribution from the calibration of the power detector. The power of sine signal recorded by the EASIER receiver is shown in Fig 4.33 as a function of the frequency for the 3 distances covered during run 1.

Figure 4 . 33 :

 433 Figure 4.33: Sine power measured as a function of the frequency at z = 100, 150, 200 m

Fig 4 .

 4 30 (right).

Figure 4 . 34 :

 434 Figure 4.34: Sine power as a function of distance for di↵erent frequencies

95

 95

3 . 68 AFigure 4 . 35 :

 368435 Figure 4.35: Factor A e↵ (✓ = 0, ⌫) • G LNB (⌫)

Figure 4 . 36 :

 436 Figure 4.36: Angular pattern relative to the gain at 0 degrees

Figure 5 . 4 Figure 5 . 6 :

 5456 Figure 5.4: Event 20830870

Figure 5 . 7 :Figure 5 . 8 :

 5758 Figure 5.7: Simulated shower profiles for a vertical shower with an energy of 10 19 eV using the parameterization given in [103].

Figure 5 . 9 :

 59 Figure 5.9: Left: Sketch of the propagation of the radiation in air. If ⌧ up = ⌧ down + ⌧ step these two part of the shower are detected at the same time. Right: Refractive index of air as a function of height used in the simulation.

Figure 5 . 10 :

 510 Figure 5.10: Time compression for several constant indices of air and a taking the exponential profile represented in Fog. 5.9 (right).

Figure 5 . 11 :

 511 Figure 5.11: Simulated microwave flux for a distance to shower axis of 300 m (left) and 1000 m (right).

Figure 5 .

 5 Figure 5.14: Left: Scheme of the setup to record at the same time the high frequency trace and the corresponding trace processed by the power detector. Right: Example of high frequency trace and the corresponding response of the power detector.

Figure 5 . 15 :

 515 Figure 5.15: Upper panel: original high frequency trace. Middle left panel: trace in dBm unit. Middle right panel: convolution function. Bottom panel: resulting convoluted trace.

Figure 5 . 16 :

 516 Figure 5.16: Sum of the squared di↵erence between the real and simulated points as a function of the time integration for the noise part (left) and the pulse part (right).

Figure 5 . 17 :

 517 Figure 5.17: Superposition of real power detector trace and simulated one for the configuration with capacitor (see text)

Figure 5 . 18 :Figure 5 . 19 :

 518519 Figure 5.18: Superposition of power detector trace and simulated one for the configuration without capacitor (see text).

Figure 5 . 20 :Figure 5 . 21 :

 520521 Figure 5.20: Superposition of traces simulated before and after the electronics for the configuration of the first setup (upper panel) and the second (bottom panel)

123 5 . 4

 54 Comparison data/simulation and interpretation Data analysis in microwave band time [25ns]

Figure 5 . 22 :Figure 5 . 24 :

 522524 Figure 5.22: Superposition of observed and simulated trace for the three events detected.

FIG. 3 .

 3 FIG. 3. Exclusion limits on the microwave emission from UHECRs, obtained with 61 days of live time measurements with the MIDAS detector. The power flux If,ref corresponds to a reference shower of 3.36 10 17eV, and the parameter characterizes the possible coherence of the emission. The shaded area is excluded with greater than 95% confidence. The horizontal line indicates the reference power flux suggested by laboratory measurements[1]. The projected 95% CL sensitivity after collection of one year of coincident operation data of the MIDAS detector at the Pierre Auger Observatory is represented by the dashed line.

  VII. ACKNOWLEDGEMENTS This work was supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through grants NSF PHY-0114422 and NSF PHY-0551142 and an endowment from the Kavli Foundation and its founder Fred Kavli, Conselho Nacional de Desenvolvimento Cientfico e Tecnolgico (CNPq), Xunta de Galicia (INCITE09 206 336 PR), Ministerio de Educación, Cultura y Deporte (FPA 201018410), ASPERA (PRI-PIMASP-2011-1154) and Consolider CPAN Inge-nio2010, Spain. The simulations used in this work have been performed on the Joint Fermilab -KICP Supercomputing Cluster, supported by grants from Fermilab, Kavli Institute for Cosmological Physics, and the University of Chicago.

Figure 5 .

 5 Figure 5.25: Left: MIDAS detector installed at the Pierre Auger site. Right: Limits on the MBR flux estimated with MIDAS (shaded area) as a function of the parameters I ref = F ref • and ↵. The horizontal line represent the reference flux measured in [73].

Figure 1 .

 1 Figure 1. Power received by the logarithmic amplifier as function of time relative to the KASCADE-Grande trigger. Shown are the event with the highest signal (top) and a stereo event (bottom). The signal thresholds of 8 dB are shown as dashed lines.

Figure 2 .

 2 Figure 2. Distribution of the viewing angle for showers passing the KASCADE-Grande and geometry selection criteria. The red histogram shows the events with a microwave signal greater than 8 dB. The black histogram shows all other events.

Figure 3 .

 3 Figure 3. Positions at which a microwave signal has been detected relative to the shower core at (0, 0). The maximum total field strength predicted by CoREAS for a typical vertical (upper plot) and a very deep vertical proton shower (lower panel) of 10 17 eV is shown.

Figure 5 .

 5 Figure 5.26: Left: Time trace of events detected by CROME experiment. Right: Position of the antenna at which microwave signals were detected with respect to the shower core. The shaded areas represent the amplitude of the simulated electric field with CoREAS code (see text).

Figure 2 - 1 .Figure 1 :

 211 Figure 2-1. Block diagram of a classic superheterodyne spectrum analyzer Figure 1: Block diagram of a spectrum analyzer operations

II

T 2 =Figure 2 - 5 . 3 .

 2253 Figure 2-5. The Y-factor noise figure measurement requires two steps: (a) Calibration, (b) Measurement of DUT.

Figure 2 :

 2 Figure 2: Measurement phase

  Left panel: Longitudinal shower profile. Shown here are the number of electrons with Ekin > 250 keV and muons with Ekin > 250 MeV (from [110]).

					J. Blümer et al. / Progress in Particle and Nuclear Physics 63 (2009) 293-338	301
		10 10									1400
			10 19 eV								1200	QGSJET II Sibyll 2.1 neXus 3.97	γ
		10 9			electrons + positrons		p			γ γ	no MF from South
	particle number	10 8			muons			Fe Fe	<X ) 2 max > (g/cm	800 1000	γ γ	from North no LPM no MF	p	Fe
											600
								p
		10 7									400
		0	200	400	600	800	1000	1200	1400
				atmospheric depth X (g/cm 2 )				14 10	15 10	16 10	17 10	18 10	19 10	20 10	21 10
											Energy (eV)
	Fig. 4.

] -2 [g/cm 0 80 100 2 m 2 (syst.) g/cm +2 -1 at.)

  SAN LUIS et al. THE DISTRIBUTION OF SHOWER MAXIMA OF UHECR AIR SHOWERS

	Ultra High Energy Cosmic Rays	1.3 The Pierre Auger Observatory
	sing events recorded
	pared to a detailed
	tector stations ar-
	d sensitive to the
	FD has 27 tele-
	different stations,
	xcitation of nitro-
	the passage of the
	er geometry is re-
	data. The number
	ortional to the en-
	shower. Using the
	attenuation of the
	or, the longitudinal
	ted. This profile is
	o determine X max
	in [6]. We consider
	ta and that have at
	easured in coinci-
	determined with an
	osol content in the
	ng data taking [10]
	easurement of the
	ed. Also the cloud
	array and periods
	ted. Furthermore,
	than 2.5 when the
	s could indicate the
	tistical uncertainty
	ated including the
	truction and to the
	ncertainties above
	vents that have an
	cope smaller than
	econstructing their
	herenkov light. Fi-
	ax we require that
	ed within the field
	s quality selection.
	t the data sample is
	omposition. Since

E [eV] 18 10 19 10 ] 2 > [g/cm max <X 650 700 750 800 850 1407 1251 998 781 619 457 331 230 188 143 186 106 47 EPOSv1.99 p Fe QGSJET01 p Fe SIBYLL2.1 p Fe QGSJETII p Fe EPOSv1.99 p Fe QGSJET01 p Fe SIBYLL2.1 p Fe QGSJETII p Fe E [eV]

  2.2 State of the art of radio detection EASIERof the muon number as well. The radio detection is a promising technique since it may give access to the electromagnetic cascade development with almost 100% duty cycle.Electromagnetic emissions in VHF band from cosmic ray air shower were detected almost 50 years ago in 1965 by Jelley and collaborators[START_REF] Jelley | [END_REF]. It was first suggested that the Cherenkov emission, already detected in optical domain could be also detectable at lower frequencies. In 1962 Askaryan[START_REF] Askaryan | Excess Negative Charge of an Electron-Photon Shower and its Coherent Radio Emission[END_REF] pointed out that in dense medium, the negative charge excess arising from the accumulation of Compton scattered electrons and positron annihilation could lead to a coherent Cherenkov emission at lower frequencies than optical ones. The first experiment was installed at the Jodrell Bank Radio Observatory and operated 72 receivers tuned at 44MHz in an array of 1800 m 2 in coincidence with three Geiger-Müller counters. It successfully detected cosmic rays in that band. Several experiments were operated in the following decade, at di↵erent frequencies from a few MHz to 3 GHz. In parallel, another possible mechanism due to charge separation in the earth magnetic field was suggested. It was already noticed by Askaryan and further developed byKahn and Lerche

	2.2 State of the art of radio detection
	VHF band

Information furnished by Analog Devices is believed to be accurate and reliable. However, no responsibility is assumed by Analog Devices for its use, nor for any infringements of patents or other rights of third parties that may result from its use. Specifications subject to change without notice. No license is granted by implication or otherwise under any patent or patent rights of Analog Devices. Trademarks and registered trademarks are the property of their respective owners. One Technology Way, P.O. Box 9106, Norwood, MA 02062-9106, U.S.A. Tel: 781.329.4700 www.analog.com Fax: 781.461.3113 ©2004-2007 Analog Devices, Inc. All rights reserved. Stability over temperature: ±0.5 dB Low noise measurement/controller output (VOUT) Pulse response time: 10 ns/12 ns (fall/rise) Integrated temperature sensor Small footprint LFCSP Power-down feature: <1.5 mW at 5 V Single-supply operation: 5 V @ 68 mA Fabricated using high speed SiGe process APPLICATIONS RF transmitter PA setpoint control and level monitoring RSSI measurement in base stations, WLAN, WiMAX, and radars GENERAL DESCRIPTION

						%"&%'(	,+*%	+ 0	0%"!
							+ 0	0'1!
					."!	."!	."!	."!
							2-$3
				+&/+
				+&-'
						2#+$	2#'$	04853-001
							Figure 1.
					567		:
	200mV/DIV	AVERAGE: 50 SAMPLES		565		;
					568		7
	OUTPUT		V S = +2.7V		<6B <6:	INPUT	C 5
	GND The AD8318 is a demodulating logarithmic amplifier, capable PULSED RF 100MHz, -45dBm of accurately converting an RF input signal to a corresponding INPUT decibel-scaled output voltage. It employs the progressive	0 '1! =>0A	<67 <65 <68 86B 86: 867	OUTPUT	< 8 9< 95 9C 97	"(('(=>?,A
	compression technique over a cascaded amplifier chain, each			865		9;
	HORIZONTAL: 50ns/DIV stage of which is equipped with a detector cell. The device is TIME used in measurement or controller mode. The AD8318 maintains accurate log conformance for signals of 1 MHz to 6 GHz and provides useful operation to 8 GHz. The input range	TIME 9:8 9;; 9;8 97; 978 9C; 9C8 95; 958 9<; 9<8 9; 8 ; $ +& =>?,@A Figure 2. Typical Logarithmic Response and Error vs. Input Amplitude at 5.8 GHz 8 9: 9:; <8 04853-052
	Input Bandwidth 10%-90% Rise Time is typically 60 dB (re: 50 Ω) with error less than ±1 dB. The In this mode, the setpoint control voltage is applied to VSET. Dynamic Range Log Conformance AD606 50 MHz 360 ns 80 dB ± 1.5 dB AD8318 has a 10 ns response time that enables RF burst The feedback loop through an RF amplifier is closed via VOUT, Limiter Ou Yes detection to beyond 45 MHz. The device provides unprece-the output of which regulates the amplifier output to a magnitude
	AD640 dented logarithmic intercept stability vs. ambient temperature 120 MHz AD641 250 MHz AD8306 500 MHz 5 V is required. Current consumption is typically 68 mA. Power provided for additional system monitoring. A single supply of conditions. A 2 mV/°C slope temperature sensor output is also	6 ns 6 ns 67 ns	50 dB corresponding to VSET. The AD8318 provides 0 V to 4.9 V ± 1 dB 44 dB ± 2 dB 95 dB ± 0.4 dB output capability at the VOUT pin, suitable for controller	Yes Yes Yes
	AD8307 consumption decreases to <1.5 mW when the device is disabled. 500 MHz	500 ns			92 dB	± 1 dB	No
	AD8309	500 MHz	67 ns			100 dB	± 1 dB	Yes
	AD8313	2500 MHz	45 ns			65 dB	± 1 dB	No
	Rev. B

The AD8318 can be configured to provide a control voltage to a VGA, such as a power amplifier or a measurement output, from Pin VOUT. Because the output can be used for controller applications, wideband noise is minimal. applications. As a measurement device, Pin VOUT is externally connected to VSET to produce an output voltage, VOUT, which is a decreasing linear-in-dB function of the RF input signal amplitude.

The logarithmic slope is nominally 25 mV/dB but can be adjusted by scaling the feedback voltage from VOUT to the VSET interface. The intercept is 20 dBm (re: 50 Ω, CW input) using the INHI input. These parameters are very stable against supply and temperature variations.

The AD8318 is fabricated on a SiGe bipolar IC process and is available in a 4 mm × 4 mm, 16-lead LFCSP for the operating temperature range of -40 o C to +85 o C.

Table 3 . 2

 32

	selection criteria	number of traces selected %
	All traces	1748	100
	mean 2 [100 ; 800] &&  150 excluding tank 432	1655 1405	95 80
	maximum 250 ADC	99	5.7
	time coincidence	36	2.1

: Selection criteria and their e ciency on radio traces.

Table 4 .

 4 5 • 1023 • V EB with V EB / ( 4.1) • ( 0.0234) • P dBm 1: Measurements performed during the installation to obtain a final calibration where #ADC is the number of ADC counts, and ADC o↵set the o↵set induced by the power detector and the EASIER board. Thanks to the measurement at the installation we can retrieve ADC o↵set , they are given for each station in Table 4.2.

	(4.2.5)

Table 4 . 2 :

 42 O↵set for the seven first detectors to apply in Eq. 4.2.5

  At the installation we added a voltage regulator to correct in part the e↵ect of the voltage supply on the baseline. We characterized all the boxes once the regulator was added to obtain

	Detector developments and sensitivity in microwave band	4.2 Electronics calibration
	[V] out V	0					10	Entries Entries Mean Mean	61 61 0.1009 0.1009
		-0.5					8	RMS 0.001017 RMS 0.001017
		-1					6
							4
		-1.5
							2
		-2
		-40	-35	-30	-25	-20	0.09 0.092 0.094 0.096 0.098 0.1 0.102 0.104 0.106 0.108 0.11 0
						in P	[dBm]	slope [V/dB]
						1 • V P D + 5.04 V	(4.2.8)

  2, only 23 on 166 traces are removed and for run 1 the table 4.3 report the selected frequencies and the number of accepted and rejected traces. The scanned parameters of the selected data are shown for the two runs in Fig 4.32. For run 1, the rejected traces are, as expected, at shorter distances and lower frequencies in agreement with the shape of the spectrum in Fig 4.30 (right).

	Detector developments and sensitivity in microwave band	4.3 Detector Sensitivity
	frequency [GHz]	d ⇠ 100 m d ⇠ 150 m d ⇠ 200 m 3.86 3.77 3.68
	accepted/rejected	56/42	167/111	177/14

Table 4 .

 4 3: Statistics of selected traces for run 1.

Table 4 .

 4 2 . Table4.4 reports the values of the fit showing a decrease of the signal power with an index k 2 ranging from 2 to 2.44. The small uncertainties on k 2 reflect an underestimation of the uncertainties on power signal. 4: Fitted exponent k 2 of the power law function k 1 /R k2

	Detector developments and sensitivity in microwave band	4.3 Detector Sensitivity
	frequency [GHz]	k 2
	3.85 -3.875 3.875 -3.90 3.90 -3.925 3.925 -3.95 3.95	2.09 ± 0.033 2.44 ± 0.04 2.23 ± 0.034 2.40 ± 0.041 2.25 ± 0.03

  19 eV. Figure5.2: Left: Maximum radio signal in the trace as a function of the di↵erence of time bins between the particle signal start time and the time of the maximum radio signal. Right: Distribution of the trace maximum of all events selected. Three events lay well above the bulk of events.

	Data analysis in microwave band								5.2 Event search
	] σ trace maximum [	8 10 12	setup 1 setup 2					# of entries	3 10			setup 1 setup 2
									2 10
		6
									10
		4
		2							1
		-700 -600 -500 -400 -300 -200 -100	0	100	200	300	2	4	6	8	10	12
						∆	t [25ns]				] σ trace maximum [
			Auger Id		12046376		20830870		21050180
			station			342			429		306
			date	2011/06/30		2013/01/03		2013/02/07
		energy [eV] zenith [ ] azimuth[ ] Distance to axis [m] t to trigger	(1.32 ± 0.12)⇥10 19 (1.71 ± 0.1)⇥10 19 (2.56 ± 0.41)⇥10 18 29.7 ± 0.3 55.2 ± 0.1 47.4 ± 0.5 343.4 ± 0.8 289.4± 0.6 33.8 ± 0.1 136 ± 40 268 ± 11 193 ± 15 1 2 2
	radio maximum [sigma]			11.86		11.23		11.05
			polarization			E-W		E-W		E-W
		time length [time bins]			2-3			1		1-2

Table 5 .

 5 1: Characteristics of the three radio events with the maximum well above the noise.

	107

  3.10, a time shift and the characteristic time decay of the

	Data analysis in microwave band						5.3 Microwave signal simulation
	2
	α	5.3
		5.2
		5.1
		5
		4.9
		4.8
		4.7
		4.6
		4.5
		4.4
		26	28	30	32	34	36	38	40	42	44	26	28	30	32	34	36	38	40	42	44
											τ	[ns]									τ	[ns]

Table 5 .

 5 .3 for iron primary accounting for two sets of simulation parameters. 2: Maximum, and the width at half height for the events detected in radio and simulation with parameters (F ref , ↵ = 1), and (F ref , ↵ = 2) where F ref = 4 ⇥ 10 16 W/m 2 /Hz. For proton primary simulated showers.

		12036476 (40K) 12036476 (80K) 20830870 21050180
	max data	2.8	2.8	3.7	3.2
	max sim (F ref , ↵ = 1) max sim (F ref , ↵ = 2) width data [25ns]	2.2 ±0.3 12.4± 4.5 3.1	1.6 ± 0.2 9.2±0.3 3.1	1.9±0.1 6.3 ± 2.1 2.0± 0.2 1.9 ±0.1 1.4 1.7
	width sim (F ref , ↵ = 1) width sim (F ref , ↵ = 2)	11 ± 5 4.3 ± 0.4	17.2±3 4.7 ±0.4	3.4 ± 1.3 4.1 ± 2.5 1.4 ±0.1 3 ± 1.6
		12036476 (40K) 12036476 (80K) 20830870 21050180
	max data	2.8	2.8	3.7	3.2
	max sim (F ref , ↵ = 1) max sim (F ref , ↵ = 2) width data [25ns]	1.8 ±0.3 6.5± 1.3 3.1	1.6 ± 0.2 5±1 3.1	2.1± 0.3 1.9 ±0.2 4.4±1 2.0 ± 0.3 1.4 1.7
	width sim (F ref , ↵ = 1) width sim (F ref , ↵ = 2)	14± 4 4.3±0.7	17.1 ± 2 3.8±0.3	3.3±2.8 2.9 ± 1.2 1.4 ±0.1 4.9±4

Table 5 .

 5 3: Maximum, and the width at half height for the events detected in radio and simulation with parameters (F ref , ↵ = 1), and (F ref , ↵ = 2) where F ref = 4⇥ 10 16 W/m 2 /Hz. For iron primary simulated showers.

  5.4 Comparison data/simulation and interpretationData analysis in microwave band the energy if the standard quality cuts are applied[START_REF] Ave | Precise measurement of the absolute fluorescence yield of the 337 nm band in atmospheric gases[END_REF].

		2
	nkov ring	20 % for
	ME data
	the obser-
	f geomag-
	ble appli-
	surement
	th a duty
	y 15 % for
	E experi-
	rande air
	Technol-
	overing a
	ntennas is
	imised for
	3 ⇥ 10 15 uilt on a
	t clusters
	with an-
	-4.2 GHz)
	parabolic
	d a multi-
	type were
	f time be-
	enna was
	ere tilted
	magnetic
	polarised
	ched feed
	5F). The
	rix in the
	eed horns
	ra during
	polarisa-
	was mea-
	[26]. The
	f the re-
	channels
	alf-power
	estimated
	s used to
	within an
	onse time
	time con-
	ery short
	µs before
	rande.
	ition, and
	SCADE-
	. The re-
	ival direc-
	nd about

a parsec (pc) is a distance unit used in astronomy. It corresponds to 3.26 light-years.

AcquisitionThe source flew at several distances, and emitted a sine wave at di↵erent frequencies. The source and the receiver have absolute GPS time, therefore we can relate the parameters of the source, like position and emission frequency, with the time at the receiver.

a fourth has been detected on the 14 th of July with a maximum of more than

. It is not shown in this thesis

Fundamentals

Data analysis in microwave band 5.3 Microwave signal simulation Data analysis in microwave band 5.4 Comparison data/simulation and interpretation

Bilan Lundi

Une matinée et une bonne partie de l'après midi passées à refaire les câblages signal et alimentation du LNA. On à essayer de suivre tout vos conseils (merci beaucoup) On a supprimé la connectique BNC sur la boite en plastique et on sort les 2 câbles RG58 par des passes-câbles. On a aussi raccourci la soudure du RG58 au LNA le plus possible (compte tenu de notre piètre capacité de soudeur...).

On a trouvé un blindage type flexible de douche mais gainé de plastique sur l'extérieur, plus pratique et bien plus efficace que le papier d'aluminium. FLEXAtight ((protective metal conduit liquid tight) de chez flexa (une boite allemande) type SPR-PVC-AS schwartz.

LNA Electronic Box

Figure 3.9: Final setup installed on the tank Vieira. The mast is tied with nylon cables. The amplifier (LNA) on top of the dipole has two cables soldered directly on it, one plugged to the power supply board, the other one to the EASIER board. Both of these board are located in a metallic electronic box placed under the dome where the SD acquisition electronic is placed too.

Installation

VHF band

[MHz] ν

Installation of the detectors

The first setup installed is a complete hexagon (7 detectors) centered on the tank Nene (local station ID: 342). The location of the EASIER detectors, in front of the FD building Los Leones, was chosen for a hybrid measurement of air showers, i.e. SD, FD and EASIER.

Detector Sensitivity

Detector developments and sensitivity in microwave band

Detector Sensitivity

The sensitivity is defined as the minimum microwave flux detectable out of the noise. We present first the expression of the sensitivity for the EASIER detector. Then we present a set of measurements performed to estimate the relevant parameter to compute the sensitivity.

Expression of the sensitivity

Noise fluctuations The noise amplitude sets the limit for a detectable signal. It was shown, for instance in [START_REF] Wilson | Tools of Radio Astronomy 5th edition[END_REF] that for an input noise signal with a Gaussian distribution processed by a square law detector, the relation between the mean noise < P noise > and its fluctuations P noise is simply :

When the RF input signal is filtered on a bandwidth ⌫ and the output of the square law detector integrated over a time ⌧ for instance with a low pass filter, the standard deviation is lowered by a factor p ⌫⌧ . In the case of EASIER the input voltage is the LNBF output and the square law detector is the power detector. The output filtering is performed first just after the power detector, and then by the low pass filter of the Auger SD front end. If we account for the factor p 2 in the integration time:

System temperature In the microwave band thermal noise is the main concern in the detector development. It can be expressed at the output of the amplification stage using the equivalent system temperature, T sys :

with k B the Boltzmann constant, G the gain of the system, ⌫ the bandwidth. T sys is the sum of the antenna noise and the electronic noise temperature.

Antenna temperature

The antenna noise temperature is related to the thermal emission of surrounding objects, it is useful to express it as the temperature that would have a black body emitting the same intensity. In the limit of h⌫ << k B T the intensity for a black body is expressed via Rayleigh-Jeans law:

For non black body emission, the same expression is kept replacing the thermodynamical temperature by the brightness temperature T B = ✏T . The brightness temperature of the sky at zenith is around 5 K whereas for the ground T B ' 300 K. To compute the spectral density of power received by the antenna one has to integrate over the solid angle accounting for its gain:

Calibration with an external source

We performed in November 2011, in collaboration with KIT researchers, a measurement with an octocopter carrying a source emitting sine waves at GHz frequencies and flying above the EASIER antenna located on the tank Jose Maria (LsId 419) in order to obtain an on site calibration of the whole detector. We first describe in detail the experimental setup used for this calibration, then a specific calibration of electronics performed in laboratory required to interpret the data, then we explain the data selection and the analysis to extract the signal of the octocopter out of the noise. Finally, we will exploit the data to reach an absolute calibration of the whole detector in the frequency band [3.65 -3.95 ] GHz.

Spiral antenna

Experimental setup

The experimental setup has two components: the EASIER detector and the signal emitter carried by the octocopter which can fly at predefined distances above the EASIER antenna.

The EASIER detector was already described in section 4.1, we describe thus only the source and the specific acquisition method.

The source The source carried by the octocopter [START_REF] Werner | [END_REF], shown in We forced the trigger of the local station to write the data from 100 th ms to the 150 th ms of each GPS second selecting a range of frequency from the source between 3.65 and 3.95 GHz. The selected range, in blue in Due to the electronics chain, the level in ADC counts decreases with the input power. Traces when the source is and is not emitting are compared to estimate the signal to noise ratio. The absolute measure of the signal is then retrieved using the absolute measure of the background noise power.

Specific electronics calibration

The response of the power detector is dependent on the waveform of signal input. The signal received when the source emits is a mixture of a sine signal and a noise waveform signal. To recover the useful signal from the source, we need a calibration for the noise only that gives us the reference power, as given by Eq. 4.2.6 and a calibration in term of signal to noise ratio is also required to retrieve the power added by the source. Such calibration was performed in laboratory.

The setup for this calibration is composed of a signal generator and a spiral antenna as a sine source and a LNBF receiver as source of noise. We record alternately the RF output and the power detector output. We first record 10 traces of pure background noise. Then we emit a sine waveform of increasing power and record for each input power 8 traces. We measured the factor A dB = 10 • log 10 ( (P sine + P noise)/P noise ) as a function of the di↵erence of voltages at the power detector output. We can then estimate the linear signal to noise ratio SN R linear = P sine /P noise knowing that A dB = 10 • log 10 (SN R linear + 1). The factor A dB is compared to the di↵erence of voltage it induces at the output of the power detector :

We recorded data at three frequencies: 3.4, 3.8, 4.2 GHz and performed a fit with the three frequencies together. The calibration curve is shown Fig. 4.31 together with a second order polynomial fit where we fix the origin point so that A dB = 0 for | V P D = 0|. The residuals shown in the same figure are taken as the uncertainties on this calibration.

Data analysis in microwave band (from [START_REF] Huege | Simulating radio emission from air showers with CoREAS[END_REF]).

Emission mechanisms in the microwave band

by the geomagnetic acceleration is expected to be polarized in the ṽ ⇥ B direction, with ṽ the arrival direction of the air shower and B the direction of the geomagnetic field. These two parameters, the distance of detection and the polarization, will help in disentangling between the underlying mechanism.

Microwave signal simulation

We present here the implementation of the simulation of the radio signal expected in case of an isotropic emission. We will then use these simulations to estimate if the events detected are compatible with such emission, and if the non detection of events at larger distance is compatible with the laboratory measurements presented in [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF]. The simulation process is composed of three main parts:

the microwave signal simulation the signal propagation from the point of emission to the antenna.

the detector simulation, comprising the antenna and the electronics.

Shower simulation

The profile simulation method is largely adapted from [START_REF] Salamida | [END_REF]. In this work, proton and iron showers at di↵erent energies from 10 17.5 to 10 21 eV are simulated with CORSIKA [START_REF] Heck | CORSIKA: A Monte Carlo code to simulate extensive air showers[END_REF]. The obtained profiles are fitted with a Gaisser-Hillas function N (X X 1 ) with X 1 the first interaction depth and:

where N max is the maximum number of shower particles and X max is the atmospheric depth at shower maximum in g/cm 2 . X 0 and are shape parameters, with related to the particle mean free path. The fit results give a parameterization in function of N max , X 0 , X 1 , X max , the primary mass and the energy of the shower. The complete description to retrieve these parameters is given in [START_REF] Salamida | [END_REF].

We used only the mean value of the parameters and their dispersion to simulate the air shower profiles. As an example, we show in Fig. 5.7 the simulated profile of 100 showers of iron and proton at an energy of 10 19 eV.

Microwave emission

The conversion from the particle profile to a microwave power is performed using Eq. 5.1.1. The reference number of particle N ref for a shower of energy E ref is taken from the parameterization in [START_REF] Salamida | [END_REF] and its value is

In [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF], the expected flux for an air shower of E ref = 3.36 ⇥ 10 17 at 10 km is found to be F E ref = 2.77 ⇥ 10 24 W/m 2 /Hz . We simulated the same shower a hundred times to check the consistency of our method. The mean flux is found to be around a factor 1.7 above

This di↵erence is caused by the choice of the reference number of electrons N ref .

The distribution of the maximum flux in the trace is shown in Fig. 5.8 (left) and the traces are depicted Fig. 5.8 (right). In order to agree with the estimation of the original paper, we normalize the flux with the corresponding factor (1/1.7).

Signal propagation

The microwave power is estimated along the shower axis at each distance in steps of 10 m. As we consider the emission isotropic, to estimate the flux at the detector we first account for a factor 1/4⇡R 2 . Then we consider the compression of the signal that occurs because of the propagation. The radiation from the air shower propagates with noise temperature The system temperature was described in chapter 4, it represents the noise power received by the antenna and the noise power added by the electronics:

The measurements of sensitivity reported in chapter 4 showed a di↵erent system temperature for the two setups installed. For the first one, the system temperature was measured between 40 and 180 K with the Karlsruhe method, and a temperature of around 50 K was deduced from the octocopter measurements. For the antenna of this setup, we will set the system temperature either at 40 K, 80 K or 180 K. For the antennas of the second setup the system temperature was found to be 30 K with the Karlsruhe method and by comparison of spectra, thus it will be set at this value for the simulations.

Radio frequency trace simulation The sum of the noise of the system and signal from EAS is not just the sum of the respective powers. The scheme in Fig. 5.12 (right) represents the di↵erent component of the total signal and the place they appear in the setup. The electric fields of the EAS signal (E signal ) and the thermal noise (E noise ) are added at the level of the antenna and yield a voltage at its output. Then the noise of the electronics amplification, V elec , is also added. These components are at high frequency and have to be summed in voltage (instead of power) to account for their random phase with respect to each other.

To simulate this e↵ect, we adopted the following method: we recorded a reference high frequency trace at the output of one antenna, and we transform P S (t) and P N into respectively V signal (t) and (V noise (t) + V elec (t)) by scaling this reference trace.

To simulate the noise temperature T sys we scale the trace such that the mean power equates the noise temperature:

where is a constant and the power is calculated on a 50 ⌦ impedance. We have then a trace of noise identical to the real background noise. The microwave signal, P S (t), obtained before is the envelope of the power. To add it to the noise trace we need to transform it in a high frequency trace. We normalize the reference

Microwave signal simulation

Data analysis in microwave band trace to obtain a waveform V norm (t) such that < V norm (t) 2 >= 1. Then the microwave signal, P S (t), is transformed to obtain the high frequency signal trace:

The total power is then estimated as:

We show for instance in Fig. 5.13 such simulation with a low system temperature to make the signal more visible out of the noise. The upper trace is the high frequency noise and the middle part shows the transformation from P S (t) to V signal (t). The lower part is the sum of the voltage traces. indicated that these detected events are di cult to explain with an isotropic emission and the parameters of emission tested.

We present here a more general study to estimate limits on the MBR flux. After defining the conditions to accept a radio event, we compare the number of real events detected with simulated events accounting for several emission parameters F ref and ↵.

As we want to set limits on an isotropic emission, we select only stations with distance to shower axis larger than 300 m. This way, we reduce the possible contribution of a beamed emission in the data. Then the noise is estimated thanks to the first part of the real traces where no radio signal is expected. The distributions of noise in trace fluctuation unit are shown for the two setups in Fig. 5.23. We find a maximum of noise1 = 7.2 for the first setup and noise2 = 8.4 for the second.

Then maxima of the radio trace are searched in a time window of 150 time bins around the particle signal start ([230-380] where the time bin of the signal start is around bin 242).

To accept a radio event, we require the maximum of the trace in the window [230-380] to be larger than the maximum noise noise . The colored distributions in Fig. 5.23 represent the maxima in the signal window and show that no event is found in the real data with the criteria defined above. We are interested in pointing limits above 10 19 eV, therefore we select events above this value. Moreover, the simulated events with a short Cherenkov peak like the one showed in Fig. 5.11 are removed by selecting only the simulations with a half maximum height larger than 100 ns.

The system temperature is taken to 180 K for the first setup to be consevative (it is the highest temperature measured in chapter 4). For the second setup, a temperature of 30 K was found with several methods and is thus chosen for the simulation. We scanned the range of parameters F ref 2 [2.5 ⇥ 10 17 16 ⇥ 10 16 ]W/m 2 /Hz and ↵ 2 [1 2] with steps of ↵ = 0.1. In total, the data set is simulated 20 times for proton and iron primary.

The number of events accepted in the simulation has to be compared with the data, i.e. no candidate in a null background. The upper limits are defined as the Feldman Cousins definition [START_REF] Feldman | A Unified approach to the classical statistical analysis of small signals[END_REF]. An upper limit with a 95% confidence level is set if more than 3.2 events are accepted in the simulation for a given set of parameters. The limits on the reference flux F ref as a function of the coherence index ↵ are given in Fig. 5.24 for proton and iron primary.

ENERGY SCALING

A scan in deposited energy was made by varying the beam current of the Van de Graaff. This changes the instantaneous number of electrons in the beam which in turn changes the energy deposit in the chamber. This scan makes it possible measure the emission scaling with energy deposit. Data was taken with all three of the low noise amplifiers in different frequency bands and in both cross polarized and co-polarized configurations. The beam intensity was monitored with the pick-up coil at the beam exit and a power analysis like that performed for the power spectrum measurements was performed. The resulting data from the energy scan is plotted in Figure 4. It is clearly seen that the signal level is consistent in both polarizations and between amplifiers. In both polarizations we have measured a signal which is increasing linearly with energy deposit.

CONCLUSION

We have measured a microwave emission signal from electron beam induced air plasma between 1 and 15 GHz. This emission is unpolarized and isotropic with a broadband continuum spectrum. This is consistent with predictions of EAS induced molecular Bremsstrahlung emission. We measure a linear 08008-p.5

Summary and Conclusions

The aim of my thesis has been to determine the feasibility of the measurement of UHECR mass composition using radio detection technique in coincidence with the Pierre Auger Observatory surface detector. Radio detection setups, in the VHF band and in the C-band (3.4-4.2 GHz), have been developed. In each band, one test hexagon has been installed on site in 2011. It was then extended to 61 units in the C-band and replaced by a new setup in the VHF band in 2012. I was deeply involved in the R&D phase, in the deployment and installation of the antennas and in data analysis.

My main contributions to the detector developments are: the choice of the suitable electronics, in terms of bandwidth and dynamic range.

the validation and the end-to-end calibration of the detector to accommodate the dynamic range of 40 dB in the VHF band and 20 dB in the C-band. the deployment of the detectors in the Argentinian pampa comprising the on site hardware tests and calibration.

In the next step, my work was focused on the determination of the detector sensitivity in the C-band by measuring the system temperature and determining the minimum detectable flux.

the noise temperature of electronics was measured by two di↵erent techniques. The use of a dedicated noise meter yielded a temperature of 201± 30 K. Using a second method, a comparison of spectra in di↵erent noise conditions, we obtained a temperature of 23 ± 2 K in agreement with the measurements performed by other groups. The high temperature found with the noise meter compared to other techniques may come from an important loss in the connections of the setup used. a measurement of sensitivity was conducted on site using an external calibrated source. The minimum detectable flux has been estimated to be F = 4 ⇥ 10 19 W/m 2 /Hz ± 11% ± 50%.

The first prototype in the VHF band has been working in stable conditions for four months. I performed a search for radio events in the data set. 36 candidates were found with a signal to noise ratio above 10 and in coincidence with the particle signal. the amplitude of the electric field detected decreases exponentially with the distance to the shower axis with a characteristic distance of around 200 m for vertical showers.

the events exhibit a preferred arrival direction, 23 events were reconstructed with a south direction compared to 9 with a north direction. This e↵ect is a combination of the expected geomagnetic contribution and the antenna pattern.

In the C-band, the data analyzed are the combination of the first hexagon data and the additional 54 detectors data. A search for events yielded a total of three event candidates largely above the noise, including the first cosmic ray event ever detected in the C-band. Their amplitudes are all above 10 , two of them have an energy above 10 19 eV and one below 3 ⇥ 10 18 eV. The maximum distance of detection is less than 300 m.

In order to interpret the observed events, I developed the entire chain for the simulations, starting from the expected shower profile up to the final data acquisition processing.

A parameterized air shower particle profile is converted to the microwave power according to the beam measurements reported in [START_REF] Gorham | Observations of Microwave Continuum Emission from Air Shower Plasmas[END_REF]. Then the propagation of the signal from its production point to the detector accounts for a realistic refraction index of air and then the signal is fed into the electronics simulations. The lateral distribution of the electromagnetic part of the shower has not yet been included in the simulation chain.

The power detector response is simulated with a time of integration of 35 ns and 5 ns respectively for the first and the second setup. It is found to describe the power detector response with an uncertainty below 1 dB.

Using the value of the reference flux observed in beam experiment (F ref = 4 ⇥ 10 16 W/m 2 /Hz), and a coherence factor ↵ = 1 or ↵ = 2, the three events observed cannot be reproduced by an isotropic emission.

Using the events with an energy larger than 10 19 eV and the detector further than 300 m, an upper limit on the expected flux has been calculated. The present limit, F ref  8 ⇥ 10 16 W/m 2 /Hz with ↵ 1 is currently the best limit on the MBR emission.

In the C-band, larger statistics of detected events will allow to characterize better the emission. An excess of detection in East West polarized antennas would sign a geomagnetic contribution. The improvement of the sensitivity can be achieved by lowering the noise temperature and by shifting the band of observation at lower frequencies to increase the e↵ective area. A noise temperature reduced by 50% and a central frequency reduced by a factor three would improve the signal to noise ratio by more than a factor 10.

Appendix B: Installation data

We report here useful data for the GHz calibration of first and the second setup. We give the GPS time of installation, the regulated voltage, the threshold voltage and the slope of the regulator for the 54 detectors. The data of two installed detectors are missing. Ultra high energy cosmic ray composition is crucial to determine their source. Current techniques measure it with a limited duty cycle of 10%. The EASIER project (Extensive Air Shower Identification using Electron Radiometer) is a radio detection system integrated with the surface detector of the Pierre Auger Observatory. Its goal is the measurement of the mass composition at high energy via the observation of the electromagnetic profile of air showers with a 100% duty cycle. The principle of EASIER was applied in the VHF band in which a coherent signal was already observed and in the C band (3.4-4.2 GHz) in which an isotropic emission is expected. A large part of this thesis describes the developments and calibration of the experimental setups in both bands. The installation of 7 detectors in the VHF band led to the detection of 36 events. Their characteristics indicate an emission beamed around the shower axis with a characteristic distance of the order of 200m for vertical showers. In the C band, 7 detector units were installed and led to the first detection of a radio signal in this band. The extension to 61 units raised the number of candidates to 4, all detected at distances to the shower axis lower than 300m. The comparison with simulations allowed us to set limits on the parameters of an isotropic emission. The distances of detection are limited by the emission mechanism and are up to now too small to fulfil EASIER goals. Improvements are underway to lower the sensitivity in both bands.

Romain GAÏOR EASIER: Extensive Air Shower Identification using Electron Radiometer