R Poschl

F Richard

N Van Der Kolk

T Naito

S Kuroda

K Kubo

O Blanco

D El Khechen

L Garolfi

Yingtao Chen

Keywords: Capteur diamant, halo du faisceau, électrons de recul Compton, ATF2, wire scanner Diamond sensor, Beam halo, Compton recoil electrons, ATF2, Wire scanner vi horizontal beam halo distributions . . . . . . . . . . . . . . 9 Compton recoil electrons measurements

L'étude détaillée des distributions transverses du halo du faisceau est importante du point de vue des pertes de faisceau et du contrôle du bruit de fond dans ATF2 et les futurs collisionneurs linéaires (FLC). Un nouveau type de capteur diamant sous vide (DSv) déplacable, avec quatre pistes, a été conçu et développé pour la mesure des distributions transverses du halo du faisceau et la détection du spectre des électrons de recul Compton après le point d'interaction (IP) d'ATF2, qui est un prototype à basse énergie (1.3 GeV) de la section de focalisation finale pour les projets de collisionneurs linéaires ILC et CLIC.

Cette thèse présente les études du halo du faisceau et des électrons de recul Compton, ainsi que la caractérisation, les études de performance et les tests des capteurs diamant (DS), tant sur PHIL, un photo-injecteur à basse énergie (<10 MeV) au LAL, que sur ATF2. Les résultats des premières mesures du halo du faisceau, utilisant des wire scanner (WS) et un DSv, sur ATF2 sont également présentés et comparés dans cette thèse.

Des simulations utilisant Mad-X et CAIN ont été réalisées afin d'estimer le nombre d'électrons composant le halo du faisceau ainsi que le nombre d'électrons de recul Compton. Les résultats des simulations ont indiqué qu'une grande gamme dynamique, supérieure 10 6 , est nécessaire pour une mesure simultanée du coeur du faisceau, du halo du faisceau et des électrons de recul Compton. Un DSv mono-cristallin, fabriqué par CVD (Chemical Vapor Deposition), a été développé dans ce but.

Avant l'installation du capteur diamant, une première tentative de mesure du halo du faisceau a été effectuée en 2013, en utilisant les wire scanners (WS) actuellement installés sur ATF2. En raison de leur dynamique limitée de ∼ 10 3 , la distribution du halo du faisceau a été mesurée seulement jusqu'à ∼ ±6σ dans la ligne d'extraction (EXT). Un paramétrage des distributions mesurées du halo du faisceau a montré que les distributions mesurées sont cohérentes avec des mesures faites précédemment, en 2005, sur l'ancienne ligne faisceau d'ATF. Durant ces mesures, une distribution asymétrique du halo vertical du faisceau a été observée pour la première fois en utilisant le WS situé après l'IP, son origine est actuellement sous investigation en utilisant le DSv.

Des études pour caractériser des capteurs diamants de dimensions 4.5 × 4.5×0.5 mm 3 ont été réalisées en utilisant des sources α et β. Les paramètres de transport des porteurs de charge (durée de vie, vitesse de saturation, etc.) ont été obtenus en utilisant la technique des courants transitoires (TCT). Par ailleurs, la linéarité de la réponse du DS a été testée sur PHIL avec différentes intensités de faisceau après la fenêtre de sortie de d'accélération. Un signal maximum de 10 8 électrons a été mesuré, avec une réponse linéaire jusqu'à 10 7 électrons. Des études similaires de la linéarité ont été faites pour le DSv sur ATF2. Nous avons pu y exploiter avec succès, pour la première fois une gamme dynamique de ∼ 10 6 , permettant de mesurer simultanément le coeur du faisceau (∼ 10 9 électrons) et le halo du faisceau (∼ 10 3 électrons). Le pick-up électromagnétique induit par le passage du coeur du faisceau et des effets de saturation, qui sont les limitations empêchant actuellement le DSv d'atteindre une gamme dynamique supérieure à 10 6 , ont également été identifiés et étudiés.

Les premières mesures de la distribution horizontale du halo, en utilisant le DSv, ont été effectuées jusqu'à ±20σ x , et ont permis de prouver que le halo du faisceau est collimaté par les ouvertures de la ligne ATF2. Une distribution horizontale du halo compatible avec les paramétrages de 2005 et 2013 a été confirmée. La possibilité de détecter les électrons de recul Compton a été étudiée. Différentes solutions pour accroître la sensibilité des mesures ont été proposées.

List of Figures

3 GHz superconducting niobium nine-cell cavity with its schematic layout (upper) and longitudinal cross section of the ILC cryomodule (Type B) (lower) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 BDS lattice layout, showing the major sub-systems. Shown is the electron BDS, which starts at the vertical dotted line. (Also shown is the positron system upstream of the electron BDS). The positron BDS is a mirror image. 2.10 Sketch of ILC collimation system (modified from ). . . . . . . . . . . . . . 2. [START_REF]ATF2 Proposal[END_REF] An earlier version of BDS optics (from the entrance of collimation system to the IP), with consumable spoilers (S) and absorbers (A) (modified from ). 2.12 Telescope optics for the FFS. . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 Chromaticity aberration from the strong final doublet for a particle with on and off-momentum respect to the nominal value (upper) and the correction of it by a sextupole magnet (lower) (modified from ). . . . . . . . 2.14 Non-local (upper) and local (lower) chromaticity correction. . . . . . . . . nal trigger given by the scintillator for all the recorded events (upper) and events above 10 mV fitted to Landau distribution (lower) . . . . . . . . . 6.14 Signal from collected electrons (negative pulse) and holes (positive pulse) 6. [START_REF] Tenenbaum | Sources of Beam Halo in the Next Linear Collider Main Linac[END_REF]

Introduction

The Standard Model of particle physics has so far been successfully predicted and classified the discovery of all the subatomic particles, including the Higgs boson, which was discovered in 2012 [START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF]2] at the Large Hadron Collider (LHC) [3]. However, despite the success of the Standard Model and the discovery of the Higgs boson, fundamental questions as the origin of the dark matter and matter-antimatter asymmetry observed in the universe remain. Moreover, a clear explanation for the origin of the Higgs mechanism, and a full confirmation of the properties of the discovered Higgs boson are not yet available. Further more precise investigations of the Higgs boson and of new physics expected beyond Standard Model requires both higher collision luminosity and energy. The LHC High Luminosity upgrade (HL-LHC) [START_REF] Zimmermann | HL-LHC: Parameter space, constraints, and possible options[END_REF] is planned to increase the peak luminosity to 5 × 10 34 cm -2 s -1 , however, in order to perform detailed studies of the Higgs boson with higher precision, lepton colliders such as a e --e + machine are essential complementary instruments.

Possible candidates for such e --e + machines include circular colliders, as planned in the context of the Future Circular Collider (FCC-ee) [5] at CERN and Circular Electron Positron Collider (CEPC) [6] in China, and Future Linear Colliders (FLC) as the Compact Linear Collider (CLIC) [7] at CERN and International Linear Collider (ILC) [8] under consideration in Japan. One of the limits of circular colliders is that, once the circumference is defined, the maximum achievable energy is restricted by the emission of synchrotron radiation. The advantage of linear colliders is their potential for upgrading the energy by extending the length. The ILC machine aims to achieve 200-500 GeV (extendable to 1 TeV) centre-of-mass with a luminosity of > 0.75 × 10 34 cm -2 s -1 , based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating technology. In order to achieve the required high luminosity, focusing of ultra-low emittance beams to nanometre level at the collision point is required.

The Accelerator Test Facility (ATF) [9] at KEK in Japan is a prototype of the damping ring built to demonstrate the small emittance beams required for the FLC. And the ATF2 [START_REF] Group | ATF2 Proposal[END_REF][START_REF]ATF2 Proposal[END_REF], which uses the extracted beam from ATF, is a scaled down Final Focus System (FFS) prototype of the FLC with the aim to demonstrate nanometre level

INTRODUCTION

focusing based on local chromaticity correction. World records of normalised vertical emittance (3 × 10 -8 m in 2003) [START_REF] Honda | Achievement of ultralow emittance beam in the accelerator test facility damping ring[END_REF] and vertical beam size (∼44 nm in 2014) [13] have been achieved by ATF and ATF2, respectively.

A major issue in ATF2 and all the future colliders is the control of beam halo before the interaction point (IP). Beam halo consists of tails extending far beyond the Gaussian core of the beam. These tail particles can likely be intercepted by apertures near the Final focusing quadrupole Doublet (FD). Fluxes of muons and other secondary particles which are then created, could easily exceed the tolerable levels at a detector by a few orders of magnitude [START_REF] Mokhov | Beam collimation and machine-detector interface at the International Linear Collider[END_REF]. Minimisation of detector background therefore needs efficient removal of the beam halo by upstream collimation. Dedicated collimation sections are planned and designed for the FLC based on the assumptions and experience from the SLAC Linear Collider (SLC) concerning the population and propagation of halo particles [START_REF] Tenenbaum | Sources of Beam Halo in the Next Linear Collider Main Linac[END_REF].

At ATF2, beam halo hitting on the FD and the beam pipe after the IP can generate a large amount of background through bremsstrahlung for the measurements of the nanometre beam size using the laser interferometer beam size monitor (Shintake monitor) [16]. Although a dedicated collimator system downstream of the IP is used to collimate such background photons at the entrance of the Shintake monitor, there is at present no dedicated collimator for the beam halo itself1 . Therefore, the beam halo issue remains and may limit the use of the largest horizontal and vertical demagnification factors available in the optics. Dedicated collimators are however now being prepared within the collaboration [START_REF] Fuster-Martínez | Design Study and Construction of a Transverse Beam Halo Collimation System for ATF2[END_REF]. The design of the collimator strongly relies on the transverse beam halo distribution which is currently unknown for the ATF2 beam line. Hence, beam halo measurements are required for the investigation of transverse beam halo distribution.

One important issue for beam halo measurements is to reach a high dynamic range. The beam halo is expected to be ∼ 10 -3 of the total beam population based on experience from the SLC and past measurements. Beam core measurement are required for the proper normalization of the beam halo. Beam halo measurements using wire scanners in the old extraction line of ATF reached a dynamic range of ∼ 10 4 [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF]. Recent wire scanner measurements in the present ATF2 beam line however only achieved a dynamic range of ∼ 10 3 due to less favourable background conditions [START_REF] Liu | Beam Halo Measurements using Wire Scanners at ATF2[END_REF]. Single crystalline Chemical Vapor-Deposition (sCVD) diamond sensors are not only sensitive to single electron but have also been tested to have a linear response up to 10 7 electrons [START_REF] Liu | Status of Diamond Detector Development for Beam Halo Investigation at ATF2[END_REF]. Two sCVD in vacuum Diamond Sensors (DSv) have been developed for this reason. The first DSv was installed for horizontal beam halo scanning after the interaction point (IP) of ATF2 in Nov. 2014. It aims not only to measure the beam halo distribution with large dynamic range (> 10 6 ), but also to investigate the possibility of probing the Compton recoil electrons produced in the interactions with the Shintake monitor laser beams.

Demonstrations of a beam halo monitor using polycrystalline CVD (pCVD) diamond detectors for observing electron beams directly inside the vacuum chamber was carried out at the SPring-8 Angstrom compact free-electron laser (SACLA) facility [START_REF] Aoyagi | Pulse-mode measurement of electron beam halo using diamond-based detector[END_REF]. In this experiment, a pair of diamond-based detectors is mounted on the upper and lower side of the beam center to measure the beam halo on the two sides of the beam core, which passes through the gap between the two detectors without interacting with them. This detector has achieved a lower detection limit of 2 × 10 3 electrons/pulse for single-shot measurement. Meanwhile, a linear response up to 10 7 electrons/pulse has also been demonstrated. However,"in vacuum" tests of diamond detector beyond 10 7 electrons have not yet been described in any reference.

In our experiment, we have successfully performed a simultaneous beam core (∼ 10 9 e -) and beam halo (∼ 10 3 e -) measurement using a sCVD based diamond sensor [START_REF] Liu | Investigation of beam halo using in vacuum diamond sensor at ATF2[END_REF]. It is the first time to our knowledge that a scanner based on a diamond sensor is used successfully to measure the beam core and beam halo with a dynamic range of 10 6 inside the vacuum chamber of an accelerator.

This thesis is divided into four parts: Part I gives a general introduction on the ILC project and on the ATF/ATF2 facility. The physics motivation and the accelerator design of ILC, with emphasis on the beam halo collimation, are described in Chapter 2. The goals of ATF2 and recent status of the progress in achieving these goals are presented in Chapter 3, together with the instruments used for beam diagnostics.

Part II presents the simulations on the beam halo and Compton recoil electron studies, in Chapter 4, followed by initial beam halo measurements using wire scanners, in Chapter 5.

Part III introduces the properties of the CVD diamond sensors, in Chapter 6, followed by the design and characterisation of the DSv, in Chapter 7.

Part IV presents the beam halo measurements done using the horizontal DSv, in Chapter 8, with a discussion on the possibility of probing Compton recoil electron, in Chapter 9, and finally a summary of the results and future prospects, in Chapter 10.

INTRODUCTION

2

International Linear Collider

Motivations for building linear colliders

The fundamental interactions including electromagnetic, weak and strong interactions between the elementary particles are explained by the Standard Model of particle physics, which has demonstrated huge and continued successes in providing verifiable experimental predictions. However, there remains some unsolved problems in particle physics, which can not be explained by the Standard Model. These problems include:

• Origin of mass: the Standard Model postulates a field, called the Higgs field, that gives rise to the asymmetrical force which creates the masses of the quarks, leptons, and bosons. However, it does not explain the properties of this field.

• Mass hierarchy: the Standard Model does not explain why the basic particles of matter are the quarks and leptons, or how many of these there should be. In the Standard Model, there is no explanation for the large difference between the masses of the different quarks and leptons. The mass of the top quark is much higher than the one of the others quarks, and this is even more dramatic if we compare to the masses of the leptons. The mass range of all the fermions runs on 11 orders of magnitude, without explanation. Besides, the Standard Model assumed that neutrinos are massless. However, the experimentally established phenomenon of neutrino oscillation requires neutrinos to have nonzero masses [START_REF] An | Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay[END_REF].

• Gravity: gravity as one of the four fundamental forces is not included in the Standard Model, the Standard Model does not explain how gravity is connected to the other forces of nature.

• Dark matter and dark energy: the estimated amount of dark matter is ∼27% of the total energy of the universe, much higher than the amount of usual matter, which accounts for only 5% of the total. The rest 68% is given by the dark energy which is thought to be very homogeneous, not very dense and is not known to

INTERNATIONAL LINEAR COLLIDER

interact through any of the fundamental forces other than gravity. The Standard Model doesn't contain an explanation for these weakly interacting particles.

• Matter and antimatter asymmetry: the Standard Model cannot explain why the universe contains atomic matter made of electrons, protons and neutrons but no comparable amount of antimatter.

Therefore, different theories beyond the Standard Model (also called new physics) are developed to explain these problems. However, in order to find the right theory, experimental validations are essential. These experiments can be divided into three groups: the energy frontier, the intensity frontier and the cosmic frontier (see Fig. 2.1) as described below [START_REF] Panel | US Particle Physics: Scientific Opportunities A Strategic Plan for the Next Ten Years Report of the Particle[END_REF]:

1) The energy frontier: direct production and investigation of new particles using high-energy colliders. These colliders including the currently in use colliders, such as LHC, and future planned colliders, such as ILC, CLIC, CEPC-SppC.

2) The intensity frontier: indirect detection of new phenomenon, using intense particle beams, such at KEKB and BEPC, to uncover properties of neutrinos and observe rare processes that will tell us about new physics beyond the Standard Model. These experiments [START_REF] Hewett | Fundamental physics at the intensity frontier[END_REF] including the reactor neutrino experiment, such as the MINOS, Double Chooz, Daya Bay [START_REF] An | Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay[END_REF] and precision measurements of quarks and leptons, such as Mu2e and COMET.

3) The cosmic frontier: direct or indirect detection of new particles (e.g. dark matter) produced in the cosmos using ground and space based detectors. Example of these experiments are AUGER, CDMS and LHAASO.

High-energy colliders, being the energy frontier, have been used to discover new particles and directly probe the architecture of the fundamental forces since the 1960s.

From the view point of colliding particles, there exist two kinds of high-energy colliders: hadron and lepton colliders. Although the hadron colliders (e.g. LHC) are powerful tools to make discoveries by collisions of composite particles (quarks, anti-quarks and gluons), lepton colliders (e.g. ILC) have the advantage of making precision measurements by the collision of "point-like" elementary particles. Beside, leptons do not interact through the strong force, so the background level is lower than with hadron collisions. Therefore, for precision measurements, lepton colliders are preferable.

From the view point of accelerator layout and design, the high-energy colliders can be divided into linear and circular colliders. Comparing with the circular colliders, linear colliders don't suffer from the energy loss by the synchrotron radiation emission1 , which limits the maximum achievable energy of the circular colliders.

Therefore, ILC, being one of the energy frontier machines and being an e --e + linear collider, can provide an ideal setting for detailed exploration of the origin and nature of the Higgs field, dark matter, and other questions of particle physics.

Design of the ILC

Figure 2.1: Three frontiers of high energy physics with the problems that can be solved by them [START_REF] Panel | US Particle Physics: Scientific Opportunities A Strategic Plan for the Next Ten Years Report of the Particle[END_REF].

Design of the ILC

ILC is a high-luminosity linear electron-positron collider based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating technology. Its centre-of-mass energy range is 200-500 GeV (extendable to 1 TeV), which has been optimised to provide the maximum attainable physics performance with a relatively low risk and minimum cost.

Parameter optimizations for ILC

One of the key requirements the physics community has to the builders of a collider is to reach a certain luminosity. The goals for ILC are particularly challenging, as a luminosity an order of magnitude larger than ever reached in a high energy electron position collider is required [START_REF] Behnke | The ILC: The next step in Particle Physics[END_REF].

The luminosity of collision is given by [START_REF] Herr | Concept of luminosity[END_REF]:

L = f rep n b N 2 4πσ x σ y H D (2.1)
where f rep is the repetition frequency of the bunch trains, N is the number of particles of the colliding bunches, n b is the number of bunches per train, σ x and σ y correspond to the horizontal and vertical beam sizes at the Interaction Point (IP), and H D is the enhancement factor resulting from self focusing of the beams during the collisions.

From the definition given by Eq. 2.1 it can be seen that for a high luminosity, high

INTERNATIONAL LINEAR COLLIDER

f rep , n b and N are important, as well as, small σ x and σ y . To obtain a given luminosity, several constraints and effects must be considered when specifying the parameters [START_REF] Renier | Implementation and validation of the linear collider final focus prototype: ATF2 at KEK[END_REF]:

• The repetition frequency f rep of the trains and the number of bunches per train n b are defined by the accelerating technology. f rep is also driven by the total power cost.

• The colliding bunch population N is mainly limited by electromagnetic wake-field effects which kick the bunches and can increase their effective size. Wake-fields are generally lower in ILC with its large cavities running at 1.3 GHz than in the Compact Linear Collider (CLIC) with its narrow cavities running at 12 GHz.

• The horizontal beam size is limited by the need to limit the emission of beamstrahlung1 [START_REF] Augustin | Limitations on Performance of e+ e-Storage rings and Linear Colliding Beam Systems at High Energy[END_REF] (see Eq. 2.2 for the beamstrahlung power emission function of the center-of-mass energy E cm ) at the level of a few % of the beam energy, while the vertical beam size is limited by the chromaticity correction which depends on the optics design and by the possibility to correct for high order beam aberrations.

The beamstrahlung can be expressed as [START_REF] Chao | Handbook of accelerator physics and engineering[END_REF]:

δ B ≈ 0.86 er 3 e 2m 0 c 2 E cm σ z N 2 (σ x + σ y ) 2 (2.2)
where e is the electron charge, r e the classical electron radius, N the number of particles colliding, and σ x,y,z the beam sizes in the three spatial dimensions.

• The longitudinal beam size is limited by the hourglass effect [32] if the beam size is long compared to the longitudinal extent of the focal point, it will decrease the luminosity. The vertical beta function at the IP must be similar to the longitudinal beam size or at least it should not be much smaller than σ z . Bunch compressors can be used to reduce the longitudinal beam size to allow a stronger focusing.

Comparing Eq. 2.1 and Eq. 2.2, it can be seen that it is desirable to make (σ x σ y ) small to maximize the luminosity while keeping (σ x + σ y ) large to reduce the relative energy loss δ B . A compromise solution for this is a "flat beam" with σ x σ y . The parameters for several center-of-mass energies including possible upgrades and staging for ILC are shown in Table 2.2. These parameters represent conservative operating points resulting from optimisation subject to the constraints imposed by the various accelerator sub-systems [8]. The ILC accelerator complex consists of polarised electron and positron sources, two damping rings (DR) with a circumference of 3.2 km, two Ring To Main Linac (RTML) transport lines, two 11 km main linacs and two 2.2 km Beam Delivery Systems (BDS) (see Fig. 2.3). The total length of the ILC complex is ∼ 31 km long.

Design of the ILC

INTERNATIONAL LINEAR COLLIDER

Accelerator components

Electron source

In a linear collider, polarised beams are preferred as the collision of two polarised beams can suppress some background processes and improve signal to noise ratio thereby enhancing the effective luminosity [33]. Therefore polarised electron and positron sources are essential.

The polarised electron sources are based on a photocathode DC gun. The schematic layout of this system is shown in Fig. 2. [START_REF] Zimmermann | HL-LHC: Parameter space, constraints, and possible options[END_REF].

The electron beam is produced by a laser illuminating a strained GaAS photocathode in a DC gun, providing the necessary bunch train with greater than 80% polarisation. Two independent laser and gun systems provide redundancy. The produced beam with a bunch charge of 4.5-5 nC and bunch length of 1 ns is bunched down to about 20 ps and pre-accelerated to 76 MeV by normal-conducting structures. After that, a superconducting linac is used to accelerate the beam up to 5 GeV. Before injection into the damping ring, superconducting solenoids rotate the spin vector into the vertical, and a separate Type A (see Section 2.2.2)superconducting RF cryomodule is used for energy compression.

Positron source

For the polarised positron source, the positrons are obtained from electron-positron pairs by converting high energy photons produced by the up to 150 GeV main electron beam passing through a 147 m superconducting helical undulator. The schematic layout of this system is shown in Fig. 2.5.

To generate photons from undulator radiation, the electron beam for collision is used. The generated polarized photons with maximum energies from ∼ 10 MeV up to ∼ 30 MeV are directed onto a rotating 0.4 radiation-length Ti-alloy target ∼ 500 m downstream, where electron-positron pairs are produced 1 . A normal conduction Lband RF and solenoid focusing system captures the positrons and accelerates them to 125 MeV. The electrons and remaining photons are separated from the positrons and dumped. The positrons are accelerated to 400 MeV in a normal conducting L-band linac with solenoid focusing. After that, the positrons undergo the acceleration, spin rotation and energy spread compression processes similar to the electrons before the injection to positron damping ring.

Damping rings

The damping rings must accept e and e + beams with large transverse and longitudinal emittances and damp them (by five orders of magnitude for the positron vertical emittance) to the low-emittance beam required for luminosity production, within the 200 ms between machine pulses (100 ms for 10 Hz mode), which is accomplished by approximately 113 m of superferric wigglers (54 units × 2.1 m) in each damping ring. This technology makes the particles radiate as fast as possible. Besides, the damping 1 Since a large amount of gamma rays concentrate on the short duration, the production target destruction is feared. To mitigate this effect, a 100 m/s target rotation speed is required [START_REF] Kuriki | Lecture I2 -ILC[END_REF].

INTERNATIONAL LINEAR COLLIDER

Design of the ILC

Ring to main linac

The electron and positron Ring to Main Linac (RTML) systems are the longest contiguous beamlines in the ILC. The layout of the RTML is identical for both electrons and positrons, and is shown in Fig. 2.7. The RTML consists of the following subsystems, representing the various functions that it must perform:

• a 15 km long 5 GeV transport line (ELTL);

• betatron-and energy-collimation systems (in ERTL);

• a 180 • turn-around, which enables feed-forward beam stabilisation (ETURN);

• spin rotators to orient the beam polarisation to the desired direction (ESPIN);

• a two-stage bunch compressor to compress the beam bunch length from several millimetres to a few hundred microns, as required at the IP (EBC1 and EBC2).

The two-stage bunch compressor includes acceleration from 5 GeV to 15 GeV in order to limit the increase in fractional energy spread associated with bunch compression. The acceleration is provided by sections of SCRF main-linac technology. A primary challenge for the RTML systems is the preservation of the emittance extracted from the damping rings; the combination of the long uncompressed bunch from the damping ring and large energy spread (after compression) make the tuning and tolerances particular demanding. However, tuning techniques developed from detailed simulations have demonstrated acceptable emittance growth [8].

Main Linac

The ILC Main Linacs accelerate the beam from 15 GeV to a maximum energy of 250 GeV with an average accelerating gradient of 31.5 MV/m. Beam acceleration is provided by ∼ 7400 1.3 GHz and 1 m long superconducting nine-cell niobium cavities operating at 2 K, assembled into ∼ 850 cryomodules (see Fig.

Beam Delivery System

The BDS is responsible for transporting the beams from the exit of the high energy linacs, focusing them to the required sizes, bringing them into collision, and transporting the spent beams to the main beam dumps. The layout of BDS is shown in Fig. 2.9. It consists of five main subsystems:

• Diagnostic: this section contains emittance measurement and matching (correction), trajectory feedback, polarimetry and energy diagnostics;

• The collimation system: the collimation system removes beam-halo particles that would otherwise generate unacceptable background in the detector and also contains magnetised iron shielding to deflect muons generated in the collimation process;

• The final focus system (FFS): the FFS uses strong compact superconducting quadrupoles to focus the beam at the IP, with sextupoles providing local chromaticity correction;

• The interaction region: the interaction region can be occupied by two detectors in a so-called "push-pull" configuration;

• The extraction line: the extraction line has a large-enough bandwidth to cleanly transport the heavily disrupted beam to a high-power water-cooled dump, and also contains important polarisation and energy diagnostics.

Design of the ILC

The collimation system and the FFS are described in more detail in the following sections.

Beam halo and beam halo collimation in linear colliders

One of the main challenges of the BDS design for the linear collider is to remove the large amplitude particles (beam halo) from the linac to minimize background in the detectors [START_REF] Seryi | Lecture 7 -Beam delivery & beam-beam[END_REF].

In linear accelerators, the sources of beam halo formation can be divided into three groups [35]:

• particle process sources: beam gas scattering, intra-beam scattering, (quasi) elastic and inelastic bremsstrahlung etc.

• optical related sources: mismatch, coupling, dispersion, non-linearities

• other sources: regeneration of particles when halo is intercepted, noise and vibration, dark currents, wake-fields, etc.

Interactions of the beam halo with the detector and other components in the BDS would create fluxes of muons and other secondaries which could exceed the tolerable levels at a detector by a few orders of magnitude [START_REF] Mokhov | Beam collimation and machine-detector interface at the International Linear Collider[END_REF]. Minimisation of detector background needs efficient removal of the beam halo. A collimation system is designed to scrape the beam halo away. The requirements of collimation system is defined by the IR layout [36,37].

INTERNATIONAL LINEAR COLLIDER

The collimators need to be placed far from the interaction point to minimise the background in the vertex detector (VX). Meanwhile, the beam halo must be collimated upstream in such a way that no beam halo and synchrotron radiation (SR) photons emitted from halo particles reach the final doublet magnets (FD) or the VX. The VX aperture needs to be larger than the FD aperture, and the exit aperture should be larger than the VX aperture.

The beam convergence depends on the optical parameters, while the maximum allowed halo convergence is determined by the geometry, in terms of the maximum allowed amplitude of particles at the entrance of the FD. The ratio θ halomax /θ beam , defined as the collimation depth, becomes tighter with larger l * or smaller IP beam size (see Fig. 2.10). A tighter collimation system may lead to problems for the machine protection system (MPS) and induce collimation wake-fields or higher muon flux from collimators [38]. The collimation depths for the ILC design are approximately 8-10 σ x * and 60-80 σ y * for the horizontal and vertical planes, respectively. [38]).

The collimation system in the BDS can be divided into two subsystems: upstream and downstream collimation. The upstream collimators are mainly used for betatron and energy collimation and the downstream collimators in the extraction lines1 serve to protect the magnets from radiation loads [36].

The betatron collimators use a two stage collimation approach: a thin (0.5-1 radiation length) spoiler followed by a thick ( 20 radiation length) absorber at the appropriate phase advance in the lattice [START_REF] Seryi | Lecture 7 -Beam delivery & beam-beam[END_REF]. This two stage design can mitigate the collimator damage due to the intense beam.

The energy collimators help to remove the degraded energy particles originating from the betatron collimation section but not absorbed there. The energy collimation section has a single spoiler located at the central high dispersion point. Fig. 2.11 shows the optics of the BDS, starting from the entrance of the collimation system to the IP. The location of the spoilers and absorbers are shown. The collimators are placed both at FD betatron phase and at IP phase with two spoilers per FD and IP phase. The energy collimator is placed in the region with large dispersion and secondary clean-up collimators are located in the final focus system (FFS). Beside, the FFS Figure 2.11: An earlier version of BDS optics (from the entrance of collimation system to the IP), with consumable spoilers (S) and absorbers (A) (modified from [37,[START_REF] Seryi | Lecture 7 -Beam delivery & beam-beam[END_REF]). includes two superconducting octupole doublets which use nonlinear focusing to reduce the amplitudes of beam halo particles while leaving the beam core untouched [37]. This "tail-folding" would permit larger collimation amplitudes, which in turn would reduce the amount of beam power intercepted and the unwanted wakefields [START_REF] Seryi | Design of the beam delivery system for the International Linear Collider[END_REF].

Final Focus System

The FFS utilises a number of quadrupoles (minimum 4) to construct a telescope to "demagnify" the incoming beam ellipse to a smaller size. The schematic layout of the telescope optics for the FFS is shown in Fig. 2.12. In this optics, two final lenses (final doublet (FD)) are used before the IP for the final focus, one mainly for x and another mainly for y. Use this optics, the beam size can be demagnified by a factor:

m = f 1 /f 2 = f 1 /l * (2.3)
where f 1 and f 2 are the focal lengths of the first two lenses and the FD respectively, and l * = f 2 represents the distance between the FD and the IP. The focal lengths are defined by the magnet strengths. For the ILC, the design value of l * is about 4 m1 . Very strong superconducting quadrupoles with gradients of the order of hundreds of Tesla per meter are required to reach focal lengths of this order.

Chromaticity aberration

If there would be no energy spread in the beam, a telescope optics could serve as the FFS. However, the electron beam with a certain energy spread (σ E ) passing through a focusing magnet can get dispersed and distorted, this effect is called chromatic aberration. Since the on-momentum (p = p 0 ) and off-momentum (p < p 0 or p > p 0 ) particles experience different kicks from the magnetic field, the beam size at the interaction point (IP) is enlarged (see Fig. 2.13). The particle displacement at the IP is given by [START_REF] Del | Optics studies and performance optimization for a future linear collider[END_REF]:

∆y * ≈ l * δθ (2.4)
where l * is the distance from FD to the IP, δ = (E -E 0 )/E 0 is the relative energy deviation with respect to the reference particle and θ is the angluar spread.

Assuming there is no initial correlation between energy and angle, the RMS vertical beam size (σ y ) at the IP can be expressed as:

∆σ * y = l * σ * θ σ E = l * β * σ E (2.5)
where σ * θ = β * is the nominal vertical angle at the IP and σ E is RMS value of energy deviation (δ). Then the chromatic dilution of the beam size can be obtained as:

∆σ * y σ * y = l * β 1 √ β * σ E = W σ E with W = l * β * (2.6)
where σ * y = √ β * is the nominal beam size and W is defined as the chromaticity, which is determined by l * , i.e. the focal strength of the FD, and β * , i.e. the depth of focus of optical image at the IP. For the ILC design with the SiD detector, where l * = 3.5 m, β * ≈ 0.4 mm and σ E ≈ 0.1%, the chromaticity dilution ∆σ * y /σ * y ≈ 9, which means that the chromatic aberration would completely dominate the IP vertical beam size, hence it is essential to correct it.

Chromaticity Correction

The chromaticity correction can be done by adding sextupoles located in the region with horizontal dispersion upstream of the FD, because the focal strength of the sextupoles is proportional to the particle energy (see Fig. 2.13 (lower)) [START_REF] Kubo | Towards an International Linear Collider: Experiments at ATF2[END_REF]. Two different conceptual designs of chromaticity correction have been developed over the last decades, which are refered to as non-local [START_REF] Brown | Basic Optics for the SLC Final Focus[END_REF] and local [START_REF] Raimondi | Novel Final Focus Design for Future Linear Colliders[END_REF] chromaticity corrections.

Non-local Chromaticity Correction

The "traditional" (non-local) chromaticity correction design utilised two pairs of -I separated sextupoles, for x and y chromaticity compensation (see Fig. 2.14 (upper)). The two pairs were typically non-interlaced, to minimise the third and higher order aberrations. All earlier designs followed this principle including the SLC and FFTB optics [START_REF] Balakin | Focusing of submicron beams for TeV-scale e+ e-linear colliders[END_REF], which were both realised experimentally. However, this way of correcting the chromaticity has several limitations due to the fact that the chromaticity is created in the FD near IP, but is pre-compensated 1000 m upstream as the bend magnets and the collimation sections have to be sufficiently long in this design [START_REF] Seryi | Experimental and theoretical progress of linear collider final focus design and ATF2 facility[END_REF]. Therefore, any disturbances to the beam for example the synchrotron radiation generated energy spread, created between the sextupoles and IP, would disturb the compensation of the chromaticity. Compensation of sextupole aberrations in such a system is also not ideal as M = -I for off-energy particles. This in particular creates large aberrations for off-energy particles and especially for the beam tails.

INTERNATIONAL LINEAR COLLIDER

Local Chromaticity Correction

In order to mitigate the problems arising from the non-local chromaticity correction, a novel final focus system with local chromaticity correction was proposed [START_REF] Raimondi | Novel Final Focus Design for Future Linear Colliders[END_REF]. The idea of this design is to correct the chromaticity as locally as possible, minimize the number of bend magnets, preserve the linear optics as much as possible and to have as few elements as possible. Here below the way of approaching this design is shown analytically.

The horizontal and vertical kick (x and y ) received by a particle with energy deviation of δ from a quadrupole of strength K Q can be written as:

x ≈ (K Q x -K Q δx) = K Q (x β + D x δ) -K Q x β δ -K Q D x δ 2 (2.7) y ≈ -(K Q y -K Q δy) = -(K Q y β -K Q δy β ) (2.8)
where x = x β + D x δ and y=y β . The first term in this equation corresponds to the focusing of the beam, the second is the chromaticity term and the third one is the second order dispersion term.

In order to correct the chromaticity term, a focusing sextupole with strength of K S can be added next to the quadruple. The horizontal kick given by this sextupole can be 2.3 Final Focus System written as:

x = 1 2 K S (x 2 -y 2 ) = K S 1 2 (x 2 β -y 2 β ) + x β D x δ + 1 2 D 2 x δ 2 (2.9) y = -K s xy = -K s (D x δy β + x β y β ) (2.10)
Here the first term corresponds to the geometric aberration, the second one is the chromaticity and the last one is the second order dispersion. Comparing Eq. 2.7 with Eq. 2.9 and Eq. 2.8 with Eq. 2.10, it can be seen that by setting K S = K Q /D x the term with δ can be cancelled directly in y, however, in x only the chromaticity term can be cancelled completely, the second order dispersion term is only cancelled by half. The geometric terms still need to be cancelled in both x and y.

For the second order term cancellation, a second focal point is introduced in a non dispersive region (see Fig. 2.11) doubling the overall chromaticity and hence the sextupole strengths required to correct it. The geometric term is cancelled in the same way as in the non-local chromaticity correction design by adding another pair of sextupoles upstream in a non-dispersive region at the same phase as the ones in the FD with a -I transformation between the two sextupoles (see Fig. 2.14 (lower)).

To summarise, in the local chromaticity correction design, the chromaticity is cancelled locally by two sextupoles interleaved with the FD, a bend upstream is needed to generate dispersion across the FD needed for sextupoles to work. Besides, the second order dispersion produced by sextupoles in the FD is cancelled locally provided that half of horizontal chromaticity arrives from upstream of FD. Furthermore, the geometric aberrations of the FD sextupoles are cancelled by two more sextupoles placed in phase with them and upstream of the bend. In addition, other higher order aberrations are cancelled by optimising the transport matrices between the sextupoles [START_REF] Seryi | Experimental and theoretical progress of linear collider final focus design and ATF2 facility[END_REF].

Comparing with the non-local chromaticity corrections, the local chromaticity corrections is much shorter and therefore less costly. Meanwhile, it is less sensitive to the beam energy variation and to the fields errors as the non linear terms introduced by the sextupoles are transported on a much shorter distance. Furthermore, it has much less aberrations and it does not mix betatron phases of non-core particles, which is in particular important for minimisation of generation of beam tails and ensuring good performance of the collimation system [START_REF] Seryi | Experimental and theoretical progress of linear collider final focus design and ATF2 facility[END_REF].

Despite these advantages, the complicated design and difficulties in beam tuning during the operation may make it difficult to realise the local chromaticity correction concept, hence it is of great importance to verify it experimentally. The ATF2 final focus, a prototype of a FF with local chromaticity compensation, was therefore designed for this purpose.

3

The Accelerator Test Facility (ATF) and ATF2 at KEK Future linear colliders such as ILC and CLIC require focusing the beams to nanometre sizes at the interaction point (IP) in order to reach the desired luminosity. The challenge of colliding nanometre sized beams at the IP involves three distinct issues: creating small emittance beams; preserving emittance during acceleration and transport; and focusing the beams to nanometre sizes before colliding them [START_REF] Bambade | Present status and first results of the final focus beam line at the KEK Accelerator Test Facility[END_REF]. The ATF and ATF2 test facilities at KEK were built with the purpose of studying these issues experimentally.

In this Chapter, an overview of ATF and ATF2 projects is given, followed by detailed descriptions of the instruments for beam diagnostics at ATF2 with emphasis on the Interaction Point Beam Size Monitor (IPBSM). The issues of beam halo and study of Compton scattered electrons at ATF2 are presented in the last section.

Overview of ATF and ATF2 Projects

The ATF facility is a prototype DR to create small emittance beams as required for ILC. The ATF DR is a ∼140 m circumference electron ring fed by an s-band linear accelerator which is used to accelerate the electron bunches produced by an RF gun to 1.3 GeV. In the normal ATF2 mode of operation, the DR delivers bunches of electrons with a 1.6 nC charge at 3.12 Hz to the extraction system. The typically measured (corrected) horizontal and vertical emittances are 2 nm•rad and 12 pm•rad respectively, which means that it has succeeded in obtainning the emittances required for the ILC (see Fig. 2.6).

The ATF2 facility, which was constructed in 2008, is a prototype of the final focus system for the future linear colliders (ILC and CLIC). It uses the beam extracted from the ATF DR to perform the nanometre beam size focusing and stabilisation with local chromaticity correction. The schematic layout of ATF and ATF2 facilities is shown in Fig. 3.1. It can be seen that ATF2 is a new extraction (EXT) beam line of the ATF DR, many of the beam diagnostic instruments (eg. wire scanners) were moved from the old 3. THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK EXT to the ATF2 beam line.

ATF2 beam line

ATF2 is a follow-up to the Final Focus Test Beam (FFTB) experiment at SLAC, but with a different beam-line optics, shorter design based on local chromaticity correction, which results in a larger energy bandwidth.

The ATF2 beam line consists 7 dipoles, 3 septa, 49 quadruples, 5 sextupoles, 4 skewsextupoles and 25 corrector magnets (see Fig. 3.1 (upper)). The total length of the ATF2 beam line is ∼90 m, with 52 m long EXT line and 38 m long final focus (FF) line.

The EXT line is used for the extraction and manipulation of the beam out of the DR and preparing it for injection into the FF. In the EXT line, the beam parameters can be measured with YAG screen monitor, wire scanners, Optical Transition Radiation monitors (OTRs) and different types of beam position monitors (BPMs). Besides, mismatch of the dispersion and betatron optical functions and betatron coupling, can be corrected with a set of dedicated upright and skew quadrupole magnets.

The optics of the ATF2 FF is a scaled-down version of the ILC design. The main design parameters of ATF2 are shown in Table 3 The ATF2 beam line is normally operated with a 10 times larger horizontal IP βfunction optics than originally designed to reduce the effect of multipole field errors to a level comparable to the tolerances of the ILC final focus design [START_REF] Okugi | Linear and second order optics corrections for the KEK Accelerator Test Facility final focus beam line[END_REF]. This optics is referred to as the "10BX1BY" optics because of the 10 times larger β *

x and the same β * y compared with the original design, while the original optics is labeled as "1BX1BY" optics. Small ("10BX0.5BY") and large ("100BX1000BY") β-function optics are also used at times for different studies.

Goals of ATF2

The two main goals of ATF2 are:

Goals of ATF2

• Goal 1 -Achievement of small (37 nm) beam size: demonstration of final focus system based on local chromaticity correction;

• Goal 2 -Control of beam position: demonstration of beam orbit stabilization with nano-meter precision at the IP, using intra-pulse feedback.

In addition to the main goals, other studies including lower β * y for CLIC, ground motion, beam halo and collimation studies are also performed at ATF2, as well as R&D on instrumentation. The first beam test at ATF2 started in Dec. 2008 focusing on the Goal 1. The history of minimum measured vertical beam size (σ y ) starting from Dec. 2010 to Jun. 2014 is shown in Fig. 3.3 (left). The beam size measurements are performed using a nanometer beam size monitor called "Shintake monitor" at the IP (see Section 3.4). The minimum measured beam size has decreased by a factor ∼6 from ∼ 300 nm in Dec. 2010 to ∼ 44 nm in Jun. 2014. This achievement results from a number of different of improvements, including the mitigation of higher order magnetic field errors and wakefield, suppression of orbit drifts and jitter in the FF, improvement of the Shintake monitor etc.. Both hardware and software upgrades have contributed to these improvements [START_REF] Yan | Precise measurement of nanometer scale electron beam size using laser interference by shintake monitor[END_REF][START_REF] Kubo | Towards an International Linear Collider: Experiments at ATF2[END_REF].

Status of Goal 1

The minimum beam size of ∼44 nm has been achieved repeatedly, but only at a beam intensity ten times lower than nominal (∼0.16 nC) 1 . An example from Jun. 2014, based on 10 consecutive measurements, is shown in Fig. 3.5. Even though this beam size (∼ 44 nm) is still larger than the nominal 37 nm beam size, it has demonstrated the feasibility of doing a local chromaticity correction. Without chromatic correction the beam size would be ∼ 450 nm. Further studies on beam jitter, wakefields and the stability of the Shintake monitor are on going to further reduce the beam size. Meanwhile, studies on wakefields are also carried out to understand the intensity dependence. Another remarkable achievement of ATF2 is the efficient beam tuning after shutdown. Since the ILC detector will be operated in a "push-pull" mode1 , it is of great importance to recover the beam quickly after the short shutdowns needed to move the detectors in and out. Fig. 3.3 (right) shows an example of the beam tuning time after 3 days shutdown. It can be seen that the beam can be squeezed from a few µm to ∼60 nm in ∼16 hours from the start of operation, while IP beam size tuning to a less than 60 nm beam only takes ∼8 hours. These results imply that the small beam size, consequently the luminosity, can be quickly recovered after each "push-pull".

Status of Goal 2

The Goal 2 of ATF2 is to demonstrate the stabilization of the beam train trajectory at the nanometer level at the IP using an ILC-like multi-bunch train structure. In order to achieve this, a Feedback On Nanosecond Timescales (FONT) system [START_REF] Group | FONT Project[END_REF] was developed and used in the extraction line beam diagnostic region to demonstrate a nm precision intra-pulse orbit feedback. This feedback system operates in 2 bunch mode with ILClike bunch spacing (up to ∼300 ns), it measures the position of the first bunch and then corrects the path of the second bunch. Sub-micron to micron level stability has been 3.3 Instruments for beam diagnostic at ATF2 achieved [START_REF] Christian | A Sub-micron Resolution, Wideband, Stripline BPM System for Driving Bunch-by-bunch Feed-back and Feed-forward Systems at ATF[END_REF][START_REF] Kraljevic | Development of a Lowlatency, High-precision, Intra-train Beam Feedback System Based on Cavity Beam Position Monitors[END_REF]. Further improvements of its performance is currently limited by the BPM resolution and bunch to bunch uncorrelated jitters.

At the IP region, special high resolution IP Beam Position Monitors (IPBPMs) [START_REF] Blanco-García | Beam dynamics in the final focus section of the future linear collider[END_REF] were installed in 2013 and 2014. This system uses a triplet (A,B and C) of BPMs based on low-Q and short gap cavities. The first block consists of two cavities (BPM A and B) installed upstream of the IP and the second block consists of single cavity (BPM C) installed downstream of the IP. Lateral and vertical adjustments can be applied in the range of 230-300 µm using 8 piezo-movers. The specified resolution of these BPMs is 1-2 nm and the presently achieved resolution is less than 50 nm with a beam intensity of 0.4 -0.5×10 10 [54, 55]. Commissioning and performance studies are ongoing for this system.

Instruments for beam diagnostic at ATF2

YAG:Ce screen monitors

Screen monitors are commonly used for the control of beam size and position. It is a destructive but direct and simple way of beam monitoring. When the screen is inserted, the electron beam collides with the inserted screen, and the screen emits light by scintillation. The emitted light guided by a lens system is then collected by a CCD camera, where the image of the beam profile is observed.

At ATF2, a Cerium activated Yttrium Aluminium Garnet (YAG:Ce) screen was installed at the location of MS1X at 7.4 m away from the exit of the DR with the purpose of measuring the vertical beam size, beam tilt and the momentum spread at the exit of the DR [START_REF] Naito | High Resolution Screen Monitor Using YAG:CE Screen[END_REF]. The screen has 10 mm diameter and it is made of 50 µm thick single crystal of YAG:Ce. A CCD camera (IMPREX IGV-B0610M) is used for the image collection. The schematic layout of the system is shown in Fig. 3.6 (upper left).

THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK

The minimum measurable beam size of YAG:Ce screen is limited by the following effects [START_REF] Naito | High Resolution Screen Monitor Using YAG:CE Screen[END_REF]:

• Blurring effect: since the YAG:Ce screen has finite thickness, the light is emitted along the whole length of a particle path and at all the angles (see Fig. 3.6 (lower left)). A lens system with certain geometrical acceptance can be used to optimize the resolution by cutting the light emitted with large angle while keeping the amount of collected light. However, still over 20 % of the radiated light reflects from the back surface of the crystal with finite emission angles, which further decreases the optical resolution. As the blurring effect depends on the thickness of the screen, thinner screens are preferred for small beam size measurement.

• Resolution of the lens: the quality of the lens is usually defined by their ability to resolve detail. The resolution of the presently used lens at ATF2 is 4.3 µm.

With this resolution a minimum beam size of 7 µm has been measured [START_REF] Naito | High Resolution Screen Monitor Using YAG:CE Screen[END_REF].

• Saturation of YAG emission: when the beam intensity is too high, both the CCD camera and the YAG screen can get saturated. While the saturation of CCD camera can be easily avoided by adding optical filters, the saturation of YAG emission is more complicated and difficult to deal with [START_REF] Vinatier | Measurement of lowcharged electron beam with a scintillator screen[END_REF]. The saturation level of YAG:Ce screen used at ATF2 is estimated to be 0.25 pC/µm 2 .

With these constrains, the measured minimum vertical beam sizes at ATF2 using YAG:Ce screen was 7 µm, while the minimum horizontal beam size was estimated to be 50 µm for the 45 • injection as shown in Fig. 3.6 (upper left). One example of the measurement fitted to Gaussian distribution is shown in Fig. 3.6 (right). It can be seen that, the dynamic range of the measurement is > 10 3 in this case, and tails on the two side of the Gaussian distribution can be observed. These tails might be caused by the beam halo (if the blurring effect can be neglected).

Optical Transition Radiation system

The Optical Transition Radiation (OTR) monitor is based on the transition radiation effect. When intercepted by a thin metallic foil, the beam emits a light cone due to a pure classical electrodynamic process when a charged particle passes from one medium into another. In the vacuum in front of the foil, the particle has a certain electro-magnetic field configuration, which is different from the field inside the medium, because the foil has a (complex) dielectric constant different from vacuum. By approaching the foil, the particles electro-magnetic field leads to a time-dependent polarization at the foil boundary. The change of this polarization emits the radiation, which combines coherently from different points at the foil to a characteristic intensity and angular distribution [START_REF] Forck | Lecture notes on beam instrumentation and diagnostics[END_REF].

As shown in Fig. 3.7 the foil is inserted at certain angle to the beam (45 • in most cases), the light is emitted in the forward direction as well as at 90 • , because the metallic surface acts as a mirror. Depending on the particle energy, the angular distribution is 3.3 Instruments for beam diagnostic at ATF2 Figure 3.6: Upper left: schematic layout of the YAG:Ce screen system at ATF2, synchrotron radiation (SR) and coherent optical transition radiation (COTR) from the upstream are reflected to 90 • ; Lower left: limitations on YAG optical resolution at large emission angles. Image from a point source is not sharp due to: finite crystal width and associated depth of focus problem (a) and light reflection from the back wall of a crystal (b) [START_REF] Murokh | Limitations on the resolution of YAG: CE beam profile monitor for high brightness electron beam[END_REF]; Right: an example of measured beam size using YAG:Ce screen [START_REF] Naito | High Resolution Screen Monitor Using YAG:CE Screen[END_REF] peaked at the angle θ = 1/γ with γ the relativistic Lorentz factor. Typically 100 to 1000 beam particles yield 1 photon in the optical wavelength range. With appropriate optics, an image of the foil is recorded with a CCD camera.

At ATF2, four OTR monitors are installed in the diagnostic section in the EXT line, each of the OTRs uses a 1 cm diameter, 1 µm thick Al target foil (or Al coated kapton). This multi-OTR monitor system (mOTR) provides fast shot-by-shot measurements of beam profile, allowing fast reconstruction of the emittance and Twiss parameters [START_REF] Faus-Golfe | Multi-OTR System for ATF2[END_REF][START_REF] Alabau-Gonzalvo | Optics and Emittance Studies using the ATF2 Multi-OTR System[END_REF]. This system has been fully operational since Sept. 2011.

Comparing with the YAG screens, the OTRs can measure smaller beam size with a better resolution. The minimum measurable spot size is ∼ 2 µm. The measurement resolution is of the order of a few percent of the measured spot size. Once the target is inserted into the beam, the OTR measures the projected x and y spot sizes and the beam tilt (x-y correlation) on every pulse. This single-shot measurement is insensitive to beam position jitter, and is very fast. Full emittance measurements (x and y, plus coupling information), with statistical averaging can be made quickly [START_REF] Woodley | ATF2 Measurement: Extraction Tuning and Matching[END_REF].

The mOTR is being used routinely for beam size and emittance measurements at ATF2 and it plays an important role in the beam phase space and cross-plane coupling correction. However, effects of the OTR monitor chamber on the IP vertical beam size were found in June 2014 due to the wakefield generated by the vertical asymmetric geometry of the chamber [START_REF] Kubo | ATF2 Report. Asian Linear Collider Workshop[END_REF]. This effect is currently under investigation.

THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK

Another important issue with the mOTR for beam size measurements is the long beam tails observed during the measurement. The beam tails can effect the Gaussian fit of the beam core, consequently the measurement resolution of the system. Their origin is not yet understood, they may come from beam halo or from chromatic aberrations of the OTR optics itself [START_REF] Fuster-Martínez | Realistic beam halo model study in the Extraction Line of ATF2[END_REF].

Wire scanners

At the ATF, wire scanners (WS) have been used to measure the beam size at the diagnostic section, IP and post-IP region. The beam is scanned by the wire and the photons generated by bremsstrahlung are detected by the photon detectors, installed downstream after a bending magnet to enable separating from the beam, using photomultipliers (PMTs). A Tapered Beam Pipe (TBP) [START_REF] Terunuma | Wakefield minimization in the ATF2 beamline[END_REF] with a radius of 8 mm was installed between QD10BFF and QD10AFF magnets (see Fig. B.1 in Appendix B) at the downstream of the diagnostic section, where β y is relatively large, to reduce the background at the IPBSM detectors without exciting the wakefield. Fig. 3.8 shows the location of the different WS and their detectors at ATF2 as well as the previous extraction line (old ATF EXT line). The distance of the WS to the entrance of the EXT line, the beam size and the phase advance at the positions where different WS are installed are listed in Table 3.2 and compared with the parameters at the TBP and IP. In 2013 there were 3 WS installed at ATF2: MW2X, MW3X and post-IP WS. In 2005, before the completion of ATF2 line, these wire scanners have been installed in the old extraction (EXT) line of ATF (see Fig. 3.1 and Fig. 3.8 (upper)) together with other two wire scanners. First beam halo measurements have been performed using these wire scanners in 2005, which will be described in more detail in Section 3.5. Similar measurements were done in 2013 at the ATF2 beamline, which will be presented in Chapter 5. ). The U wire, which is 45 • to X and Y wire is used to measure the correlation between horizontal and vertical measurements. In addition, two 10 µm tungsten wires with +10 • and -10 • tilts from the X direction are used to measure the tilt angle of the beam profile. As the resolution of the beam size measurement depends on the wire diameter, three Y wires with different diameters (7 µm, 10 µm and 50 µm) were installed to measure different vertical beam sizes (σ y ). The effect of the wire diameter on the beam size measurement can be taken into account by the following formula [START_REF] Matsuda | Beam Size Measurements by 7µm Carbon Wire Scanner[END_REF][START_REF] King | Analysis of the Influence of Fibre Diameter on Wirescanner Beam Profile Measurements[END_REF]:

σ 2 true ≈ σ 2 measured - d 4 2 (3.1)
where d is the wire diameter. This approximation is valid as long as the diameter is sufficiently small compared with the beam size. If the diameter is much larger than the beam size, the distribution of detected gamma rays might be different from a Gaussian distribution. The 7 µm wire can be used to measure beam sizes larger than 3.3 µm with an error less than 1%, while the 10 µm wire is used to measure beam size larger than 4.5 µm as shown in Ref. [START_REF] Matsuda | Beam Size Measurements by 7µm Carbon Wire Scanner[END_REF]. Near the IP, another carbon wire scanner (MWIP) with 5 µm thick wires is used as the first part of the IP beam size minimization procedure (σ > 1µm).

Laser wire

Although wire scanners can be used to measure beam sizes of several µm, heat destruction can limit the performance of the carbon or tungsten wires especially for a high intensity beam [START_REF] Matsuda | Beam Size Measurements by 7µm Carbon Wire Scanner[END_REF]. Therefore, laser beams can be alternatives of the material wires for intense electron beams. Similar to wire scanners, laser wires can also be used for beam size measurement by measuring the photons generated by the inverse-Compton scattering between the laser and the electron beam.

Since the minimum observable electron beam size by a laser-wire is determined by the laser spot size, and the Compton scattering cross section is small, a high power pulsed laser source with strong laser focusing is required. A laser wire system with submicrometer resolution is installed in the "matching" region of the ATF2 beam line as shown in Fig. 3.8. This system uses a 150 mJ, 71 ps laser pulse with a wavelength of 532 nm. A minimum vertical beam size of 1.07 ± 0.06(stat) ± 0.05(sys)µm was measured using this system [START_REF] Nevay | Laserwire at the Accelerator Test Facility 2 with submicrometer resolution[END_REF]. The laser wire system uses the same Cherenkov detector for Compton photon detection as used for the wire scanners in the EXT line [START_REF] Nevay | Laserwire at the Accelerator Test Facility 2 with submicrometer resolution[END_REF][START_REF] Boogert | Micron-scale laser-wire scanner for the KEK Accelerator Test Facility extraction line[END_REF]. The schematic layout of the laser wire system is shown in Fig. 3.10.

Figure 3.10: Schematic layout of the laser wire interaction region installation. The laser beam enters the interaction chamber from one side, interact with the beam and exit from the other side, where it is absorbed by the laser power meter. The APD detector is used for timing purposes [START_REF] Nevay | Laserwire at the Accelerator Test Facility 2 with submicrometer resolution[END_REF][START_REF] Boogert | Micron-scale laser-wire scanner for the KEK Accelerator Test Facility extraction line[END_REF] 3. THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK

The Interaction Point Beam Size Monitor

At the IP of ATF2, as the designed vertical beam size is 37 nm, a speical beam size monitor is necessary for the tuning and for demonstrations of the focusing at nanometer level. For this purpose a so-called Shintake monitor (IP Beam Size Monitor (IPBSM)) is used. This monitor was invented by T. Shintake and first tested at the Final Focus Test Beam (FFTB) experiment at SLAC, where ∼60 nm transverse beam sizes were successfully measured in the nineties [START_REF] Shintake | Experiments of nanometer spot size monitor at FFTB using laser interferometry[END_REF]. The schematic layout of the IPBSM is shown in Fig. 3.11. A Nd:YAG Q-switch laser source is used to generate laser pulses of 532 nm wavelength. The laser beam is split into two: upper path and lower path. The two laser beams can be injected either separately to scan the beam, in the same way as the laser wire (laser wire mode), or they can be injected at the same time and intersect at the IP (IPBSM mode). In the latter case, the interference pattern formed by the two laser beams is then used to scan the beam.

Compton scattered photons are generated when the beam passes through the interference fringes. A CsI(Tl) calorimeter-type gamma detector (scintillator), installed 6.2 m downstream of the IP, is used for the Compton photon detection. In addition, another fast Cherenkov detector is under development for the 2 bunch operation, as the response of the CsI(Tl) scintillator is relatively slow to separate the signals from two subsequent bunches [START_REF] Kano | IP-BSM -Two bunch operation[END_REF].

IPBSM mode

A well focused beam passes through the almost the same phase of the fringes, resulting in a large modulation in the photon signal, while a diluted beam passes through wider range of phases of the fringe pattern, leading to a small modulation. This behaviour is 3. [START_REF] Zimmermann | HL-LHC: Parameter space, constraints, and possible options[END_REF] The Interaction Point Beam Size Monitor illustrated in Fig. 3.11. The modulation (M) of the Compton signal can be expressed as:

M = N + -N - N + + N - (3.2)
where N + and N are the maximum and minimum Compton signal intensities during a scan. For a Gaussian beam profile, the modulation can be expressed as a function of the laser crossing angle (θ) and electron beam spot size (σ):

M = |cosθ| exp(- 2π 2 σ 2 d 2 ) with d = λ 2sin(θ/2) (3.3)
where d is the interference fringe pitch i.e. the distance between adjacent peaks and λ=532 nm is the laser wave length. From Eq. 3.3 it can be seen that the beam size measurable range is determined by the interference fringe pitch and that the effective fringe pitch is defined by the laser crossing angle θ.

For the IPBSM mode, the crossing angle of the two laser beams can be mechanically switched among 174 • , 30 An example of a vertical beam size measurement using the IPBSM is shown in Fig. 3.12. The Compton photon signal (G) is fitted using the following formula:

G(θ) = G 0 (1 -M cos(θ + θ 0 )) (3.4)
from where a modulation of M = 0.314 is obtained. The phase between two successive maxima of 2π corresponds to 266 nm. The beam size extrapolated from M using Eq. 3.3 is 64.4 nm without any systematic error correction applied [START_REF] White | Experimental Validation of a Novel Compact Focusing Scheme for Future Energy-Frontier Linear Lepton Colliders[END_REF].

Laser wire mode

For the laser wire mode, the injection angle is usually set between 2 • to 8 • for σ y measurement and 174 • for σ x measurement. However, since the laser spot size is typically 10-15 µm, which is comparable to the thickness of the carbon wires (5 µm), beam size measurement is usually performed using the MWIP wire scanner at the beginning of beam tuning. On the other hand, the laser wire mode is used to measure the laser spot size σ laser and to finely align the laser position in the transverse plane after a preliminary alignment using screen monitor [START_REF] Yan | Precise measurement of nanometer scale electron beam size using laser interference by shintake monitor[END_REF]. The nominal laser energy is 1.4 J/pulse. However, in order to improve the laser profile, the operating power is first reduced to 1.1 J/pulse. Then it is cut by 60% by a beam splitter on the laser table to prevent mirror damages. Besides, the laser transmission loss is estimated to be about 10%. Therefore, the final laser energy becomes ∼ 0.4 J/pulse with two laser paths (IPBSM mode) and ∼ 0.2 J/pulse for a single laser path (laser wire mode) [START_REF] Okugi | [END_REF].

THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK

Background sources for IPBSM

Backgrounds in the gamma detector are crucial to control for a good modulation resolution to be obtained. At ATF2, the background (BG) sources for the IPBSM are [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF][START_REF] Yan | Precise measurement of nanometer scale electron beam size using laser interference by shintake monitor[END_REF]:

• Low energy (a few keV) photons generated by synchrotron radiation at the final doublet location, which can be stopped easily by the beam pipe aperture;

• Negligible amount of photons generated by the beam gas scattering;

• Slow neutrons from the dump in the end of the beamline, which can be separated from the signal in time by adjusting the detector's ADC timing gate;

• Bremsstrahlung photons generated by the beam halo hitting the final doublet magnets and the BDUPM bending magnet. These photons can have a high energy, up to the total energy of the electron beam (1.3 GeV).

Since the first three BG sources are either negligible or separable, the main BG remains the high energy bremsstrahlung photons generated by the beam halo, which can be controlled only by using dedicated collimators either for the beam halo itself or for the bremsstrahlung photons. At present, there is no dedicated collimator for beam halo at ATF2, background from the upstream is shielded by adjusting the vertical position of the TBP, installed in the high β y location (see Fig. 3.8). Meanwhile, a dedicated 3.5 Issues of beam halo at ATF2 collimator system is being designed and will be installed in the EXT line for beam halo collimation [START_REF] Fuster-Martínez | Design Study and Construction of a Transverse Beam Halo Collimation System for ATF2[END_REF].

For the bremsstrahlung photons collimation, three gamma collimators were installed in the post-IP region: a intermediate collimator inside the bending magnet, a fixed collimator and a movable collimator (see Fig. 3.13). This collimator system plays an important role in reducing the amount of BG photons and increasing the S/N ratio during fringe scans. However, since the bremsstrahlung BG photons generated at the FD propagate nearly parallel to the signal photons emitted at the IP, it is difficult to collimate a sufficient amount of BG while still maintaining signal acceptance. Thus bremsstrahlung photons remain a major source of BG in the detector. Although this can be partly mitigated by separating the signal from the BG in the analysis [START_REF] Yan | Precise measurement of nanometer scale electron beam size using laser interference by shintake monitor[END_REF], further improvement of the performance of the IPBSM will require a good understanding and control of the beam halo.

Issues of beam halo at ATF2

As shown in the previous section, the nanometer beam size measurement using the IPBSM is very sensitive to background photons, the main source of which being photons generated by the beam halo hitting on the beam pipe. Thus, it is of great importance to understand the beam halo distribution and to find ways to control the background generated by the beam halo.

Beam halo in the damping ring

Beam halo consists of tails extending far beyond the Gaussian core of the beam. Although halo can be generated in many processes including beam-gas and thermal photon scattering, transverse wakefields, nonlinear fields in the magnets etc., the main source 3. THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK of transverse beam halo at ATF2 is expected from beam gas scattering while the longitudinal beam halo is dominated by the beam gas bremsstrahlung in the ATF damping ring [START_REF] Wang | Analytical estimation of ATF beam halo distribution[END_REF].

Halo distributions due to several physical processes in ATF were estimated analytically based on the theory developed by K. Hirata and K.Yokoya [START_REF] Hirata | Non-Gaussian distribution of electron beams due to incoherent stochastic processes[END_REF]. Beam halo distributions due to beam-gas scattering, beam-gas bremsstrahlung and intra-beam scattering were studied and compared to data by D. Wang in Ref. [START_REF] Wang | Analytical estimation of ATF beam halo distribution[END_REF]. The estimated beam halo transverse distribution due to beam gas scattering effect is shown in Fig. 3.14 with different vacuum pressures.

Beam halo measurement using wire scanners

First beam halo measurements were done in 2005 using the five WS located in the old EXT line of ATF, these measurements provide us with the first information about beam halo distribution in the EXT line [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF]. In Fig. 3.15 we can see the beam core and beam halo distribution which were measured. Parametrizations for the horizontal and vertical distributions were proposed (see Fig. 3.15 bottom). These measurements have shown that the beam halo distribution depends on number of σ rather than absolute distance from the beam center. Assuming a Gaussian distribution for the beam core (3σ) the parametrizations for the horizontal, ρ H , and vertical, ρ V , beam halo distribution are expressed as:

ρ H = 2.2 × 10 9 X -3.5 (3.5) ρ V = 2.2×10 9 X -3.5 with 3 < X < 6 3.7×10 8 X -2.5 with X > 6 (3.6)
where X is the number of sigmas, and ρ H and ρ V are proportional to the number of particles, N , being N = 10 10 electrons in that case. In general, the distribution can be normalized to the number of particles and the resulting parametrization independent of N is:

ρ H /N = 0.22 × X -3.5 (3.7)
ρ V /N = 0.22×X -3.5 with 3 < X < 6 0.037×X -2.5 with X > 6 (3.8)
In 2013 the coefficients of the parametrization were recalculated taking the 4 σ position 3. THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK as 1/500 of the peak intensity1 (see Fig. 3.15) giving the following parametrization [START_REF] Wang | ATF2 background and beam halo study[END_REF]:

ρ H /N = 0.102 × X -3.5 (3.9)
ρ V /N = 0.102×X -3.5 with 3 < X < 6 0.017×X -2.5 with X > 6 (3.10) Since these parametrizations were obtained from the old EXT line and the present ATF2 EXT line differs from the old one, new measurements using the WS are required to verify the beam halo parametrization. Measurements using the MW2X and the post-IP WS installed at ATF2 were performed and are presented in Chapter 5. These measurements can also serve as references for the beam halo measurements using diamond sensors at the post-IP region.

Beam halo measurement using YAG:Ce screen

As the YAG:Ce screen was installed near the exit of DR, where the beam halo distribution is not affected by other effects during transport along the ATF2 beam line, it can provide important information on the beam halo generated in the DR. Therefore, beam halo measurement using YAG:Ce screen was proposed [START_REF] Naito | YAG screen test in ATF2 extraction line for halo measurement[END_REF] and first measurements were carried out by T. Naito in 2014. In order to increase the measurement dynamic range, a 1 mm wide slit in the center of the screen is cut out in the vertical direction, so that the beam core can go through without any interaction (see Fig. 3.16). The first measurement results were presented in Ref. [START_REF] Fuster-Martínez | Beam halo measurements and beam halo collimation at ATF2[END_REF] and shown in Fig. 3.17. The left plot shows the vertical distribution of the beam halo for a beam intensity of 0.15×10 10 electrons. The red line shows the Gaussian distribution of a 20 µm vertical beam size. The beam halo exists over 200 µm (10σ y ) on both sides. The calibration of the core intensity is difficult due to saturation effects of the YAG:Ce screen. The right plot shows the intensity measurement of the beam core. The intensity is saturated even at the low intensity. The peak of the Gaussian distribution was estimated from the linear extrapolation. The dynamic range of the measurement is limited to ∼ 10 3 due to the saturation effect as shown in Fig. 3.17 (right). Besides, the measured beam halo may be effected by the blurring effects as mentioned in 3.3.1. More measurements are planned in 2015 to investigate the beam halo distribution as a function of beam intensity and beam size. Further measurements can be done at the exit of the DR (at a dispersion free location) to compare the distribution with the simulated DR beam halo distribution.

Compton scattering and Compton recoil electrons

In Section 3.4 we mentioned that the Shintake monitor is based on the detection of the modulation of the signal from the Compton scattered photons. As the photons are separated from the electrons after the BDUMP bending magnet, it is possible to detect

THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK

and study the spectrum of the Compton scattered electrons (Compton spectrum) after the bending magnet using the "in vacuum" DS.

Motivation for Compton spectrum measurement

The main purpose of measuring the Compton spectrum is to investigate the higher order contributions to the Compton process.

If we consider the Compton process as the interaction of an electron with a classical plane wave of frequency ω, then in the laser electric field (E), the maximum (transverse) velocity reached by an electron at rest v max = eE m ω c, the speed of light, an electron interacts with only one single photon (with the frequency ω) and radiates another photon [START_REF] Bamber | Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses[END_REF]. Therefore, the electrons radiated intensity is a linear function of the intensity of the incident wave. This process can be expressed as:

e + γ → e + γ (3.11)
However, in strong field, v max approaches c, higher multipole radiation becomes significant, the electron can absorb multiple (n) photons from the laser field but radiates only a single photon. Therefore, the radiated intensity is no longer a linear function of the intensity of the incident wave. This process is called nonlinear Compton scattering and it can be expressed as:

e + nγ → e + γ (3.12)

A dimensionless parameter η was used to qualify the nonlinearity:

η = eE rms mω = e m ρ ω ω (3.13)
where E rms is the RMS electric field, m is the mass of the electron, ω and ρ ω is the frequency and the number density of the laser photons. The nonlinear effects become significant only when η approaches or exceeds unity. The nonlinear Compton scattering was observed in collision of 46.6 GeV and 49.1 GeV electrons of the Final Focus Test Beam (FFTB) at SLAC with η ≈0.4 [START_REF] Bula | Observation of nonlinear effects in Compton scattering[END_REF][START_REF] Bamber | Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses[END_REF]. The experimental set up for this experiment is shown in Fig. 3.18. In this experiment, a silicon-tungsten calorimeter (ECAL) was implemented for the Compton spectrum measurement. Nonlinear Compton scattering with the absorption of up to four laser photons in a single scattering event was observed in this measurement. At ATF2, with an experimental set up similar to FFTB at the IP and post-IP region, it would be in principle possible to study the nonlinear Compton process and investigate its higher order contributions.

However, with the laser presently available, the factor η is calculated to be ∼7×10 -4 is 1. For nonlinear Compton scattering detection, a high power laser is required. This can be done by upgrading the laser system at ATF2 in the future. Calculated factors η for different laser settings can be found in Ref. [START_REF] Combes | Etude de la separation du spectre des electrons de recul Compton d'ATF2[END_REF].

As a preparation for future studies of nonlinear Compton scattering, detection of the first order Compton scattering spectrum using the "in vacuum" DS is planned. In

Compton scattering and Compton recoil electrons

Compton scattering

Compton scattering is the inelastic scattering of a photon (with energy hv m e c 2 ) by a charged particle (usually an electron). In this process, the incident photon with energy hv and momentum hv/c transfers part of its energy to the electron and is scattered with a decreased energy hv and momentum hv /c. This was first discovered and measured by Arthur Compton in 1922 [START_REF] Compton | Secondary radiations produced by x-rays[END_REF].

Inverse Compton scattering

When an electron is not at rest, but colliding with a soft photon, the recoiling photon gains its energy by the transfer from the incoming electrons. This process is called inverse Compton scattering [START_REF] Yoshida | Photon Radiation and Its High Energy Astrophysics Implication Photon radiation[END_REF]. The difference between Compton scattering and inverse Compton scattering is shown in the schematics in Fig. 3.19. As the electrons at ATF2 are ultra-relativistic electrons, the Compton scattering in our experiment refers to the inverse Compton scattering.

Compton cross section and estimated rates

In the electron rest frame (denoted with *), the energy conservation and momentum conservation law is expressed as (see Fig. supposing the photon injected from +x direction (collision angle θ is considered as 0 • ) and the scattering angle for the photon is φ and for electron is ψ, then the 4-momentum can be written as: The energy of the scattered photon (E * γ ) in the electron rest frame can be derived from 3.14 and 3.15 as:

p * γ = E * γ c     c 1 0 0     , p * e = mec 2 c     c 0 0 0     , p * γ = E * γ c     c cosφ * sinφ * 0     , p * e = mec 2 c     c cosψ * sinψ * 0     (3.16)
E * γ = E * γ 1 + E * γ mec 2 (1 -cosφ * ) (3.17)
where E γ is the initial energy of the photon, m e c 2 =0.511 MeV is the electron rest mass energy and φ is the scattering angle of the photon. The differential cross section of photons scattered from a single free electron in lowest order of quantum electrodynamics can be expressed by the Klein-Nishina formula [START_REF] Klein | Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac[END_REF]:

Compton scattering and Compton recoil electrons

dσ dΩ = r 2 e 2 E * γ E * γ 2 E * γ E * γ + E * γ E * γ -sin 2 φ * (3.18)
and the total cross section can be expressed as a function of x =2

E * γ mec 2 : σ = 2πr 2 e 1 x 1 - 4 x - 8 x 2 log(1 + x) + 1 2 + 8 x - 1 2(1 + x) 2 (3.19)
at lower frequencies ( hv mec 2

1) this formula can be written as:

σ ≈ σ T 1 -x + 13x 2 10 + ... (3.20)
and at higher frequencies ( hv mec 2

1) it can be written as:

σ = 3 4 σ T 1 x ln(x) + 1 2 (3.21)
where

σ T = 8π 3 r 2 e = 6.65 × 10 -29 [m 2 ] (3.22)
is the cross-section of Thomson scattering, which is considered as the low-energy limit of Compton scattering and represents the elastic scattering of a low energy photon by an electron at rest [START_REF]Compton Scattering[END_REF].

The parameters in the electron rest frame can be transformed to the parameters in the lab frame using the Lorentz transformation (see Fig. 3.21) [START_REF] Combes | Etude de la separation du spectre des electrons de recul Compton d'ATF2[END_REF][START_REF] You | A study of optical enhancement cavity with short pulse laser for laser electron beam interaction[END_REF]:

E * γ = γE γ (1 -βcosφ * ) with γ = 1 + E e m e c 2 (3.23) cosφ * = cosφ -β 1 -βcosφ (3.24)
Inserting Eq. 3.23 and Eq. 3.24 into Eq. 3.17, the maximum (φ=0) and minimum (φ = π) energy of the scattered photon can be calculated to be ∼29.5 MeV and ∼1.17 eV, respectively [START_REF] Yan | Precise measurement of nanometer scale electron beam size using laser interference by shintake monitor[END_REF].

At ATF2, the laser wavelength is λ l =532 nm, therefore the single photon energy Eγ= 2π c λ l =2.33 eV, the electron energy (E e ) is 1.3 GeV, the Lorentz factor γ=2544, and therefore, the parameter x in Eq. 3.19 can be calculated to be x =2 γEγ mec 2 = 0.0116 and the total cross section can be calculated according to Eq. 3.21 to be σ= 0.65 barn.

Knowing the total cross section, the number of scattered photons (Nγ) can be calculated as: where L is the luminosity for the Compton collision. Assuming the profile of the laser and electron beam to be Gaussian and that the two beams collide with an angle of θ and neglecting the divergence of the two beams, the luminosity can be expressed as [START_REF] Suzuki | General formulae of luminosity for various types of colliding beam machines[END_REF]:

N γ = L • σ (3.25)
L = N e N l f cos θ 2 2π 1 σ 2 ye + σ 2 yl (σ 2 xe + σ 2 xl )cos 2 θ 2 + (σ 2 ze + σ 2 zl )sin 2 θ 2 (3.26)
where N e , N l are the number of electrons in a bunch and the number of photons in a pulse, respectively, and f the number of collisions per unit time (Hz), θ is the collision angle, σ x,y,ze and σ x,y,zl are the three dimensional bunches r.m.s sizes for the electron beam (e) and for the laser beam (l).

The nominal laser and electron beam parameters at the IP of ATF2 are shown in Table 3.4.

Laser Beam Electron Beam

Single photon energy (Eγ) 2. 33

L = N e N l f 1 2π 1 σ yl σ xl (3.27)
Combining Eq. 3.25 and Eq. 3.26 one can get the ratio of scattered photons to the total number of electrons per unit time as:

N γ N e 1 f = N l 1 2π 1 σ yl σ xl σ = E l E γ 1 2π 1 σ yl σ tl σ = 3.622 × 10 -7 (3.28)
From Eq. 3.28 it can be seen that the value highly depends on the laser settings, with higher laser power and smaller laser beam size, a higher rate of scattered photons can be obtained. The calculated value of 3.622×10 -7 is based on the present laser beam parameters shown in Table 3. [START_REF] Zimmermann | HL-LHC: Parameter space, constraints, and possible options[END_REF].

As the number of Compton recoil electrons1 equals the number of scattered photons, assuming a total number of electrons of 10 10 , the expected number of Comptons should be 3.622 × 10 3 , which is 7 order of magnitude less than the total beam. This level of signal is quite small comparing with the signal from beam halo, the total number of which is estimated to be in the order of 10 -3 of the total beam [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF] and it may cover the Comptons. However, since the Comptons differ from the beam halo in energies2 , it may be possible to sperate them using the BDUMP bending magnet installed after the IP. Nevertheless, as the beam halo distribution after the IP is unknown, prior to the detection of Comptons, measurement of beam halo distribution is essential. Besides, the beam core measurement is also required for the calibration of the beam halo and Comptons distribution. Thus, a total dynamic range of 10 7 is required for an instrument with capability of doing self-calibration.

Diamond sensor

In order to cover the large dynamic range required by detection of the Comptons, instead of using ECAL as detector for Comptons as the experiments done at FFTB(see Fig. 3.18), utilisation of diamond sensors (DS) was proposed for the detection of Compton signal at ATF2. Detailed description of the advantages of using DS are described in Chapter 6.

The schematic layout of using a diamond sensor for beam halo and Compton spectrum measurements is shown in Fig. 3.22. The DS is installed after the BDUMP bending magnet. The Comptons have less energy than the beam, thus they are deflected more than the beam and can be separated.

Studies of the separation of the beam and Compton spectra, and of the optimal location of the DS are performed in Ref. [START_REF] Combes | Etude de la separation du spectre des electrons de recul Compton d'ATF2[END_REF] and Ref. [START_REF] Khvastunov | BDSIM-GEANT4 modeling of beam halo regeneration from vertical beam losses in BDUMP magnet beam pipe[END_REF]. The schematic layout of the deflection of electrons with different energies by the bending magnet is shown in Fig. 3.23. The angle of the bending magnet θ=20 • (see Fig. B.2). If the beam energy is E 0 =1.3 GeV then the electrons with energy E 0 -∆E are deflected with an angle of θ + ∆θ which results in horizontal displacements of ∆x 0 and ∆x at the exits of the

= (R • 1 -cosθ cosθ + d • tanθ) ∆E E (3.29)
where R=3883.25 mm is the radius of the bending magnet, d is the distance from the exit of the bending magnet to the DS and ∆E E is the energy spread. For the Comptons, since the maximum energy loss of the Comptons was calculated to be ∼29.5 MeV, the maximum energy spread is ∆Emax E =2.27%. Besides the uncertainty in displacement of the electrons due to their energy spread, the horizontal angular divergence (σ θx ) of the beam and beam halo can also be an important factor for the spectrum at the DS location. The spread of the beam (δ xb ) at 52 3.6 Compton scattering and Compton recoil electrons the DS location due to angular divergence at the IP is given by:

δ x b = σ θx (l + d) with σ θx = x β x (3.30)
where l=2.77 m is the distance from IP to the exit of the bending magnet. For the beam with nominal parameters (1BX1BY optics) given in Table 3.2, the angular divergence σ θx is calculated to be σ θx = 2×10 -9 4×10 -3 =0.707 mrad. However, the angular divergence of the beam halo can be N times larger than the beam. Therefore the spread of the halo (δ xh ) at the DS location can be expressed as:

δ x h = N × δ x b (3.31)
In order to detect the Comptons, the spectrum should not be dominated by angular divergence, therefore the following condition is required:

∆x > δ x b,h (3.32)
As the distance between exit of bending magnet and the end of beamline (DUMP) is limited ∼ 2.5 m, and the DS should be kept at a certain distance to the DUMP to reduce the background from the backscattered particles from the DUMP, the horizontal DS location was chosen to be d=1.35 m. For the Comptons, with d=1.35 m and ∆Emax E =2.27%, the calculated ∆x max =16.8 mm, while δ x b =2.91 mm which is much smaller than ∆x. However, for a beam halo with 10 times larger angular divergence of the beam (N=10), δ x h =29.1 mm, which is larger than ∆x max .

Nevertheless, by increasing β x , δ x b,h can be decreased. Therefore, during the experiments for Comptons detection, large β x optics are preferred. First attempt of measuring Comptons spectrum were performed and described in Chapter 9.

Simulations

Beam core and beam halo generations

The beam core and beam halo are generated using Monte Carlo method. Random numbers are generated to fill in defined distributions for the beam core and beam halo.

Input parameters for the ATF2 beam line are defined from the output parameters of the damping ring. The beam core is generated with a Gaussian distribution up to ±3σ with β x =6.85 m and β y =2.94 m. Beam halo is generated outside the beam core (< -3σ and > 3σ) according to the measured beam halo distribution in 2005 (see Section 3.5.2). For simplicity, the beam halo is generated in polar coordinate using Eq. 4.1 assuming the same parametrisation for x and y:

ρ r = K × r -3.5 with r = x 2 + y 2 (4.1)
where K is the normalisation factor to match the beam core and beam halo distribution. The angular distributions of the beam core and beam halo are calculated according to the solution of the equation of motion (Hill's equation) [START_REF] Courant | Theory of the alternating-gradient synchrotron[END_REF][START_REF] Wiedemann | Particle accelerator physics[END_REF]:

u(s) = √ βcos(φ -φ 0 ) (4.2)
and its derivative:

u (s) = - √ α √ β cos(φ -φ 0 ) - √ √ β sin(φ -φ 0 ) (4.3)
combining the two equations, an invariant of the motion (Courant-Synder invariant) can be obtained:

γu 2 + 2αuu + βu 2 = with γ = 1 + α 2 β (4.4)
Therefore, the angular distribution of the beam can be generated either according to Eq. 4.3 or Eq. 4.4.

SIMULATIONS

An example of the generated beam core and beam halo distribution profile and histogram in number of σ x,y is shown in Fig. 4.1. In order to increase the statistics for beam halo, in the simulation, we generated N h = 104 of beam halo up to ±40σ x,y , while the beam core is generated up to ±3σ x,y with the number N c = 10 51 .

Compton recoil electron generations

The Comptons are generated using a software called CAIN [START_REF] Yokoya | User's Manual of CAIN[END_REF], which was developed by K.Yokoya at KEK for the study of e -and e + beam-beam interaction and their interaction with a laser. CAIN is a code written in FORTRAN and it uses the Monte-Carlo algorithm to calculate the beam-beam interactions for electrons, positrons and photons including the linear and non-linear Compton scatterings.

Quantum electrodynamic processes (QED) including Compton scattering, Breit-Wheeler process2 can be added in the program for the laser particle interaction. In our simulation, we are interested only in the Compton scattering process. Linear and nonlinear Compton scattering processes can be chosen for the simulation.

The input parameters used in the simulation are the same ones as listed in Table . 3.4. The electron beam Twiss parameters are defined in the program according to the nominal Twiss parameters at the IP.

In the simulation, macro-particles with a certain particle weight3 are generated. These macro-particles undergo the Compton scattering process with the calculated probability, and when the Compton scattering happens, one new macro-particle is generated to represent the generated photon.

In the output files, the parameters including generation, weight, space-time location of the particle, energy-momentum, Stokes parameters 4 are provided for each macroparticle.

In our simulation, 10 4 macro-electrons with a weight of 10 6 are used to present the real number of electrons (10 10 ) in the beam. As a result, 360 macro-photons with a weight of ∼10 are generated for the designed BX1BY1 optics. This number is quite close to the previously calculated expected counts of 3.622×10 3 from Eq. 3.28. Simulations were done also for BX10BY1 optics and BX100BY1000 optics. The estimated counts for different optics are listed in Table 4.1. The estimated counts can serve as a reference for our experiments with different optics. In order to increase the statistics of Comptons, in the tracking simulations, Comptons generated using E l = 1.4J are used.

The energy spectrum of Comptons and the input electron beam is shown in Fig. 4.2 for BX1BY1 optics with E l =1.4 J. It can be seen that most of the Comptons have less energy than the beam and their energy spectrum is much wider than the beam, this permits us to separate them from the beam using the BDUMP bending magnet. The maximum energy loss of the Comptons was calculated in Section 3.6.4 to be 2.27% of the total energy. This result is consistent with the simulated value as shown in Fig. 4.2.

Tracking of beam halo and Comptons

In order to study the beam halo and Compton spectrum at the DS location, tracking was performed using Mad-X [START_REF] Schmidt | MAD-X User's guide[END_REF] and BDSIM [START_REF] Agapov | BDSIM: A particle tracking code for accelerator beam-line simulations including particlematter interactions[END_REF]. Mad-X is a program widely used in the field of particle accelerator design and simulation to describe particle accelerators, simulate beam dynamics and optimize beam optics. In this program, parameters like β functions, tune, dispersion, chromaticity can be propagated numerically. Fig. 4.3 shows the transverse profile of the beam, halo and Compton distributions at the DS location simulated by Mad-X for the BX10BY1 optics. A rectangular shape with sharp edges can be seen on the halo distribution, these edges are caused by the cut of beam halo by the upstream apertures. One of the limits of using Mad-X is that in Mad-X once the electrons hit the aperture of the beam pipe, they are stopped by it, whereas in reality they lose part of their energy by emitting a low momentum bremstrahlung photon and may subsequently remain in the beam pipe. Since such electrons with slightly reduced energies are a source of background for the detection of Comptons, complementary simulations in BDSIM were performed by I. Khvastunov to investigate this background [START_REF] Khvastunov | BDSIM-GEANT4 modeling of beam halo regeneration from vertical beam losses in BDUMP magnet beam pipe[END_REF].

BDSIM is a GEANT4 [START_REF] Agostinelli | GEANT4-a simulation toolkit[END_REF] based extension toolkit for simulation of particle transport in accelerator beamlines. The simulations were done only for the region from the IP to the DUMP with the BDUMP bending magnet and DS in between and connected to each other using beam pipes. Fig. 4.4 shows the simulated horizontal halo and Compton distributions at the DS location in Mad-X and in BDSIM. In the Mad-X simulation the total number of halo macro particles was set to 10 4 and then the obtained halo distribution at the DS location was scaled by factor 5.7×10 3 in order to be consistent with the total number of N h =5.7×10 7 electrons calculated in Ref. [START_REF] Khvastunov | BDSIM-GEANT4 modeling of beam halo regeneration from vertical beam losses in BDUMP magnet beam pipe[END_REF] for the BDSIM simulation. The Compton distribution is obtained from CAIN with the 1.4 J laser energy setting, therefore total number of Comptons is ∼2.8×10 4 as listed in Table 4.1.

In Mad-X the halo is generated up to 40σ x,y , whereas in BDSIM, different levels of halo extension were generated to verify the impact of the electrons with lower energy.

From Fig. 4.4 (upper plot) it can seen that in Mad-X the halo is cut by apertures in the beam pipe, therefore even with 40σ x,y extension it seems the Comptons can be still detected.

In BDSIM, the halos are generated at the IP with angular divergences of 7.5σ xp and 10-30σ yp . From Fig. 4.4 (lower plot) it can be seen that although with 10σ yp extension the distribution is similar to the one in Mad-X, an asymmetrical growth of halo can be observed after generating 15σ yp of halo. More halo is observed on the low energy side than on the high energy side as expected. After adding the beam halo up to 20-30σ yp , the beam halo is dominating the distribution on the low energy side and the Compton signals are covered by the halo in this case. Also an edge at ±50 mm location can be observed which correspond to the cut of beam halo by the aperture of the beam pipe1 . This information is quite important for the detection of Comptons and can be verified in the experiments by measuring the horizontal beam halo distributions. If this is true, then beam halo should be collimated upstream of the IP to certain level (eg. < 15σ yp ) to enable the detection of Comptons.

Cut of beam halo by apertures

As mentioned in the previous section, the cut of beam halo by the apertures can be verified experimentally, and also can serve as important information for the detection of Comptons. Furthermore, in Mad-X the apertures can be used as "collimators". Therefore, simulations were done to study the cut of beam halo by apertures and to find the best location for collimators.

At present, there is no dedicated beam halo collimator in the ATF2 beamline. However, the apertures of kickers, magnets, BPMs and beam pipes on the beamline can cut the beam halo both in the horizontal and vertical planes. In order to study the beam halo collimation, simulations using MAD-X have been performed to check the cut on the beam halo by the present apertures on the ATF2 beamline.

The beam sizes are shown as a function of positions along the ATF2 beam line in Fig. 4.5. The apertures are shown as a function of positions in unit of sigmas of the beam sizes in the horizontal and vertical directions in Fig. 4.6 (a) and Fig. 4.6 (b), respectively, for the BX10BY1. The vertical apertures for the BX10BY0.5 are also shown in Fig. 4.6 (c).

The BX10BY1 and BX10BY0.5 optics have almost no difference in the scaled horizontal aperture. However in the vertical plane the beam halo is cut less in the BX10BY1 optics than in the BX10BY0.5 optics as the beam size is smaller at the aperture locations. The comparison of cut values is shown in beginning of the beamline. They introduce a cut on the beam halo at 16.01σ x . And at DS location, which is 1.35 m from the BDUMPB, the cut is around 25.86σ x . This cut is caused by the beam pipe installed after the BDUMP with a radius of 31.5 mm. Since the cut of beam halo by the C-Band BPMs is tighter than the cut by the beam pipe after BDUMP, we would expect to see this cut on the horizontal beam halo distribution at the DS location.

In the vertical plane, a tappered beam pipe (TBP) was installed at 61.39 m location between the QD10BFF and QD10AFF magnets, where the vertical beam size is very large. The radius of this TBP is 8 mm. It can serve as a collimator for the vertical beam halo to control the background for the beam size measurement using wire scanners or Shintake monitor. The vertical cut by the TBP is estimated to be at ∼20σ y for BX10BY0.5 optics and ∼27σ y for BX10BY1 optics.

As the beam is focused to nm scale at the IP, the beam diverges very large after the IP. Thus the tightest vertical cut is given by the BDUMP bending magnet, and at the BDUMPB location, which is the exit of the BDUMP magnet, the cut goes down to ∼10σ y and ∼13σ y for the BX10BY0.5 and BX10BY1 optics, respectively. This cut on beam halo may generate large background for beam halo measurement at the DS location as shown in the BDSIM simulation in Fig. 4.4. The TBP may be moved vertically to limit this background in the horizontal direction. However, more dedicated beam halo collimation system located upstream are more suited for this purpose [START_REF] Fuster-Martínez | Design Study and Construction of a Transverse Beam Halo Collimation System for ATF2[END_REF]. Only positions with a normalised horizontal aperture of less than 30 or with a normalised vertical aperture of less than 50 are shown here.

5

Beam halo measurements using wire scanners

Prior to the diamond detector installation, a first attempt of beam halo measurements has been performed in 2013 using the currently installed wire scanners in the Extraction Line (EXT) and behind the IP (post-IP). Based on these measurements, the beam halo distribution was parametrised and compared with old measurements done in the past at the old EXT line of ATF [START_REF] Liu | Measurement of Beam Halo Transverse Distributions Using Wire Scanners at ATF2[END_REF]. Such parametrisations allow modelling of the beam halo which could be useful for the study of a transverse halo collimation system, aiming at reducing the background for the measurements using diamond detectors. In this chapter, the experimental setup and measurement procedures are described, measurement limitations are discussed, then data analysis procedures and measurement results are presented.

Experimental setup

EXT line wire scanners

In our experiment MW2X and MW3X wire scanners are used in the EXT line. The schematic layout of the wire scanners is presented in Section 3.3.3. A Cherenkov detector at around 26 m downstream of MW2X and 22 m downstream of MW3X is used to detect the bremsstrahlung photons generated by the wire scanners [START_REF] Mccormick | Air Cerenkov Wire Scanner Detectors for ATF[END_REF]. It should be noticed that in 2005 this Cherenkov detector was installed at around 5 m downstream of MW2X, in the old EXT line [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF].

For the measurements in the EXT line, where the vertical beam size is relatively small, as can be seen in Table 3.2, we used the 50 µm tungsten X wire for horizontal scan and the 10 µm tungsten Y wire for vertical scan. Before doing the experiment, we checked the gate width and the timing1 of the PMTs. As shown in Fig. 5.1, the gate width is 500 ns and the timing is 180 ns. The signal from the PMT is connected to a 14 bit charge sensitive ADC, which integrates the signal detected inside the gate and converts the charge into a number (for the ADC used the limits are from 0 to 16383). The pedestal is subtracted from the ADC output number in a program specially prepared for wire scanner control and data taking. In this program, the beam intensity detected by the Integrating Current Transformers (ICT) at the EXT line is recorded simultaneously while the wires are moving, so that the fluctuation of the wire signal caused by beam intensity variations can be corrected by renormalizing the wire signal to the beam intensity, either online or offline. Beam position correction can also be done manually by taking data from the Beam Position Monitors (BPMs) near the wire scanners. The resolution of the stripline BPMs in the EXT line is 1-5 µm [START_REF] Medvedko | NEW BEAM MON-ITORING INSTRUMENTATION AT ATF2[END_REF], which is close to the position jitter of beam, estimated to be 2.4-4.4 µm [START_REF] Hayano | Wire scanners for small emittance beam measurement in ATF[END_REF]. Therefore, the beam position jitter was not corrected in these measurements.

Post-IP wire scanners

The post-IP wire scanner (post-IPW) is located 75 cm downstream of the IP. It uses a plastic scintillator detector (BG monitor) at the same location as the photon detector used for the Shintake-monitor and is also connected to a PMT. The post-IPW has the same configuration and characteristics as the wire scanners at the EXT line (MW2X and MW3X), a picture of this device can be seen in Fig. 5.2. For the measurements with the post-IPW, the beam size is in the 100 µm range (see Table 3.2) therefore, we used 50 µm tungsten X and Y wires for horizontal and vertical scans, respectively. Before doing the experiment, we checked the gate width and the timing of the PMT finding 410 ns and 180 ns, respectively. An example of output signal pulse from the PMT at the post-IPW is shown in Fig. 5.1. Furthermore, during the measurements using the post-IPW, we moved vertically the Tapered Beam Pipe (TBP) located 28 m upstream of the IP, to check the effect of this movement on the background level and beam halo distribution.

Limitations of wire scanners

Limitations of wire scanners

The wire scanners at ATF2 were designed for performing beam size measurements. In each wire scanner eight wires are arranged next to each other (see Fig. 3.9). This fact could limit this device for beam halo measurements, because the measurements using one wire can be affected by the background noise generated by the interaction of beam halo with the other neighbouring wires. An example of scan from 0 to 80 mm is shown in Fig. 5.3. The data out of the background clearly indicate the wire positions. A normalization by √ 2 should be applied since the wire scanner is 45 • with respect to the horizontal axis. Except for the first 50 µm Y wire, which is about 10 mm from the starting point of the scan, the measurements using the other wires are all affected by background from other wires.

As the background generated by neighbouring wires depends both on their thickness and orientation, different background levels could lead to different limitations to the dynamic range of the wires used to probe the beam halo. This can be seen in the results presented in Fig. 5.7, where the 10 µm Y wire has a dynamic range of 7 × 10 3 , and in Fig. 5.6 where the 50 µm X wire only has a dynamic range of 10 3 . Moreover, the dynamic range of the measurement is limited by the gain of the PMTs and the 14 bit ADC used for the photon detection. Therefore, in order to get better resolution for the beam halo measurement, we first applied to the PMT the lowest voltage to measure the beam core and then the voltage was increased step by step to scan the beam halo (see Fig. 5.4 (upper)). The signal strength measured by the photon detectors is corrected by the total beam charge measured by the ICT to take into account the fluctuations in beam intensity. Furthermore, the data taken at higher voltages is normalized according to the overlap region with the data taken at lower voltages (see Fig. 5.4 (lower)). It should be noticed that at lower voltages, the PMT is not sensitive to the background signal and the fluctuations in the flat parts are caused by the electronic noise, thus from the lowest voltage only the beam core data is considered (not the background level). The background level is extracted from the measurements at higher voltages. The normalization procedure is explained in more detail in Section 5.3.1.

Measurement results from 2013 campaign

Different sets of halo measurements were performed in April, June and December 2013 using MW2X in the EXT line and the post-IPW. During these runs the beam energy was 1.3 GeV and the optics configuration was: 10β *

x × 1β * y . The intensity given in number of particles of the beam, the date, the wire scanner used and the kind of measurements (horizontal or vertical) taken at each run are summarized in Table 5.1. In this chapter only some of the measurements (corresponding the bolded dates) are presented. More detailed analyses and results can be found in Ref. [START_REF] Liu | Measurement of Beam Halo Transverse Distributions Using Wire Scanners at ATF2[END_REF].

Data acquisition and analysis

All of the data treatment has been done using the program root [START_REF] Brun | Root[END_REF]. The acquisition and analysis of the data is performed as follows:

1. Data acquisition: For all the experiments the data were taken at different PMT voltages in order to be sensitive to the beam halo particles. Then the data corresponding to the lowest voltage was fitted with a Gaussian function plus a constant in order to determine the beam size and mean position as it is done in the ATF2 control room software in normal operation. The information is used afterwards to normalize the wire

10th of April SWING MW2X-10A-H 5 × 10 9 MW2X H 16th of April OWL MW2X-16A-H 7 × 10 9 MW2X H MW2X-16A-V 7 × 10 9 V 17th of April SWING Post-IPW-17A-H 7 × 10 9 Post-IP H Post-IPW-17A-V 7 × 10 9 V 14th of June DAY Post-IPW-14J-V 1 × 10 9 Post-IP V 12th of December OWL Post-IPW-12D-V 6 × 10 9
Post-IP V scanner position to the number of standard deviations of beam core (σ) from the beam center.

Data normalization:

• Intensity normalization: The data collected is corrected by the intensity of the beam given by the ICT to take into account beam charge changes during the run.

• Wire orientation correction: The wire position has to be corrected due to the orientation of the wire scanner (see Fig. 3.9), by dividing the wire position data by √ 2.

• Number of σ normalization: Then the data is normalized to the number of σ using the information calculated in step 1.

• Voltage normalization: In order to combine the data taken with different voltages we perform a normalization by defining the ratio between the lowest voltage data and other voltages data in the overlap region. Then all the data of a given voltage is divided by the ratio obtained for the corresponding voltage.

Data binning:

In order to reduce the fluctuation of the data taken we performed a binning procedure. The bin size has to take into account the step of the wire scanner measurements in order to not have empty bins and the number of bins is chosen in order to minimize the reduced χ 2 of the fit. The criteria we followed was to accept the fits with values 0.5 < χ 2 /N DOF < 3 where N DOF = N bin -2 is the number of degrees of freedom. The value of each bin corresponds to the mean value of the points in this bin and the error bar correspond to the statistical error as the mean. Fig. 5.5 shows an example of data taken on the 10th of April of 2013 with (right) and without (left) binning the data.

4. Fitting range: Before data fitting, the fitting range should be defined. Following Suehara's parametrization (see Eq. 3.9 and Eq. 3.10) we try to fit for 3 < X < 6 and for X > 6. However, for some cases, new ranges were defined in view of the data taken.

In principle the two sides of the halo are supposed to be symmetric, however, in most cases we performed the analysis for both sides of the halo in order to test this assumption.

5. Normalization factor in the parametrisation: For the parametrization of the halo we used the same parametrization as shown in Eq. 3.6 and Eq. 3.8. However as the data taken is in signal strength, this data should be normalized to the number of particles by the following procedure. First, we assume a function similar to Eq. 3.6 and Eq. 3.8 for the halo density distribution as a function of the number of σ:

ρ H,V = AX -b (5.1)
where X corresponds to the number of σ and A is a constant. Assuming a Gaussian density distribution for the core, the maximum of this distribution normalized to the number of σ can be calculated as:

ρ max = N √ 2π (5.2)
where N is the number of electrons in the beam. From the fitting of the data, we can obtain the signal strength as a function of the number of σ:

ρH,V = aX -b (5.3)
where X corresponds to the number of σ and a is a constant given by the fit. The maximum signal strength measured is ρmax . Then, the ratio between the maximum signal strength measured for the core, ρmax , and the amount of halo at 3σ, ρH,V , in units of signal strength, has to be equal to the ratio of the number of particles of the core corresponding to the maximum of the Gaussian, ρ max , and the amount of halo at 3 σ in units of number of particles, ρ H,V :

ρH,V ρmax = ρ H,V ρ max (5.4)

BEAM HALO MEASUREMENTS USING WIRE SCANNERS

Replacing Eq. 5.1 and Eq. 5.3 in Eq. 5.4 we can get a relation between the constants A and a: A = N a ρmax √ 2π (5.5)

Then, the distribution to be compared with Suehara's parametrisation (Eq. 3.6 and Eq. 3.8), independent on the number of particles, is:

ρ H,V /N = (A/N )X -b (5.6)
where A can be calculated from Eq. 5.6.

In some particular cases we also fit the beam halo distribution measured by a Gaussian plus a constant function, as it is done in the ATF2 wire scanner control room software in normal operation to determine the beam core, using the following parametrization:

ρ H,V = me -(X-n) 2 2l 2 + p (5.7)
Then Eq. 5.7 is defined in units of number of particles and independent of N as:

ρ H,V /N = (M/N )e -(X-n) 2 2l 2
+ P/N (5.8)

In the following section we will apply the analysis described for the different sets of data and compare the results with Suehara's parametrisation. However, when doing the comparison we have to take into account that the measurements done in 2005 were done for the old EXT line in ATF and the 2013 measurements have been done for the ATF2 beam line with stronger focusing optics and new elements with tighter apertures.

Measurement results from 2013 campaign

MW2X WS measurement results

Horizontal distribution

For this measurement we used the 50µm X wire to measure the horizontal beam halo. The combination of all the data after voltage normalisation is shown in Fig. 5.6 (upper). It can be seen that the data taken with 2000 V in the halo region has a large fluctuation due to the large background. Therefore data binning is required to make the distribution more clear.

The left and right hand side halo were fitted separately using the power function It can be noticed in Fig. 5.6 that beyond 5σ x the distribution is flat and the dynamic range is less than 10 3 .

The fit results are summarized in Table 5.2. The beam intensity here is N = 7 × 10 9 electrons. It can be seen that the power factor for left and right beam halo distribution has a small difference, which indicates that the beam halo horizontal distribution may be asymmetric. This asymmetry was observed in the WS measurements done in 2005 also (see Fig. 3.15).

Vertical distribution

For this measurement we used the 10µm Y wire to measure the vertical beam halo. The combination of all the data after voltage normalisation is shown in Fig. 5.7 (upper). Similar to the horizontal distribution, large fluctuations can also be observed in the data taken with 2000 V in the halo region for the vertical distribution. Fig. 5.7 (lower) shows the fit for the right hand side halo tail. In this case beyond 5 σ x the distribution observed is also flat. However, the dynamic range (∼ 7 × 10 3 ) is a little bit higher than for the horizontal measurement using the 50µm X wire (< 10 3 ).

The fit results are summarized in Table 5.3. Comparing with the horizontal distribution, it can be seen that there is almost no difference between the left and right distribution, which may indicate a symmetric vertical distribution. Meanwhile, the power factor (∼ -7) is twice that obtained in 2005, which means that the vertical beam halo population may be lower than in 2005 in the region of 3σ y to 5σ y .

BEAM HALO MEASUREMENTS USING WIRE SCANNERS

ρ H /N = (A/N )X -b ρ H,l /N = (1.1 ± 0.1)X -(4.8±0.1) 20 3 < X < 5 ρ H,r /N = (2.8 ± 1.2)X -(5.6±0.3) 8 ρ H,l /N = (0.0010 ± 0.0001)X -(0±0.3)
2.3 X > 5 ρ H,r /N = (0.0011 ± 0.0001)X -(0.2±0.1) 0.6

ρ H /N = (M/N )e -(X-n) 2 2l 2 + ρ H /N = (0.89 ± 0.01)e - (X-(0.12±0.01)) 2 2(0.96±0.01) 2
+ 2.4 -30 < X < 15 +P/N +(0.107 ± 0.001)

ρ V /N = (A/N )X -b ρ V,l /N = (9 ± 5)X -(7.3±0.4) 1 3 < X < 5 ρ V,r /N = (8 ± 2)X -(7.2±0.2)
5.6 ρ V,l /N = (0.001 ± 0.001)X -(1.1±0.3) 4.5 X > 5 ρ V,r /N = (0.0010 ± 0.0004)X -(1.0±0. 1) 3

ρ V /N = (M/N )e -(X-n) 2 2l 2 + ρ V /N = (

Post-IPW measurement results

Horizontal distribution

For this measurement we used the 50 µm X wire to measure the horizontal beam halo distribution. The combination of all the data after voltage normalisation is shown in Fig. 5.4 (lower). Data with fitting after binning is shown in Fig. 5.8. The fit of the beam core corresponds to the data taken at the lowest voltage (500 V). The fit results are summarized in Table 5.4. As the flat distribution start at ∼ 6σ x fitting of the halo was done from 3σ x to 6σ x . In this case the dynamic range also is very limited (< 10 3 ). However, it can be seen from Fig. 5.8 that the measured horizontal distribution fits quite well with the 2005 model from 3σ x to 6σ x . Nevertheless, since post-IPW is located after the IP, where large photon background can be generated for the detection, distribution beyond 6σ x could not be measured using the post-IPW.

Vertical distribution

For this measurement we used the 50 µm Y wire to measure the vertical beam halo distribution. This wire is the first wire which interacts with the beam when the WS moves from the lower to the upper part (see Fig. 3.9). Therefore, we expect the background from other wires to be lower for the measurements using this wire especially on the downside of the beam (left side in the plots).

The combination of all the data after voltage normalisation and data binning is shown in Fig. 5.9, together with the enlarged fit of the right hand side distribution and comparing with the 2005 model. The fit results are summarized in Table 5.5.

From the fit results, we could notice that the distribution of the halo is not symmetric. More halo is observed on the left hand side (lower part of the beam) than the right hand side (upper part of the beam). Meanwhile, from the upper plot in Fig. 5.9 an obvious edge can be seen on the left side of the distribution, at ∼ 14σ y position. This cut could be caused by the TPB, where the β y is relatively large. However, more systematic measurements are needed to confirm this hypothesis. Therefore, fitting was done until 14σ y on the left side before the observed edge.

Measurement results from 2013 campaign

ρ H /N = (A/N )X -b ρ H,l /N = (6.2 ± 0.8)X -(3.5±0.1) 4 3 < X < 6 ρ H,r /N = (10.2 ± 1.2)X -(4.2±0.1)
4.5 ρ H,l /N = (0.020 ± 0.003)X -(0.002±0.02) 4

X > 6 ρ H,r /N = (0.007 ± 0.001)X -(0±0.02) 1.7

ρ V /N = (A/N )X -b ρ V,l = (2.4 ± 0.3)X -(1.9±0.1) 15 3 < X < 6 ρ V,r = (4.9 ± 0.4)X -(2.7±0.1) 11 ρ V,l = (11 ± 3)X -(1.2±0.1)
76 x > 6 ρ V,r = (0.5 ± 0.2)X -(0.45±0.02) 50

Table 5.5: PostIPW-17A-V Modeling summary

Beam halo as background for Shintake monitor

The BG monitor used for the post-IPW signal measurement is located about 10 cm upstream of the Shintake Monitor gamma-ray detector (a Cherenkov detector). Therefore, relating the beam halo distribution and background levels can be very useful in the context of background studies for the Shintake monitor.

As mentioned in Section 3.3.3, the main background are photons generated by the vertical beam halo hitting the final doublet and BDUMP bending magnets, and a TBP was installed 28 m upstream of the IP for the purpose of reducing this background. The half aperture of the TBP is 8 mm, which corresponds to a value of ∼27σ y where the calculated σ y = 216.1µm as shown in Section 4.4. The post-IPW measured beam size was 293.5 µm and 314.7 µm on the 17th April and 12th June 2013, respectively. Taking into account the mismatch factor (k) of σ y between measurement and calculation given by the post-IPW :k = σ measured /σ calculated , the expected cut by TBP is at ∼19σ y position. Since the TBP gives the tightest aperture upstream of the post-IPW (see Fig. 4.6 (b)), the cut observed in the post-IPW measurements for vertical beam halo at ∼ 14σ y in April and in June 2013 (see Fig. 5.10) could originate from the aperture of TBP, and the asymmetric distribution could be correlated to the position of TBP.

As the location of the TBP has 3π phase difference with the post-IPW (see Table 3.2), the effect of the TBP movement on the beam halo distribution can be investigated by the beam halo measurements using the post-IPW. Therefore, we performed a series of measurements moving the TBP vertically. Fig. 5.11 (upper) shows the beam halo distribution measured with the post-IPW corresponding to different TBP positions. Taking into account the 3π phase difference, the upside of the beam at TBP location represents the downside of the beam at the post-IPW location (left side of the plot). Therefore, by moving the TBP up, we would expect to observe more halo on the downside of the beam, whereas, by moving the TBP down, we would expect to observe less halo on the downside of the beam at the post-IPW location.

However, what we observed is not exactly what we expected. From Fig. 5.11 (upper) it can be seen that by moving the TBP up by 1 mm, we observe less beam halo on the downside of the beam and slightly more halo on the upside of the beam at the post-IPW location; By moving the TBP down by 0.5 mm, we observe more beam halo on both side of the beam. This different behaviour between moving the TBP up and down may indicate an asymmetry beam halo distribution at the TBP position. This difference was the motivation for installing the TBP as a shield against the background at the IPBSM. However, the origin of the asymmetric beam halo distribution is unknown.

The change of background level during the movement of the TBP was measured both with BG monitor and with the Cherenkov detector. The measured background level while moving the TBP is shown in Fig. 5.11 (lower). It can be seen that the BG level measured is quite consistent with the change of beam halo level. The background level is slightly decreased by moving the TBP up from 0 mm up to 3 mm, however, moving the TBP down caused large increase of background level. This confirms the measured beam halo distributions in Fig. 5.11. However, the reasons for the difference between the expected and the observed changes of beam halo distribution are unknown.

BEAM HALO MEASUREMENTS USING WIRE SCANNERS

During the measurement using Shintake monitor, the TBP can be moved both horizontally and vertically to find the optimised position with minimum background level. However, as the TBP is not a "real" collimator for beam halo, it can reduce the background only by a relatively small amount. Therefore, another collimator system is utilised 6.2 m downstream of the IP to collimate the bremsstrahlung photons. However, as discussed in Section 3.4.3, to further improve the performance of IPBSM, a dedicated collimator device is required to collimate the beam halo upstream of the IP [START_REF] Fuster-Martínez | Design and Feasibility study of a transverse halo collimation system[END_REF]. This device is under design, the design parameters will be defined according to the current measured beam halo distributions and the requirement for Compton signal measurements. Thus, precise measurements of beam halo using DS with a large dynamic range are of great importance. This studies could be performed in the future in a systematic way with a dedicated collimator device.

Measurement results from 2013 campaign

CVD diamond sensors

In this Chapter general properties of CVD diamond are introduced. Characterisation using radioactive sources is presented and the charge-carrier lifetime is determined for our sCVD diamond sample. Tests using electron beam were performed at PHIL and the dependence of the signal on the beam intensity is shown.

Properties of CVD diamond

Diamond is a metastable allotrope of carbon, it has a face-centered cubic structure [START_REF] Kobashi | 2.1 Structure of diamond[END_REF] (see Fig. 6.1 (a)) formed by the carbon atoms in a covalent network lattice (sp 3 -bonds) 1 and it is known as the hardest bulk material with highest thermal conductivity. The diamond manufactured using "chemical vapour deposition"(CVD) method is usually called CVD diamond. CVD diamond technology was discovered in the 1950s, after the high pressure and high temperatures (HPHT) diamond growth technique, which was commonly used to convert graphite into diamond.

CVD process

Different from the HPHT method, the CVD process uses gas-phase chemical reactions above a solid surface to grow the diamond. Under normal conditions, the thermodynamically stable crystalline phase of carbon is graphite rather than diamond. Hence, the main requirement of diamond CVD is to deposit carbon and simultaneously suppress the formation of graphitic sp 2 -bonds 2 [START_REF] Diamond | An extreme material for extreme applications[END_REF].The simplified diamond growth conditions for microwave plasma assisted CVD are shown in Fig. 6.1 (b). A mixture of hydrogen (>90 %) and methane gas is activated in microwave plasma, methane is used as Carbon 1 A mixed hybridization state formed by one s-orbital and three p-orbitals, namely px, py and pz.

Diamond consists purely of sp 3 hybridized bonds. (see Ref. [START_REF] Peschel | Carbon-Carbon bonds: Hybridization[END_REF]).

2 The sp 2 -hybridization is the combination of one s-orbitals with only two p-orbitals, namely px and py. Graphite consists purely of sp 2 hybridized bonds [START_REF] Peschel | Carbon-Carbon bonds: Hybridization[END_REF] 6. CVD DIAMOND SENSORS supply and hydrogen molecules are dissociated into atomic hydrogen. A high supersaturation of atomic hydrogen can not only break up double bonds thus converting graphite bonds into diamond bonds, but also etch graphite from the surface, prevent the built up of polymers and keep the diamond lattice stable by termination of the surface. Typical deposition conditions are: 1% methane in hydrogen as source gas, 700-1000 • C deposition temperature and gas pressures in the range 30-300 Torr (i.e. 4-40 kPa) [START_REF] Ramamurti | Synthesis of diamond thin films for applications in high temperature electronics[END_REF].

CVD diamond classification

Depending on the substrate used for diamond deposition, the CVD diamond can be divided into two groups: single crystalline (sCVD) diamond and polycrystalline CVD (pCVD) diamond.

For the growth of sCVD diamond, surface-treated HPHT diamond crystal is usually used as substrate. In this case new carbon atoms are added to the existing diamond lattice. Therefore the size of sCVD diamond depends mainly on the size of the seeds, and the availability of large area seed crystals is very limited and costly. The restricted size of the HPHT seeds is about 4.5×4.5 mm 2 . The sCVD diamond is separated from the HPHT substrate after the growth by a laser-cutting technique and polished to the desired thickness [START_REF] Weiss | A CVD Diamond Detector for (n,α) Cross-Section Measurements[END_REF]. Free-standing diamond membranes mounted on a silicon support have been demonstrated with thicknesses as low as 30 nm. On the other end of the scale diamond disks with more than 2 mm thickness are commercially available [START_REF] Diamond | An extreme material for extreme applications[END_REF]. The typical dimension of a sCVD diamond is 4.5×4.5×0.5 mm 3 as the samples used in our experiments (see Fig. 6.1 (c)).

For the growth of pCVD diamond, non-diamond substrates can be used with pretreatment of the surface to allow diamond formation. E.g. by polishing a silicon substrate with diamond powder tiny diamond particles remain on the surface that act as seeds for the growth of small diamond crystals. During deposition the size of these crystals increases until they form a continuous compact layer of small diamond crystals. This 6.1 Properties of CVD diamond allows pCVD diamond to form as large area disks or coatings.

Although pCVD diamond can be formed in larger area than sCVD diamond, they contains many grain-boundaries which act as charge trapping centers for free charge carriers, therefore, the lifetime of the electron and holes are shorter than in the sCVD diamond, which consequently lead to a decreased charge collection distance (CCD). Therefore, the electric properties of pCVD diamond are less favorable comparing with sCVD diamond. The pCVD diamonds have an area of few cm 2 range and a CCD up to 300 µm were tested for several experiments (ATLAS, CMS at CERN, HADES at GSI). The measured CCD for different samples in Ref. [START_REF] Kuznetsova | Design studies and sensor tests for the beam calorimeter of the ILC detector[END_REF] range from 6 to 60 µm with an electric field of 1 V/µm. The pCVD diamond detector, used as beam halo monitor at the SPring-8 Angstrom compact free-electron laser (SACLA) facility [START_REF] Aoyagi | Pulse-mode measurement of electron beam halo using diamond-based detector[END_REF], only reached a charge collection efficiency (see Eq. 6.5) of ∼0.7% with a bias voltage of +100V (i.e. an electric field of 0.33 V/µm). However, using sCVD diamond, ∼100% CCE can be obtained after applying more than +150 V (i.e. an electric field of more than 0.3 V/µm) (see Fig. 6.15).

Advantages of using CVD diamond

Comparing with other types of semiconductor detector such as silicon detector, detector based on CVD diamond has the following advantages:

• Optimal band gap: the band gap of diamond is 5.5 eV compared with 1.1 eV for silicon. This result in a lower noise level and a quasi negligible leakage current.

On the other hand, also due to the larger band gap, the average energy required to liberate an e-h pair in diamond is 13.1 eV, 3.6 times larger than for silicon (3.6 eV), resulting in a smaller signal. However, the overall signal to noise ratio (SNR) is slightly higher for diamond than for silicon as reported in Ref. [START_REF] Tsung | Signal and noise of diamond pixel detectors at high radiation fluences[END_REF]. In Ref. [START_REF] Krammer | Silicon Detectors[END_REF] it was also pointed out that the optimal band gap for large SNR could be around 6 eV.

• High mobility: the signal pulse width depends on the mobility of the charge carriers: high mobility leads to short pulses. The charge carrier mobility depends on the purity of the diamond and the published values for CVD diamond varies from 1300 to 4500 cm 2 • V -1 • s -1 for electrons and from 2050 to 3800 cm 2 • V -1 • s -1 for holes [START_REF] Weiss | A CVD Diamond Detector for (n,α) Cross-Section Measurements[END_REF]. The typical pulse width from a sCVD diamond sensor is at several ns level which enables fast enough data acquisition for 100 MHz bunch frequency.

• High radiation hardness: diamond is radiation hard up to several MGy of photons and electrons, up to 10 15 (neutrons and high energetic protons)/cm 2 and > 10 15 pions /cm 2 [START_REF] Bruzzi | Radiation hardness issues in diamond. 1st ADAMAS Workshop at GSI[END_REF]. In such conditions, leakage current remains negligible and charge collection distance (see section 6.1.5) decreases only slightly. Hence, diamond is considered as an ideal material for particle detectors in harsh radiation environments.

• High breakdown field: the breakdown field denotes the maximal field strength the material can withstand intrinsically without breaking down. Diamond has a much 6. CVD DIAMOND SENSORS higher breakdown field of 1000 V•µm -1 than that of silicon (30 V•µm -1 ).

• Large thermal conductivity: the thermal conductivity of diamond was measured to be about 2000 W/m•K, which is about 5 times higher than that of copper [109].

• V -1 • s -1 ] 1300∼4500 [104] 1500 Hole mobility, [cm 2 • V -1 • s -1 ] 2050∼3800 [

Energy deposition of electrons in diamond

Low energy electrons passing through diamond deposit energy mainly by ionization (collision) processes while high energy electrons (>10 MeV) loose energy mainly due to bremsstrahlung (radiation) processes. The particles with energy loss rates close to the minimum are called minimum ionizing particles (MIP), and all particles with energies above the MIP energy are considered as approximately minimum ionizing in solid state detectors [START_REF] Friedl | Diamond Detectors for Ionizing Radiation[END_REF]. The mean energy loss (stopping power) due to ionization can be calculated from the Bethe-Bloch formula [START_REF] Bethe | Passage of radiations through matter[END_REF]. The left plot in Fig. 6.2 shows the stopping powers as a function of energy of incident electrons. It can be seen that the MIP energy of electrons is around 1.6 MeV. Simulations were done in GEANT4 to get the distribution of deposited energy by the MIPs inside a 500 µm diamond. The result is displayed in the right-hand plot of Fig. 6.2. This distribution is well fitted by a Landau distribution, which is used to describe the energy spectrum observed in thin layers. The Most Probable Value (MPV) fitted from the Landau distribution gives an energy loss of 245.9±0.1 keV for 500 µm diamond, which corresponds to 4.92 MeV/cm of energy loss. The calculated mean energy loss ( dε dx ) from the Bethe-Bloch formula is around 5.5

Properties of CVD diamond

MeV/cm. As the energy required to create an electron-hole pair in diamond (E pair ) is reported to be between 13 eV and 16 eV, the average number of electron hole pairs per minimum ionizing particles (ñ) can be calculated as [START_REF] Zhao | Characterization of the electrical properties of polycrystalline diamond films[END_REF]:

ñ = dε dx E pair (6.1)
Therefore, using the simulated and calculated value of mean energy loss, the averaged number of electron hole pairs per 100 µm can be calculated to be in the range between

4.92M eV /cm

16eV * 100µm = 3075 to 5.5M eV /cm 13eV * 100µm = 4231. The mean value of in this range is 3653, which is close to the reported value of 3600.

Charge collection process and charge collection distance

Charge collection process

According to the Shockley-Ramo theorem [START_REF] Shockley | Currents to conductors induced by a moving point charge[END_REF][START_REF] Ramo | Currents induced by electron motion[END_REF], the instantaneous current i induced on a given electrode due to the motion of a charge is given by:

i = E v qv (6.2)
where q is the charge of the particle;v is its instantaneous velocity, and E v is the component of the electric field in the direction of v at the charge's instantaneous position, under the following conditions: charge removed, given electrode raised to unit potential, and all other conductors grounded. When the particles go through the diamond, the electron-hole pairs are generated due to the ionization processes. If a bias voltage is applied to the electrodes on the surfaces of the diamond, then an electric field is formed in the bulk of diamond. Under the force of this electric field, the electrons and holes start to move and this movement 6. CVD DIAMOND SENSORS induces the current on the electrodes as described by the Shockley-Ramo theorem. Once the charge-carriers have arrived at the electrodes, the signals are "over" [START_REF] Riegler | Signals Formation in Detectors[END_REF].

Charge collection distance

During the charge collection process, the electrons and holes have a certain probability to get trapped or recombined due to different kind of defects inside the diamond bulk. Among all the defects, the grain boundaries are suspected to be charge trapping and recombination centers [START_REF] Weiss | A CVD Diamond Detector for (n,α) Cross-Section Measurements[END_REF][START_REF] Kuznetsova | Design studies and sensor tests for the beam calorimeter of the ILC detector[END_REF]. Neglecting border limits, the sum of the mean free paths for electrons and holes gives the overall average distance that electrons and holes drift apart in an electric field. This value has been defined as the charge collection distance [START_REF] Friedl | Diamond Detectors for Ionizing Radiation[END_REF] .

The charge collection distance (d c ) is considered as a common figure of merit to characterise the manufacture quality of a diamond, especially for the pCVD diamond, the d c of which is usually much less than the thickness of the diamond (d). However, for the sCVD diamond, the d c can sometimes be equal to or even greater than the thickness of the diamond.

As the average minimum-ionizing particle generates about 3600 electron-hole pairs in each 100 µm of diamond, the total charge generated (Q gen ) can be calculated as Q gen = 36×d, where d is in units of µm .

If the electrons and holes get trapped or recombined after separating by the distance d c , then the charge collected by the electrodes (Q coll ) can be expressed as:

Q coll = Q gen × d c d (6.3)
Knowing the charge collected, the charge collection distance can be calculated as:

d c = Q coll 36 e -/µm (6.4)
The ratio between the total generated charge and the charge collected by the elec-

Properties of CVD diamond

trodes is defined as the charge collection efficiency (CCE):

CCE = Q coll Q gen (6.5)
Combining Eq. 6.3 and Eq. 6.5, d c can then be written as:

d c = d × CCE (6.6)
The CCE has a dependence on the applied bias voltage and it can be measured using the beta sources as described in Section 6.2.1.

I-V measurement

Diamond has a very large resistivity (> 10 12 Ω•cm), therefore the dark current of diamond is very low. However, as the dark current depends both on the quality of the diamond (crystallographic defects) and on the metallization quality of the diamond surfaces, I-V measurement should be done for each individual diamond to characterise the quality of fabrication. I-V measurement is the measurement of the dark current through a diamond sample as a function of the applied bias voltage. This measurement is essential to define the operational bias voltage range, within which the dark current is below certain level (normally in the pA range).

For the I-V measurement a Keithley 6517B Electrometer was used [START_REF] Instruments | Model 6517B Electrometer Reference Manual[END_REF]. This device can provide up to ±1000 V at 1 mA and it can measure DC current from 10 aA to 21 mA. For the I-V measurement, the Force Voltage Measure Current (FVMI) method was used. By using this method, the ammeter LO is connected to the V-source LO internally as shown in Fig. 6.4. The LabWindows program was used for the control of the Keithley and for data taking. During the measurement, the bias voltage was changed with 10 V/step with a 95 6. CVD DIAMOND SENSORS waiting time 1 of 60 s/step and the current was measured 10 times after the waiting time and averaged for each bias voltage. A measurement loop from -400V to 400V was set to measure the hysteresis behaviour of the I-V curve.

DS samples

For the I-V measurement, we tested two samples of diamond. Sample No.1 is a sCVD diamond pad with a dimension of 4.6×4.6×0.5 mm and metallised with Ohmic DLC 2 /Pt/Au (4/20/200 nm) as electrodes on two surfaces (see Fig. 6.5 top left). This diamond pad was packaged in a dual ended isolated aluminium detector package with 2 SMA female connectors. The diamond is glued on the electrode from one side (for bias voltage), and connected via bonding wires from the other side (for signal readout), each side is connected to an SMA connector. The aluminium package serves also as a shielding for RF electromagnetic waves. On the top of the package there is a 1mm thick Al window with 2 mm aperture.

Sample No.2 is a "B1-HV sCVD Beam Loss Detector" fabricated by the CIVIDEC company (see Fig. 6.5 top right) [START_REF] Griesmayer | [END_REF]. This sample uses also a sCVD diamond pad with a dimension of 4.5×4.5×0.5 mm and metallised with gold as electrodes. It has a high-voltage input for the supply of the bias voltage and the signal is read out from the low-voltage side. The detector uses two PCBs to clamp the diamond in the middle and forms a 'sandwich'-like compact design with the two PCBs serving both for the electrical contact and for the RF shielding. Besides, an aluminium box can be used to cover the diamond with extra RF shielding.

Different from sample No.1, sample No.2 has a low-pass filter for the high-voltage supply and charging capacitors are implemented in order to compensate for the detector discharge. The charging capacitors have a capacity of 100 nF. The electronic circuit for sample No.2 is also shown in Fig. 6.5.

Measurement results

Examples of the measured I-V curve for samples No.1 and No.2 are shown in Fig. 6.6 for bias voltages from -400 V to 400 V. A clear hysteresis behaviour can be observed.

The measured dark current level is higher for sample No.2 than for sample No.1. This might due to the electronic circuit on sample No.2. For both samples, the measured dark current is a little bit higher for the positive bias voltage than for the negative bias voltage. The maximum dark current is at 100 pA level, which is quite low comparing with the expected signal level (∼ µA). Therefore, it can be concluded that the operational range from -400 V to 400 V is safe and with a very low dark current, which can be neglected. 1 After applying a bias voltage, it requires some time for the current to get settled. This settling process is studied in more detail in Ref. [START_REF] Kuznetsova | Design studies and sensor tests for the beam calorimeter of the ILC detector[END_REF] and also discussed in Section 7.2.1.

2 Diamond-Like-Carbon (DLC) layer.

Capacitance of CVD diamond

If we consider the diamond sensor as a parallel-plate capacitor constructed of two parallel plates, then the capacitance of a diamond sample can be calculated as:

C = 0 S d ≈ 2pF (6.7)
where 0 =5.7 is the dielectric constant of diamond and the vacuum permittivity (electric constant) = 8.85×10 -12 F/m, the diamond surface area is S=4.5×4.5mm 2 and the diamond thickness d=500 µm. Therefore, for our sample a capacitance of 2 pF is expected.

For the measurement of the real capacitance of the diamond, which depends both on the quality of the diamond and on the metallization quality, a HP 4262A LCR meter was used. The LCR meter has a Wheatstone bridge inside and it can be used for the impedance measurement. The measurement circuit is displayed in Fig. 6.7. The LCR meter feeds an alternating current i = i a sin(ωt) with ω=10kHz to the diamond sample via a PCB on which two large capacitors C C =50 nF and two large resistors R C =600 MΩ are mounted. A Keithley 2410 source-meter allows to apply a DC voltage to the sample.

CVD DIAMOND SENSORS

Z D = R D • 1 ωC D R D + 1 ωC D ≈ 1 ωC D (6.8)
The total measured total impedance is then:

Z = 1 ωC C + 1 ωC C + Z D ≈ 1 ωC D (6.9)
6.2 sCVD diamond characterisation using radioactive sources from which the capacitance of the diamond can be obtained.

The measured diamond capacitance is 1.68±0.01 pF for all the voltages. Therefore, no capacitance-voltage dependence was observed for this sample, and the measured capacitance is quite close to the expected value.

sCVD diamond characterisation using radioactive sources

Tests with radioactive sources were performed in a specially equipped clean room at LAL before testing the diamond detector at PHIL with large intensity electron beams. These tests are the standard tests to characterize each individual diamond detector. The measurements using β sources permit us to study the Landau distribution of MIPs and measure the CCE, and the measurements using α sources can be used for the study of mobility, saturation velocity and lifetime of electrons and holes separately.

Measurements using β source

Electrons with energy more than 1.6 MeV are considered as MIPs for diamond [START_REF] Kuznetsova | Design studies and sensor tests for the beam calorimeter of the ILC detector[END_REF]. For the characterisation of CVD diamonds, Strontium-90( 90 Sr) sources are usually used. 90 Sr undergoes β -decay into Yttrium-90 ( 90 Y ) with a maximum decay energy of 0.55 MeV, and its half-life time is 28.8 years. 90 Y undergoes β -decay to Zirconium-90( 90 Z) with a half-life of 64 hours and a maximum decay energy of 2.28 MeV. The activity of the 90 Sr source used for our measurement is 37 MBq. The pulse shape of the signal from 90 Sr source is shown in Fig. 6.9. The signal pulse shown is from averaging 1000 events. As the electrons and holes are generated all along the track of the MIPs, they start to be absorbed by the corresponding electrodes right after their generation, therefore, the pulse has a triangular shape [START_REF] Weiss | A CVD Diamond Detector for (n,α) Cross-Section Measurements[END_REF]. The FWHM of the pulse is around 4 ns. The pulse was obtained in self-trigger mode with 5 mV trigger level. The noise RMS and signal amplitude for the 1000 events is shown in Fig. 6.10 (a). The noise level obtained from the measurements is 2.0±0.2 mV and the signal amplitude is 16.0±2.8 mV (before normalisation by 40 dB). As the signal was obtained with 5 mV of self-trigger level, the electrons which deposit less energy are eliminated in the system. Therefore, we collected a mean charge of 13.45 fC instead of 2.88 fC as expected for 1 MIP as shown in Fig. 6.10 (b). As the expected 6.2 sCVD diamond characterisation using radioactive sources signal amplitude for 1 MIP is around 3.6 mV (with 40 dB amplifier), it is difficult to detect 1 MIP with the C2 amplifier in self-trigger mode. Therefore, a new system with a charge amplifier and a scintillator as external trigger were prepared for the detection of MIPs. The measurement set-up is shown in Fig. 6.11 together with the amplifier used the measurements. The amplifier (C6) used is a fast charge amplifier with a rise time of 3.5 ns and a Gaussian pulse shape with a FWHM of 10 ns. It is optimized for highspeed single MIP particle detection. The equivalent noise charge (ENC) is 1000 electrons comparing to 10000 electrons for C2 current amplifier. The gain of the amplifier is 4 mV/fC and the signal to noise ratio (SNR) is 6/fC.

Measurements using current amplifier

Measurements using charge amplifier

A 4 cm long aluminium collimator with diameter of 4 mm was used to collimate the emitted electrons. Under the collimator there is the DS and the scintillator. The distance between DS and sintillator is around 1.5 cm. The surface of the scintillator is 3×3cm 2 , which is relatively large compared to the DS. Therefore, we expect that in addition to the electrons which pass through both the DS and the scintillator, there are electrons which pass through the edge of the collimator and reach the scintillator without passing through the DS. These electrons can generate a signal on the scintillator and set a trigger for DS, but they don't deposit energy in the DS.

During the experiment, around 10 5 events were taken. The waveforms on the scintillator and the DS are shown in Fig. 6.12. The noise RMS was calculated for each waveform by taking the RMS of the first 400 points (before the signal start). Fig. 6.13 shows the histogram of the noise RMS (in blue) and of the amplitude of the waveforms. From the upper plot in Fig. 6.13, it can be seen that the measured noise level is 0.515±0.167 mV, which is quite consistent with the expected noise level: 1000e -×1.6 × 10 -19 × 4mV /f C = 0.64mV.

However, for the signal amplitude, besides the Landau distribution, which starts from 10mV, we observed many events triggered on the electrons which didn't go through the DS. In order to get the Landau distribution, the events with amplitude below 10 mV were 6. CVD DIAMOND SENSORS Figure 6.12: Signal waveforms of scintillator (blue) and DS (red) with trigger on scintillator eliminated from the data, and the rest of the events was fitted to a Landau distribution as shown in the lower histogram in Fig. 6.13. For the fit a Most Probable Value (MPV) 1 of 11.48 mV was obtained. This indicates an integrated charge of 2.87 fC, which confirms the former calculated expected value of 2.88 fC for MIPs.

Measurements using α source

As the estimated penetration depth of α particles is less than 20 µm in diamond, which is small compared to the 500 µm thickness DS, the electron hole pairs generated in this process can be considered as a thin layer of charge. Therefore, the measurements using α sources are considered as one of the transient current techniques (TCT) for detector characterization.

To supply α particles, an 241 Am source with an activity of 3.9 kBq was mounted at a distance of 2 mm above the diamond, where a 1 mm diameter hole was specially made in the PCB for this test. The energy of the α particles emitted from 241 Am source is around 5.4 MeV.

When a bias voltage is applied to the DS, the width of the signal collected by the electrode close to the source is only in the order of several ps (around 6 ps for 400 V of bias voltage supposing a drift mobility of 2000 cm 2 /V/s), thus it can not be seen on a scope with a sampling speed of 10 Gs/s. Therefore, the signal displayed on the scope is generated only by the charge (either electrons or holes) collected by the other electrode. By changing the polarity of the bias voltage, we can study signal from the electrons and holes separately. Fig. 6.14 shows pulse shapes from electrons and holes by averaging 1000 events, for different bias voltages. A Matlab [124] program was written to control the power supply and the scope simultaneously. The bias voltage was changed from -100 V to 400 V with .13: Signal and noise distribution measured using charge amplifier with external trigger given by the scintillator for all the recorded events (upper) and events above 10 mV fitted to Landau distribution (lower) steps of 50 V. The waiting time between each step was 600 s. A self-trigger level of ±10 mV was applied for positive and negative bias voltage separately. The 40 dB C2 current amplifier was used for the measurements. For the measurements with lower than -100 V for electrons and lower than 100 V for holes, the ±10 mV trigger level is too high. A trigger level is limited by the noise level of the C2 amplifier, we couldn't lower down the trigger level below this value. From Fig. 6.14 it can be seen that pulse widths increase as the bias voltage decreases. The rise time of the current signal is dominated by the time constant of the electronic circuit. With around 2 pF of capacitance for the DS, the rise time is around 0.1 ns. After this fast rise, the signal level should keep constant during the drift of charge-carriers. However, as there is a net effective space charge in the diamond bulk, we observe an increasing current for electrons and a decreasing current for holes, which indicates a negative space charge in the bulk. This space charge effect is explained in more detail in Ref. [START_REF] Pernegger | Charge-carrier properties in synthetic single-crystal diamond measured with the transient-current technique[END_REF].

In the 1000 events taken at each voltage, there are small part of "bad" events which maybe caused by the RF pick-up in the outside environment. Therefore, signal selection criteria were set, requiring a collected charge Q coll > 20f C and t F W HM > 6ns for all the events. Fig. 6.15 shows the distribution of Q coll for the selected events at 400 V and Q coll as a function of applied bias voltage. The collected charge gets saturated by applying higher than ∼150 V for both holes and electrons. The maximum collected charge at 6.3 Charge carrier parameters in DS 400 V is 67.7±1.9 fC for holes and 66.6±5.0 fC for electrons. Since the energy of the α source is around 5.4 MeV, assuming a mean ionization energy in diamond of 13 eV, the expected charge from the α source is around 66.5 fC. Therefore, the CCE of this diamond sample is 100% for both electrons and holes at 400 V.

Charge carrier parameters in DS

The lifetime of the charge-carriers (τ e,h ) is defined as the time for the total generated charge Q 0 to decrease by factor e -1 . It can be derived from the measurement using α sources. Besides, the charge-carrier mobility and saturation velocity can also be determined using the TCT method. We followed and applied this method described in Ref. [START_REF] Pernegger | Charge-carrier properties in synthetic single-crystal diamond measured with the transient-current technique[END_REF] and Ref. [START_REF] Pomorski | Development of single-crystal CVD-diamond detectors for spectroscopy and timing[END_REF] to obtain the charge carrier parameters for diamond sample No.2.

The instantaneous current (i(t)) induced by the charge-carrier movement in an intrinsic DS can be described using the simplified relation as shown in Eq. 6. 10 [125]:

i(t) = Q 0 • µ e,h • E 0 d e t τ ef f e,h -t τ e,h (6.10)
where Q 0 is the total induced charge, µ e,h the mobility of electrons and holes, E 0 the electric filed, d the thickness of the DS, τ e,h the lifetime of electrons and holes, and τ ef f e,h the space charge effect time constant.

The mobility of electrons and holes in Eq. 6.10 can be calculated as:

µ e,h = v dr d V with v dr = d t tr (6.11)
where v dr is the drift velocity, V the bias voltage, d the thickness of diamond and t tr the transit time of the charge carriers.

The space charge effect time constant in Eq. 6.10 is defined as:

τ ef f e,h = 0 e 0 • µ e,h • N ef f ≈ 0 t tr V e 0 • d 2 • |N ef f | (6.12)
where 0 and are the dielectric constant of diamond and vacuum permittivity, e 0 the electron charge, N ef f the net effective fixed space charge in the diamond bulk.

The drift velocity of the charge-carriers in the diamond as a function of electric field E can be described using the empirical formula [START_REF] Pernegger | Charge-carrier properties in synthetic single-crystal diamond measured with the transient-current technique[END_REF][START_REF] Li | Modeling and simulation of charge collection properties for neutron irradiated silicon detectors[END_REF]:

v dr = µ 0 e,h • E 1 + µ 0 e,h vsat e,h • E (6.13)
where µ 0 e,h is the low-field mobility for electrons and holes and v sat e,h the saturation velocities for electrons and holes.

In the measurements, the drift velocity can be defined as v dr (E) = d/t tr as shown in Eq. 6.11. The transit time (t tr ) was taken as the FWHM of the signals in Ref. [START_REF] Pomorski | Development of single-crystal CVD-diamond detectors for spectroscopy and timing[END_REF] 6.4 Tests of in air diamond sensor at PHIL taken as the total transit time t tr =t e -t s in Ref. [START_REF] Pernegger | Charge-carrier properties in synthetic single-crystal diamond measured with the transient-current technique[END_REF]. In our data analysis, we took the FWHM of the signals. Fig. 6.16 shows the drift velocity as a function of applied electric field. The curves for electrons and holes were fitted according to Eq. 6.13. From the fit parameters of the curves, the mobility and saturation velocity of electrons and holes can be obtained.

The total induced charge can be defined as the integration of the measured current pulse:

Q e,h (V ) = ttr 0 i m e,h (V, t) dt (6.14)
by inserting Eq. 6.10 into Eq. 6.14 and assuming τ e,h t tr , we can get a solution as:

Q e,h (V ) = Q 0 e,h τ e,h t tr 1 -e - t tr τ e,h ≈ Q 0 e,h (1 - t tr 2τ e,h ) (6.15)
as t tr can be expressed by the inverse drift velocity as d/v dr , the measured charge Q e,h (V ) can be plotted as a function of inverse drift velocity 1/v dr as shown in the bottom plot in Fig. 6.16. The data were fitted linearly to extrapolate the lifetime using Eq. 6.15.

The extrapolated values of low-filed mobility (µ 0 ), saturation velocity (v sat ), lifetime (τ ) and the calculated maximum charge collection distance (d cmax = v sat ×τ ) of electrons and holes are shown in Table 6.2. It can be seen that the d cmax 500µm, the thickness of DS. with low emittance (10π • mm • mrad) and low energies from 3 MeV to 5 MeV [START_REF] Vinatier | Dynamics and diagnostics of few MeV high brightness electron beams[END_REF]. The electrons with this energy can be considered as MIPs. The bunch frequency at PHIL is 5 Hz. The electron beam charge can be varied from less than 1 pC to 2.2 nC at the exit window by changing the laser intensity shining on the Mg cathode. The laser intensity can be adjusted either by adding filter cards with discrete values (eg. 3%, 50%, 70%) or by rotating a filter window with continuous values. However, as the dependence of the ejected electron beam intensity on the laser intensity is not linear, the charge of the electron beam should be measured each time after changing the laser density. The charge of the electron beam can be measured by the two Integrating Current Transformers (ICT1 and ICT2) installed along the beam line. ICT1 is about 1 m from 6. CVD DIAMOND SENSORS the cathode and ICT2 is just before the 18µm thick Ti exit window, at the end of the 5 m straight line. After the exit window, the charge can be measured by another removable ICT (ICT3) or by a Faraday cup, the measurement ranges of which are from 1 pC to 2 nC. For charge measurements below 1 pC, a 100 µm thick YAG:Ce screen with a CCD camera can be used, this can bring the lower charge measurement limit to 0.5 pC. For lower than 1 pC measurement, we used a LANEX (R) screen, which has higher light yield and less blurring effects. The light emitted from the LANEX screen was calibrated with the charge measured by Faraday cup (see Fig. 6.18). The calibration was done for different gain factors to enable measurement with a large dynamic range. Extrapolating that calibration below the sensitivity of the Faraday cup enabled the LANEX screen to be used for beam charges as small as 33±11 fC [START_REF] Vinatier | Measurement of lowcharged electron beam with a scintillator screen[END_REF].

µ 0 , [cm 2 /Vs] v sat , [µm/ns] τ , [ns] d cmax , [
The beam size at PHIL can be measured by the two YAG:Ce screens (YAG1 and YAG2) in the beam line and by the YAG:Ce screen (YAG3) or the LANEX screen installed after the exit window. The typical beam size is around 2 mm×2 mm at the exit window.

Experimental set-ups

Tests of in air diamond sensor at PHIL Coaxial cables and signal attenuation

Since 100 m long coaxial cables are used for the fast signal transmission at PHIL, it is essential to study different types of coaxial cables and to check the possibility of avoiding significant signal attenuation and distortion by using high enough quality coaxial cables.

The coaxial cable conducts electrical signal using an inner conductor (usually a solid copper, stranded copper or copper plated steel wire) surrounded by a dielectric layer and all enclosed by a shield, typically braided flexible shield or solid tube semi-rigid shield. Outside of the shield the cable is protected by an outer insulating jacket (see Fig. Signal attenuation (loss) on the coaxial cable depends on the loss in the dielectric material filling the cable, and on resistive losses in the center conductor and outer shield. These losses are frequency dependent, the losses becoming higher as the frequency increases [128]. The loss per meter of a cable can be calculated according to the following equations:

α conductors = 11.39 Z * f * ( √ ρ rd d + √ ρ rD D ) (6.16) α dielectric = 90.96 * f * √ ε r * tan(δ) (6.17)
where:

• α conductors = losses in the conductor in dB/m

• α dielectric = losses in the dielectric in dB/m

• d = outside diameter of inner conductor in mm

• D = inside diameter of outer conductor in mm

• ε r = relative dielectric constant • f = frequency in GHz
• ρ rd = inner conductor material resistivity relative to copper

• ρ rD = outer conductor material resistivity relative to copper The loss on the inner conductor is also called Skin Effect losses. It is the dominating loss when the signal frequency is below 10 GHz as shown in Fig. 6.21. This loss can be reduced by increasing the inner conductor diameter of the cable. A cable with twice the diameter will have half the skin effect resistance. Ignoring dielectric and other losses, the thicker cable would halve the dB/meter loss.

• δ = loss tangent

Measurements of cables

In order to avoid signal attenuation and prevent the deformation of the pulse shape due to the cable, coaxial cables with 50 Ω impedance are used for the fast signal transmission. The cables were tested at LAL using a fast pulse generator (Picosecond step generator 4050B). An input square pulse with 10 ns width, ∼45 ps rise time and 5.22 V amplitude was generated and sent to the oscilloscope. The pulse shapes were compared for the signal transmission with and without the cables. Tests of all the types of cables with different lengths are summarised in Table 6 Two examples of the test results for 50 m RG58 and 1/4 inch Heliax cable are shown in Fig. 6. [START_REF] Liu | Investigation of beam halo using in vacuum diamond sensor at ATF2[END_REF]. We can see that the attenuation and deformation of the pulse is much less for the 1/4 inch Heliax cable than for the RG58 cable. Thus for long distance (>10m) signal transmission, we have chosen the 1/4 inch and 1/2 inch Heliax cables. And we used RG58 cables only for short distance signal transmission in the tests.

Experimental results

Pulse waveforms

In the tests using β source we have shown that the typical pulse width for a MIP particle is around 4 ns (see Fig. 6.9). However, at PHIL we have observed that with increasing number of incident electrons, the pulse width also increases. Fig. 6. [START_REF] An | Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay[END_REF] shows examples of pulse shapes for different beam intensities. The charge of the beam was measured by the LANEX screen. We can see that the pulse fall time increases with the beam intensity, while the rise time stays almost constant.

The rise time of the current signal is dominated by the time constant of the electronic circuit. Therefore, it doesn't change with the input beam intensity. However, the fall time, which indicates the time for the charge carriers to arrive on the electrodes, highly depends on the charge carrier drift velocity. We have shown before that the drift velocity depends on the electric field as expressed by Equation 6.13, therefore, the increasing fall time indicates a decreasing electric field in the DS. This can be explained by the voltage drop on the 50 Ω resistor which is used for the signal readout and for the impedance matching for the coaxial cable as shown in Fig. 6.3. The voltage drop (V drop (t)) can be expressed as:

V drop (t) = I(t) × 50Ω (6.18)
therefore the effective bias voltage (V ef f (t) applied on the DS can be estimated as: where V bias is the applied bias voltage.

V ef f (t) = V bias -V drop (t) (6.19)
In order to study the effect of the voltage drop on the linearity of the response of the signal amplitude and signal charge, measurements were done for a large range of incident beam intensity using the calibrated LANEX screen to evaluate the total charge.

Number of incident electrons

In the experiment, the LANEX screen is not only used for the total charge measurement, but also for the beam size measurement. As the beam core follows a Gaussian distribution after the exit window, knowing the beam size, the number of electrons intercepted on the diamond can be calculated by the following formula:

N = N t 2 * π * σ x * σ y 1 2 lx -1 2 lx e -x 2 2σ 2 x dx 1 2 ly -1 2 ly e -y 2 2σ 2 y dy (6.20)
where N t is the total number of electrons, σ x and σ y the measured horizontal and vertical beam sizes, l x and l y the horizontal and vertical width of the electrode metallization on the diamond sample (4 mm).

Dependence of signal amplitude on intensity

The dependence of signal amplitude on intensity is shown in Fig. 6.24. During the measurement, 10 images were taken by the LANEX screen at each intensity to get the averaged charge and beam size for calculating the number of intercepted electrons. It 6.4 Tests of in air diamond sensor at PHIL can be seen that the fluctuation of the measurements is much more significant for lower intensity than for higher intensity. The pulse amplitude starts to get saturated after an injection of more than 2×10 6 electrons (0.32 pC). The saturation of pulse amplitude can be explained by the voltage drop on the DS when a large current goes through the 50 Ohm terminator, which means a reduction of the electric field and consequently of the drift velocity of the electrons and holes. This can also lead to electron-hole recombination if the charge collection time gets larger than the recombination time. in Eq. 3.1, the effect of strip width on the beam size measurement can be taken into account:

σ 2 DS ≈ σ 2 f it - d √ 12 2 (6.21)
where d is the strip width, σ f it is the beam size from the fit and σ DS is the real measured beam size by DS. More detailed explanation about the signal convolution is given in Section 7.5.3. The measurement set-up and results are presented in Fig. 6.26. The measurement conditions and beam size comparison with the YAG screen measured beam size are shown in Table 6. [START_REF] Zimmermann | HL-LHC: Parameter space, constraints, and possible options[END_REF]. From this table it can be seen that the DS measured beam size is close to the YAG screen measured beam size (σ Y AG ) only if the beam size is close to or bigger than the strip width, when the beam size is smaller, the measured beam size is larger than the real beam size.

Therefore for the design of the in vacuum DS at ATF2, as the simulated beam size at DS location is around 1.5 mm, the strip width should not exceed 1.5 mm for the beam core measurement.

7

The in vacuum diamond sensor An in vacuum diamond sensor (DSv) was designed for beam core and beam halo measurements with large dynamic range. The design of the in vacuum diamond sensor was done in collaboration with the CIVIDEC company [START_REF] Griesmayer | [END_REF]. This DSv was characterized using the radioactive sources at CERN and tested using the electron beam at PHIL before the installation at ATF2. Further measurements were done at ATF2 to define the dynamic range and linearity response. In this chapter we will describe the design of the DSv, the measurements we have done to characterize the DSv and discuss the different effects observed during the measurements.

Design of the in vacuum diamond sensor

For the measurements at ATF2, a large signal range from 10 2 /mm 2 for Compton and 10 4 /mm 2 for beam halo to 10 8 /mm 2 for beam core is required (see Table 7.1). As in first approximation the signal strength is proportional to the metallised surface of the electrode on the diamond, a geometry with four strips was adopted to help cover this large dynamic range (see Fig. 7.1). The two strips for beam halo scanning are on the two outer sides, with dimension 1.5 mm× 4 mm, and the other two in the center are for beam core scan, with dimension of 0.1 mm×4 mm. Besides, one 0.5Ω resistor was added to one of the narrow strips (CH2) on sample No.1 to act as a current divider. On sample No.2 there is no 0.5Ω resistor. Sample No.1 was used for the tests at PHIL and sample No.2 was installed at ATF2 for the horizontal beam halo measurement.

Name

Total

PCB and electrical circuit design

For the in vacuum application a ceramic PCB is used. The ceramic PCB uses silverplatinum conductor produced in thick-film technology. The PCB and the electrical circuit for the diamond detector are shown in Fig. 7.2, a low pass filter together with the charging capacitors are mounted on the backside of the ceramic PCB. The parameters of this circuit were set based on the following considerations:

• The cut-off frequency for variations of the supplied high voltage should be as low as possible to maintain the stability;

• The amount of charge stored on the capacitors should be large enough for measurements of large beam intensities, up to 1 µC on the narrow strips;

• The charging time constant should be small to enable measurements of successive bunches, the bunch repetition rate being 5 Hz at PHIL and 3 Hz at ATF2;

The simulated cut-off frequency for the present circuit is 8 Hz with 500 µC maximum stored charge at 500 V and the charging time constant is 44 ms.

Mechanical design

The diamond sensor is designed to be installed in vacuum with a holder to scan the beam core and beam halo. The mechanical design (see Fig. 7.3) was done and fabricated at LAL. The whole setup is 744 mm long and it can be oriented either horizontally or vertically to scan in different axes. The vacuum chamber, with inner diameter of 72.1 mm, is connected to the beam pipe, which has a diameter of 63 mm. It is installed after the BDUMP bending magnet at ATF2 via two DN63CF flanges. At ATF2 the DSv is inserted from the low energy (LE) side to the high energy (HE) side. This design is compatible for PHIL and ATF2. Therefore, it was installed and tested at PHIL before the implementation at ATF2.

Characterization of DSv

First tests of the DSv were done at CERN together with the CIVIDEC company in May 2014, including I-V curve measurements and tests using radioactive sources. Then the DSv with the mechanics were installed at PHIL for tests in vacuum using electron beams. In the tests, different strips are refereed to as different channels. CH1 and CH4 represent the wide strips, CH2 and CH3 represent the narrow strips.

Characterization of DSv

I-V measurement

Prior to the I-V measurement, the dark current settling time 1 is measured. Fig. 7.5 shows an example of the measured dark current settling after applying 10 V and 50 V. It can be seen that, in this example, the dark current settles after ∼5 s for both cases. However, in our experiments the waiting time was set longer ( 15 s) to ensure a stabilised dark current level. For the measurement of sample No.1, we changed the bias voltage with 50 V steps up to ±600 V. The current was recorded each 0.2 s, but only the data taken after the 15 s waiting time (∼20 points) were averaged to get the dark current (see Fig. 7.6). However, for sample No.2, the dark current level was much higher than for sample No.1 and the settling time was also longer (>30 s) 2 . Therefore, we did the measurement by manually changing the bias voltage continuously 3 . Fig. 7.6 shows the hysteresis loop of I-V dependence for CH1 of sample No.1 and CH4 of sample No.2. The measured dark current for CH1 of sample No.1 is below 0.6 pA. The other channels on sample No.1 had similar levels of dark current. However, for sample No.2, the measured dark current level is ∼100 pA at +500 V and ∼60 pA at +400 V. This is 100 times higher than sample No.1, however, as long as the dark current is below nA level, it is acceptable, since the current generated by 1 MIP is ∼1 µA.

In principle the bias voltage applied to DSv can be raised to 1000 V, however, as the other components (resistors and capacitors) can only stand a bias voltage of 500 V, and 1 After the voltage change, a long settling process was observed for the measured current. The settling time is the time it takes for the current to settle down [START_REF] Kuznetsova | Design studies and sensor tests for the beam calorimeter of the ILC detector[END_REF].

2 We assume this is due to the different levels of impurity between the two samples, since the settling time and the dark current level are both related to the crystallographic defects inside the diamond bulk [START_REF] Kuznetsova | Design studies and sensor tests for the beam calorimeter of the ILC detector[END_REF].

3 For a given waiting time, the measured dark current level is lower by changing the bias voltage continuously than changing it in steps.

123 7. THE IN VACUUM DIAMOND SENSOR as we have observed a sudden rise of dark current after applying more than 400 V for sample No.2, we defined the safe operation bias voltage range as ±400V .

Measurements using β source

Measurements using β source were done for the two samples of DSv. Four 40 dB current amplifiers were used for simultaneous signal readout of the four channels. The measurement set-up is similar to the one described in section 6. From these figures we can see that when the MIPs pass through one channel, small signals on the other channels can also be observed. The signals on the other channels are from the induced current due to capacitive coupling. This effect can be caused by the capacitance between the strips on the DS itself and by the capacitance between the signal readout lines on the PCB (see Fig. 7.4). Therefore, even though CH1 and CH3 is separated by CH2, as their readout lines are next to each other, CH3 has a stronger induced current than CH2 when the signal is triggered on CH1. The same effect can be seen when the signal is triggered on CH4 (see Fig. 7.8).

Tests of DSv at PHIL

The DSv was installed at PHIL in Sept.2014. It was installed horizontally in the end of the beam line just before the exit window. The main purpose of the tests was to prepare our data acquisition system, test the motor system and verify the signal response on different channels of the DSv. The experimental set-up is similar to the tests in air after the exit window of PHIL (see section 6.4.1). In order to test two channels at the same time in the control room, we added another cable line using 50 m 1/2 inch Heliax cable plus 50 m 1/4 inch Heliax cable. As we didn't have additional Heliax cables, simultaneous tests for four channels were done by putting the Agilent scope inside the experiment hall and connecting to the DSv using 2 m long RG58 coaxial cables.

In order to increase the maximum input signal voltage into the scope from 4 V to 40 V, four 50Ω terminators were added in parallel to the four channels on the scope. This enables the usage of the 1MΩ input impedance on the scope, with a maximum input signal of 40 V.

Outgasing issues

After first installation we found an outgasing issue caused by the Allectra coaxial cables which are used to transmit the signal inside the vacuum chamber, from the PCB to the feedthrough (see the schematic in Fig. 7.13). This issue prevented the vacuum to be pumped below 10 -4 Pa. Since the main component of the gas was found to be water molecules, the whole system was pre-baked before installation for mitigation of outgasing. This procedure allows to reach better than 5 × 10 -6 Pa pressure as long as the system is not vented for longer than four hours before installing and pumping again.

Signal pick-up and reflections

As the ceramic PCB, on which the DS is mounted, is not shielded, when the beam pass by/through the PCB, a bipolar current pulse is induced on the signal readout lines on the PCB. The signal given by the induced current is called pick-up signal.

Pick-up signal was observed during the tests using the DSv without applying a bias voltage. An example of pick-up signal waveforms is shown in Fig. 7.9. The integrated charge of the pick-up signal is at the level of 1pC. This level of signal doesn't effect the beam core measurement at PHIL with the signal level of 100 pC.

For the tests at PHIL, we applied -300 V bias voltage to the DSv. Fig. 7.10 shows the waveforms obtained for the 4 channels when the beam is centered on CH1. An obvious periodical reflection with a delay of ∼30 ns can be seen on each channel. This reflection is due to the impedance mismatch of the 50 Ω terminators1 with respect to the cable impedance. Tests of those 50 Ω terminators were done using the Time Domain Reflectometry (TDR) technique, which will be explained in Section 7.4.2.

Beam core scan

After investigating the signal waveforms, it is important to verify the signal strength. As prior tests with a DS pad (DS sample No.2) were done in air (see Section 6.4), and the signal was calibrated, it is worthwhile to compare the signals obtained from the DSv with those from the DS pad in air. Therefore, we installed the DS pad after the exit window as shown in Fig. 7.11. The distance between the DSv and the DS pad is around 133 mm. Both the DSv and the DS pad were connected to a 12 dB attenuator. The beam is aligned vertically using the steerer upstream. The input beam intensity is 62 pC and the beam size measured at the YAG3 screen, which is 22 cm upstream of the DS, was σ x =1.57±0.08 mm and σ y =1.92±0.06 mm. The bias voltages applied on the DSv and DS pad were -300 V. Fig. 7.11 (lower left) shows the signals on each channel of the DSv when the beam is centred on CH1, and Fig. 7.11 (lower right) shows the signal on the in air DS pad. It can be seen that the signal amplitudes are of the same order of magnitude (-4.5 V for CH1 of the DSv and -3.25 V for the DS pad). Although the DS pad has a larger surface than the DSv CH1 strip, as the beam is diverging both in X and in Y, the signal level on the DS pad in air can be smaller. Beam core scans using the DSv were done by applying -300 V of bias voltage. The integrated charge of the waveforms was plotted during scanning. The distribution of the integrated charge is shown in Fig. 7.12. As CH2 is connected to a 0.5 Ω, and the scope resolution is not optimised for this channel, the distribution on CH2 is almost flat. However, for the other channels we can clearly see negative peaks which indicate the signal level when the beam passes through the center of each channel. The distance between these peaks corresponds well to the distance between the centers of different channels.

In addition, positive peaks can also be seen in the distributions, the origin of which are still under investigation.

Experimental set-up at ATF2

The first set of DSv was installed at ATF2 in Nov.2014. It was installed horizontally for the purpose of measuring the horizontal beam halo distribution and investigating the possibility of measuring the Compton recoil electrons, which are distributed on the low energy side after the BDUMP bending magnet.

Data acquisition system

For the reason of radiation safety, the oscilloscope and other readout electronics were located in the IP laser room outside the tunnel. Therefore, in order to collect the signal 128 7.4 Experimental set-up at ATF2 stepping motor, the resolution of the steps is 10 µm and the repetition accuracy is up to 3µm. The precision we set in the Matlab program is 50 µm.The maximum scan distance is 110 mm. The moving speed and acceleration can be adjusted. This motor can be controlled via a commercially developed software called "Festo". Also one can check the status of the motor via the web interface. However for the integration into the control system, we used the Matlab program to connect to the motor and use web commands to control the motor. In our program we used two moving speeds, one with 1 mm/s for fast moving before reaching the destination with a resolution of 100 µm, and once this resolution is reached, we use a slower speed (crawling velocity) of 0.25 mm/s to adjust the position up to 50µm of resolution. The acceleration was set to 0.2 m/s 2 .

In order to calibrate our DSv signal using the ICT measured charge and also verify the beam jitter level at the DSv location, we connected to the EPICS [START_REF] Clausen | EPICS: Experimental physics and industrial control system[END_REF] system via SSH on Matlab and read data simultaneously from the ICT located after the BDUMP bending magnet and from the C-band BPM "MPIP" located after the IP. Fig. 7.14 shows the data taken via the EPICS system during the DSv scan. The data is synchronised to the DSv data pulse to pulse.

TDR measurements and impedance matching

In order to define the length of the cables and the impedance matching level of the whole system, Time Domain Reflectometry (TDR) measurements were performed using the Tektronix 80E04 TDR module. Time Domain Reflectometry (TDR) measures the reflections that result from a signal travelling through a transmission environment (e.g. a circuit board trace, a cable, a connector and so on) [START_REF]TDR Impedance Measurements: A Foundation for Signal Integrity[END_REF]. TDR measurements are described in terms of a Reflection Coefficient, ρ. The coefficient ρ is the ratio of the reflected pulse amplitude to the incident pulse amplitude:

7. THE IN VACUUM DIAMOND SENSOR ρ = V ref lected V incident (7.1)
For a fixed termination Z L ,ρ can also be expressed in terms of the transmission line characteristic impedance, Z 0 and the load impedance Z L .

ρ = V ref lected V incident = (Z L -Z 0 ) (Z L + Z 0 ) with Z L = Z 0 1 + ρ 1 -ρ (7.2)
where Z 0 = 50Ω in our case. If there is no reflection, then ρ=0 and Z L = Z 0 . When there is a short circuit, then ρ=-1 and Z L =0. When there is an open circuit, then ρ=1 and Z L = ∞. Figure 7.15 shows the TDR measurement for the DSv No.1 by connecting each channel to the TDR module using the 64 cm long Allectra vacuum cable, which is used to transmit the signal from the PCB to the feedthrough. The measurement result is shown in Figure 7.13 bottom. As CH2 is connected to a 0.5 Ω the response is close to a short circuit. The valley in the plot shows the impedance mismatch of the PCB. The difference of the valley width between CH1 and CH4 indicates the different length of path on the PCB.

The mismatch of impedance will cause the reflection of signals along the transmission line. This effect can be observed in the signal waveforms in Fig. 7.10 and Fig. 7.17.

The measurement for the experimental set-up with all the cables is shown in Figure 7.16. In our experiment, we have used the 1/4 inch LDF1-50 Heliax cable (with foam polyethylene dielectric), RG58 coax cables (with solid polyethylene dielectric) and vacuum cable (with kapton dielectric).

The velocity of signal propagation in the coaxial cable depends on the material of the insulator surrounding the inner conductor. The ratio between the transmission velocity in the cable and the speed of light is called the velocity factor (VF), which can be calculated as:

VF = 1 √ κ (7.3)
where κ is the dielectric constant (relative permittivity).

For the foam polyethylene dielectric, the VF is 82% and for the solid polyethylene dielectric and kapton dielectric they are 66% and 58.7%, respectively. Knowing the signal propagation speed and signal reflection time measured by TDR, we can calculate the length of the cable.The measured lengths of the cables are indicated in the figures (see 7.16).

TDR measurements were also done for the 50 Ω terminators that were connected to the scope to enable the usage of the 1 MΩ input impedance on the scope, which increases the maximum input signal voltage from 4V to 40V. The tests show that the impedance mismatch caused by the 50 Ω terminators is much higher than the mismatch of the cables and PCB. Besides, as the 50Ω terminators are connected to the end of the signal transmission line, the reflected signal has a delay of ∆t=2*L t /(C*VF), where L t is

THE IN VACUUM DIAMOND SENSOR

the total cable length and C is the speed of light. The estimated delay for the system is around 200 ns for the setup at ATF2 and this reflection can easily be seen on the signal waveforms as shown in Fig. 7.17. Therefore, we can confirm that the signal reflections we have observed both at PHIL and at ATF2 were caused by the impedance mismatch cased by the 50 Ω terminators, which are not perfectly 50 Ω. In order to mitigate the reflection, 50 Ω terminators with better quality than the ones used at PHIL are used at ATF2 for further measurements (see Fig. 7.17).

Scope vertical range setting

The scope resolution depends on the vertical range (VR) applied on the scope setting. The Agilent scope we used has a vertical resolution of 8 bits and a vertical sensitivity from 2 mV/div to 5 V/div. The measurement resolution of the scope can be calculated as:

Resolution = V R 2 8 (7.4)
Therefore, for the minimum scope range of 2mV/div, we have the maximum measurement resolution of 62.5 µV.

For the measurements of beam halo, as a large dynamic range is required, the scope VR should be adjusted for different measurement ranges. To achieve this, one can either set the VR manually for a certain range of scanning and change it for another range or change the VR at each position automatically as will be explained in the next paragraph. Fig. 7.18 shows the difference of these two VR setting methods. By changing the VR manually at each range, we observe a distribution with several steps, and normalization between the steps will be needed as done for the measurements using wire scanners (for the data taken at different bias voltage). However, by changing the VR automatically at each position, a continuous beam halo distribution can be obtained. Fig. 7. [START_REF] Liu | Beam Halo Measurements using Wire Scanners at ATF2[END_REF] shows the distribution of the VR set for the scope during the beam halo scan. In the program, at each point we set three VRs: 50 mV, 500 mV and 5 V to test which VR gives the best signal to noise ratio (SNR) without going into saturation, then we take the amplitude measured at this VR and multiply it by factor 4. In this way, the signal fills 1/4 of the full screen with a certain offset 1 . However, from Fig. 7. [START_REF] Liu | Beam Halo Measurements using Wire Scanners at ATF2[END_REF] we can see that: 1) On the two edges of the beam halo, as the signal amplitude is given by the pickup signal, the VR which is set is relatively large. At 0 mm position, when the DS is completely out from the beam, the VR is ∼ 0.2 V. According to Equation 7.4, the scope measurement resolution is then 0.78 mV, which corresponds to a level of ∼100 electrons supposing a FWHM of 10 ns 2 . Therefore, if there is no signal pick-up, a smaller VR can be set, and we should be able to measure less than 100 electrons. 2) Near the beam core, when the signal reaches the limit of the screen (20 V w/o offset) during the test, the output VR will be 80 V which is more than the limit of the VR (40 V), then the VR is set to 40 V by default. This explains the saturation level of 40 V as shown in Fig. 7.19. To avoid the saturation of VR, the scan range should be set with care (normally > 3σ or < -3σ ). In the data analysis, the ones taken with a saturated VR are excluded from the distribution.

1 Also to prevent the saturation of signal and to register the full waveform in the beam halo region with the existence of pick-up signal, which has a bipolar waveform shape.

2 Assuming a minimum SNR value of 2 to perform the measurement, the minimum measurable amplitude is V=0.78×2 mV and the minimum measurable charge Q=10 ns×0.78×2 mV/50 Ω ≈300 fC, which corresponds to ∼100 electrons

For the first effect, we need to avoid the pick-up signal in the measurements, therefore shielding of the PCB will be required. The shielding procedures are under discussion together with the CIVIDEC company.

For the second effect, as the pick-up signal has a much higher frequency than our signal, we can add a low pass filter (LPF) in the data analysis to recover the signal waveforms.

Fast Fourier Transform and Low Pass Filter

Fast Fourier Transform (FFT) is an algorithm for transforming data from the time domain to the frequency domain. In frequency domain, we can see clearly the frequencies of different components of the signal that we have measured. In Fig. 7.21 the FFT of signal waveforms from CH1 are shown for different ranges of motor position during pickup scanning as shown in Fig. 7.20. Except for the waveforms near the beam core region (50-70 mm), where the distribution is dominated by the lower frequency signal1 , we can find a common peak at around 0.3 GHz. We suppose that this frequency correspond to the pick-up signal frequency.

With a Low Pass Filter (LPF), the signals with frequency higher than the defined cutoff frequency (known as stopband) are attenuated, and only the signals below the cutoff frequency can pass through without attenuation. By removing some frequencies, the filter creates a smoothing effect. That is, the filter produces slow changes in output values to make it easier to see trends and boost the overall signal-to-noise ratio with minimal signal degradation [131]. Fig. 7. [START_REF] Liu | Investigation of beam halo using in vacuum diamond sensor at ATF2[END_REF] shows an example of the signal before and after applying the LPF. The LPF applied is a 1-D digital filter with a cutoff frequency of 0.2GHz.

Signal Convolution

In Section 3.3.3 we have mentioned that wire scanner measured distributions can be considered as convolutions of a cylindrical distribution and a Gaussian distribution. For the measurements using DSv strips, we can similarly consider the measured distribution (S(ξ)) as the convolution of a uniform distribution (L(x)) and a Gaussian distribution (I(x)).

The uniform distribution can be expressed as:

L(x) = 1 |x| ≤ l 2 0 |x| > l 2 (7.5)
where is the width of the DSv strip. The Gaussian distribution with maximum intensity of I 0 , beam size of σ and mean value of µ can be expressed as:

I(x) = I 0 e -(x-µ) 2 2σ 2 (7.6)
Therefore, we can get the convoluted signal at position x = ξ, which can be expressed as:

S(ξ) = K(L * I)(ξ) = ∞ -∞ KL(x -ξ)I(x) dx (7.7)
where K is a constant. The convolution of the uniform and the Gaussian distribution (S(ξ)) can also be expressed using the error functions 1 as shown in Equation 7.8. This equation is used 1 The error function is defined as: erf (x) = x √ π

x 0 e -t 2 dt.

THE IN VACUUM DIAMOND SENSOR

for the beam core fit in the Matlab program to get the beam size σ after the beam core scan.

S(ξ) = KI 0 ξ+ l 2 -ξ-l 2 e -(x-µ) 2 2σ 2 dx = KI 0 (erf ( ξ + l 2 -µ √ 2σ ) -erf ( ξ -l 2 -µ √ 2σ
)) (7.8)

Linearity of DSv response

The linearity of the DSv response is considered as one of the most important characterization aspects as it defines the linear region of operation and provides corresponding normalization factors for the calibration in the non-linear region.

In order to check the linearity, the beam intensity should be changed. This can be done in two ways: 1) change the input laser intensity at the photo-cathode; 2) change the DSv position in the beam core.

The ICT sensitivity allows measuring beams of more than 10 9 electrons. In order to measure lower beam intensities we changed the DSv position in the beam core. At each position we changed the beam intensity from 10 9 to 7 × 10 9 electrons and took 100 waveforms for each beam intensity. Two campaigns of measurements were done in Dec.2014. Before the measurement, the beam was aligned vertically as described in Chapter 8.2.1. The beam core was then scanned horizontally and fitted according to Eq. 7.8 to get the horizontal beam size (see Fig. 7.23 (a)).

For the calculation of the number of incident electrons, similar to the measurements done at PHIL, as the beam core follows a Gaussian distribution, the number of electrons intercepted on each channel N CH at different positions can be calculated by adding a horizontal offset (d x ) to formula 6.20 as shown below:

N CH = N t 2 * π * σ x * σ y 1 2 lx+dx -1 2 lx+dx e -x 2 2σ 2
x dx 1 2 ly -1 2 ly e -y 2 2σ 2 y dy (7.9)

The horizontal beam size in the formula is the measured beam size by the DSv, which can be obtained from the fit of the beam core. However, as the vertical beam size can not be measured at the DSv location, it was obtained either by simulation using Madx or by extrapolating from the Post-IP measured beam size. The difference between the two methods are compared in Section 8.4.4.

For the first measurements, the DSv was put at 1σ away from the beam core (60.02 mm motor position), as shown in Fig. 7.23 (a). The measured beam size is ∼1.7 mm. The bias voltage was changed from 40 V to 200 V and 400 V to investigate the change of Charge Collection Efficiency (CCE) as a function of bias voltage. From Fig. 7.23 it can be seen that by increasing the bias voltage, the collected charge is increased which indicates an increasing CCE.

The charge collected by CH2 and CH3 seems quite consistent with CH1, for which the slope starts to deviate from the expected value. However, the signal on CH4 seems much less than what we expected. This might be the caused by the same effect as what we have observed at PHIL. When a high intensity beam goes through one channel, there is an inverted signal on the other channels, then the signal measured on the other channels is the combination of the inverted signal and the beam generated signal. From Fig. 7.12 we can see that the inverted signal level on one wide strip (CH1 or CH4) is about 20% of the measured signal on the other wide strip (CH4 or CH1) which is centered. After correcting CH4 for this 20% effect, the signal on this channel becomes much more consistent with signals on other channels, as shown in Fig. 7.24. Since the inverted signal on the narrow strips are negligible, correction was done only for CH4. From Fig. 7.24 we can see that the deviation of the signal from the expected value starts at a beam intensity of 10 7 electrons. This can be explained by the voltage drop on the 50 Ω resistor on the scope. This voltage drop (V drop ) is proportional to the number of input electrons and it will reduce the effective bias voltage on the DSv (V ef f ), which can be defined as:

V ef f = V bias -V drop (7.10)
V drop can be read out directly from the waveforms on the scope and it changes together with the current. Fig. 7. [START_REF] Hewett | Fundamental physics at the intensity frontier[END_REF] shows the signal waveforms of CH2 and CH4 in the beam center. The calculated number of input electrons (N CH ) using Eq. 7.9 is ∼ 10 7 and ∼ 10 8 for CH2 and CH4, respectively. From the waveforms it can be seen that, immediately after the passage of a high intensity beam, a sudden rise of current is induced due to the fast movement of electrons and holes in the externally applied electric field (reaching rapidly their saturation velocities (v sat )). The instantaneous current generated by the N CH input electrons can be calculated using the Shockley-Ramo formula (see Eq. 7.11) as:

I = E v • q • v sat with q = N CH × 2.88 f C (7.11)
where E v is the normalized electric field. Assuming an averaged saturation velocity of v sat ≈ 100µm/ns according to our measurements results for the in air DS (see Table 6.2), an instantaneous current of I ≈ 5.76A can be obtained for N CH = 10 7 , which corresponds to ∼288 V of output voltage. This calculated output voltage is quite consistent with the signal amplitude for CH2 as shown in Fig. 7.25 (a). However, immediately after the arrival of this instantaneous current at the 50Ω resistor, a large voltage drop (∼288 V) is created, resulting in an effective bias voltage of 7.5 Characterisations of the DSv at ATF2 V ef f ≈ 112V . Since the CCE depends on the V ef f (see Fig. 6.15 (b)), when a large voltage drop occurs the drift velocities of electrons and holes are decreased, the charge collection time is extended, which increases the recombination probability and consequently less charge is collected. This increase of charge collection time can be observed from the long tails in the waveforms in Fig. 7. [START_REF] Hewett | Fundamental physics at the intensity frontier[END_REF].

Except for the voltage drop, space-charge effect is another reason for the increase of charge collection time. Modelling of charge collection processes taking into account these two effects was done by V. Kubytskyi and is explained in Ref. [START_REF] Kubytskyi | Modeling/Measurement Comparison of Signal Collection in Diamond Sensors in Extreme Conditions[END_REF]. The simulations have shown that V drop V bias for less than 10 5 input electrons, and for N CH = 10 6 the V drop is estimated to be ∼ 25V , which still does not strongly affect the charge collection dynamics. However, when N CH > 10 6 the signal V drop reaches values even larger than V bias , which is unphysical and contradictory with our measured signals, therefore, V drop at maximum can reach the values close to V bias (see Fig. B. This behaviour is similar to the what we have observed from Fig. 7.23, however, as the beam intensity is 10 times higher, the correction factor may be higher than 20%. Corrections were done with 20% and 40% of the signal from the channel that is centred, the comparison of the signals with different correction factors is shown in the Fig. 7.26 (c and d). It can be seen that with 40% correction the data fits better than with 20% correction. After correction the data is quite consistent with the data taken on 12th Dec. 2014 (see Fig. 7.24) with the same saturation level at 10 7 electrons. However, we don't have a clear argument why the correction should be 40% rather than 20% as observed in the PHIL measurements. This point requires further study.

Part IV

Measurements using diamond sensor 147

Beam halo horizontal distribution measurements at ATF2

After characterising the "in vacuum" diamond sensor (DSv) at ATF2, beam core and halo transverse horizontal distributions were measured at ATF2 in Nov.-Dec. 2014. Beam core measurements were used for the normalisation of the beam halo distribution.

In this chapter, the data taking and analysis procedures are described. Beam core and beam halo distributions measured with different beam intensities and beam optics are presented and compared.

Data taking procedures

The data taking procedures defined for the measurements were as follows:

• DSv horizontal centering: beam core scan using DSv with low bias voltage (-40 V) to find the horizontal beam center;

• Vertical Alignment (VA): move the AQD0FF mover to steer the beam vertically and find the vertical beam center, where the signal on the DSv is maximum;

• Post-IP wire scanner beam core scan: scan the beam core using the Post-IP wire scanner to get the horizontal and vertical beam sizes for beam size verification;

• DSv beam core scan: beam core scan using the DSv after VA with high bias voltage (-400 V) and 30 dB attenuators;

• Beam core fitting: fit the beam core to get the beam size and define the beam halo scan region;

• DSv beam halo scan: beam halo scan using the DSv with a bias voltage of -400 V without attenuators in the region of <-3σ for the low energy (LE) side (left side) and >3σ for the high energy (HE) side (right side). AT ATF2

Data analysis procedures

The data analysis procedures consist of pedestal subtraction, ICT correction and data binning, which are explained in more detail in the following subsections. Signal waveforms have a certain level of pedestal as the Agilent oscilloscope is not well calibrated. The pedestal level of each channel is different and it changes with the vertical range (VR) setting. Therefore, pedestal subtraction is quite essential for the data analysis.

Pedestal subtraction

The pedestal level is defined for each waveform by taking the average value of the points before the arrival of the signal (see Fig. 8.1). In order to get a better statistics for the pedestal calculation, in the experiment a delay of 1 division of full timebase (1/10 of full timebase) was set to ensure at least 100 points for averaging. Then the pedestal level is again averaged over 10 waveforms. After that, the averaged pedestal level is subtracted from each waveform. Fig. 8.2 shows the measured average pedestal level during the scan and the beam core and beam halo distribution before and after pedestal subtraction. It can be seen from Fig. 8.2 (a) that for the beam core scan, as the scope VR is a constant, the pedestal level is also stable during the scan. However, for the beam halo scan (Fig. 8.2 (c)), as the scope VR changes at each point, the pedestal level is also changed. Depending on the signal level, the pedestal level can range from several mV for beam halo to ∼100 mV for the beam core. From after pedestal subtraction the integrated signal charge from CH1 is more consistent with the signal from CH4 than before pedestal subtraction.

ICT correction

The ICT data, obtained through the EPICS system as mentioned in 7.4.1, provides the information of the total number of electrons (N t ) in the beam. As N t may fluctuate from pulse to pulse, ICT correction was done to check the effect of beam intensity variations on the beam halo distribution.

For the ICT correction, first the mean ICT value (ICT mean ) was calculated from all the ICT values registered during the whole scan. As 10 waveforms were taken at each AT ATF2 The integrated charge for each waveform (Q i ) can then be corrected as:

Q icorrect = Q i × ICT i ICT mean (8.2)
Fig. 8.3 shows the averaged integrated charge along the scan positions before (in blue) and after (in red) ICT correction. The calculated ICT mean value here is 4.466×10 9 e - while the standard deviation of ICT is 0.442×10 9 e -(i.e. ICT=(4.466±0.442)×10 9 e - ). It can be seen that the effect of ICT correction on the integrated charge is negligible.

Meanwhile, the beam jitter during the scan is estimated to be around 45.60 µm on X and 31.97 µm on Y at the post-IP BPM location, which is also very small compared with the strip width of 1.5 mm for CH1 and CH4 and 0.1 mm for CH2 and CH3. Therefore we assume that the fluctuations on the charge distribution are due to the signal pick-up as presented in Section 7.5.1. Since the auto scope vertical range setting system (see section 7.4.3 and 7.5.1) takes the signal amplitude as a criterion to define the VR, and the charge is integrated for the whole waveform, a relatively high amplitude of signal pick-up caused a relatively high VR, consequently, a bad resolution.

Data binning

In order to reduce the fluctuations in the distribution, the data were re-binned. The number of bins is chosen in order to ensure at least 1 data point per bin. The value of each bin corresponds to the mean value of the points in this bin. Before measuring the horizontal beam halo distribution, we have to make sure that the beam is vertically centered. Therefore, vertical alignment (VA) is required. For the VA at the DSv location, we first do a horizontal scan to find the horizontal beam center and keep the DSv in the horizontal center, and then move the beam vertically at the IP by changing the AQD0FF vertical mover position (AQD0FF mover position scan). The mover position can be changed by ±1500 µm vertically and ±2000 µm horizontally. The nominal vertical value of the mover was at 160 µm during one data taking. During the alignment we moved the mover by 50 µm/step from 100 µm to 900 µm and took 100 waveforms at each mover position. The integrated charge is plotted as a function of the vertical position of QD0, i.e. AQD0FF, as shown in Fig. 8.5. From the plot we can find the position where the DSv collects the maximum charge (minimum value in the plot, since the bias voltage applied to the DSv is negative), which means that the beam is vertically centered. If the beam is not tilted, the vertical center should be the same for both channels, which is the case shown in Fig. 8.5 (b). However, if the beam is tilted in the transverse AT ATF2 plane, then the vertical center can be different for different channels. This can be seen from Fig. 8.5 (a) where the valley of CH1 and CH4 are at different mover positions. In this case, it is more difficult to define whether the beam is centered vertically or not and the measured beam halo distribution will not be correct. Therefore, for the beam halo measurement, it is important to make sure that the beam is not tilted by doing the AQD0FF mover position scan and correct the beam tilt if it exists. The beam core scan before and after vertical alignment is shown in Fig. 8.6. Obviously, after VA the collected charge is increased in all channels. However, after VA we also found that the signal strength on CH4 is different from CH1, while there is almost no different between CH2 and CH3 (see Fig. 8.7). From Fig. 8.7 it can be seen that the signal strength difference between CH1 and CH4 exists mainly in the region from 57 mm to 60 mm of motor position. This region correspond to the bias voltage supply line on the PCB and the region next to this is where the resistors and capacitors are situated. Therefore, we suspect that the difference in the signal strength on CH1 and CH4 in this region might be due to the beam core hitting the bias voltage supply line. This effect is not so strong when the beam is not centered vertically as shown in Fig. 8.6 (left), which means it can be verified by steering the beam vertically and comparing the signal strengths on CH1 and CH4. Further measurements need to be taken to verify this effect.

Beam core size verification

Comparison of beam core size measured by different channels After the VA, the beam core is scanned using the DSv and the measured beam core signal is fitted using Eq. 7.8. An example of beam core fit is shown in Fig. 8.9. The

BEAM HALO HORIZONTAL DISTRIBUTION MEASUREMENTS AT ATF2

fitted beam size (σ) using Eq. 7.8 is corrected by the strip width (l ). Each data point is weighted by a weight w=1/σ 2 , and the fit weighted least-squares regression minimizes the error estimate S= n i=1 w i (y i -ŷi ) 2 , where y i is the measured value, ŷi is the fitted value. The errors of the fitted parameters are obtained from the 95% confidence interval.

The beam sizes measured by different channels are compared in Table 8.1 for different beam optics. From the table it can be seen that CH1 and CH4 measures a larger beam size than CH2 and CH3. This is due to the saturation of the collected charge in the beam core, which could be mitigated by applying appropriate calibrations. Thus, for the normalization of beam halo measurements, it is preferable to use the beam size measured by CH2 and CH3.

Comparing the beam sizes measured by CH1 and CH4, it can be seen that CH4 measures a smaller beam size than CH1. This is due to the previously mentioned effect that the signal strength on CH4 is higher than CH1. This effect gets stronger when the vertical beam size (σ y ) gets smaller1 . As the BX100BY1000 optics has the smallest σ y comparing with the other two optics (see Table . Comparison between simulation and measurement Table . 8.2 shows the comparison between simulated and measured beam sizes for the post-IP wire scanner (post-IPW) and DSv. The simulated values are obtained from the Mad-X simulation. The DSv expected values are calculated by multiplying the simulated value by the discrepancy factor obtained from the post-IPW. It can be seen that the discrepancy between simulated and measured beam size is larger for the post-IPW than for the DSv. It could be that the DSv CH2 provides a more reliable beam size measurement than the post-IPW. This can be verified in the future by further measurements using the vertical DSv scanner. If the discrepancy in the vertical plane is also smaller than the post-IPW, then the DSv could serve as an instrument for beam size tuning in the future.

In the BX100BY1000 optics, as simulated the σ y is around 6.9 µm which is much smaller than the wire scanner thickness (50 µm), the post-IPW measured σ y is not valid. Therefore, we couldn't calculate the expected σ y for DSv.

For the calculation of the number of intercepted electrons (N CH ) in Section 7.5.4 (see Equation 7.9), the DSv measured beam horizontal beam size by CH2 is used for σ x , and the expected σ y is used as vertical beam size except for the BX100BY1000 optics, where we used the simulated value. However, as the vertical width of the DSv is 4 mm, which is quite large compare to σ y , the difference between using simulated or expected value is negligible. After doing a complete beam halo scan, a "strange" peak on the high energy side of the beam was found at around 26σ x from the beam center. This peak was caused by the beam core hitting the coaxial cables which were inserted into the vacuum chamber without proper fixing, because the distance between the cables and the beam center is ∼40 mm, which correspond to ∼26σ x , as observed. The difficulty in fixing the cables is due to their rigidity. Besides, the PCB is very fragile and the connections to the MMCX connectors are very rigid. In order to settle this problem, the coaxial cables in the vacuum chamber were rearranged and fixed to the holder using more copper wires. Fig. 8.10 shows the photo and measurements taken before and after fixing the cables. It can be seen that after fixing the cable, the "strange" peak disappeared while the beam distribution before this peak stayed almost unchanged. This indicates that the signal background from the cables have a strong effect on the signal measured only when the beam core is hitting the cable, if the cables stays sufficiently far from the beam core (>3σ), such effects from the cables can be neglected.

Cut of beam halo by the apertures

Except for the "strange" peak observed on the beam halo distribution, obvious edges can also be found at ∼30 mm and ∼90 mm locations of the beam halo distribution, as shown in Fig. 8.11. We assume that these edges are caused by the interception of the beam halo by the apertures, as simulated in section 4.4.

In order to investigate which aperture caused this cut, in the experiment, we moved the beam horizontally at the QF9AFF quadrupole position, from 0 mm to -3 mm, to 8. BEAM HALO HORIZONTAL DISTRIBUTION MEASUREMENTS AT ATF2 by CH1), which is more than the 16σ x , as we expected from the simulation.

As the distance between two edges of cut is around 65 mm, we suspected that this cut is given by the beam pipe installed after the BDUMP, which has a diameter of 63 mm (see Fig. 7.3). Therefore, we changed the BDUMP bending magnet strength to move the beam horizontally in the bending magnet. If the cut is due to upstream apertures, then the cut position should move together with the beam core, if not, then the cut will still stay at the same position. By changing the strength by +4 A the beam core is moved by around 5 mm toward the LE side. In Fig. 8.12 we show the change in beam halo distribution for changes of the BDUMP bending magnet strength. From the figures we can see that by changing the BDUMP bending magnet strength from the initial value of 367.75 A (+0 A) to 381.75 A (+14 A), 389.75 A (+22 A) and 395.75 A (+28 A), the cut position of edge stays always at around 95 mm. Thus we can conclude that the beam halo is intercepted by the beam pipe after the BDUMP exit rather than the aperture of the C-Band BPM. The simulated value in section 4.4 predicted a cut by the vacuum beam pipe installed after the BDUMP at around ±25.8σ x position, and the measured cut is at around ±20σ x position. Taking into account the small mismatch factor between simulation and measurement and the fact that the CH1 is slightly larger than real beam size, the expected cut should be at ∼ ±24.4σ x position, which is quite consistent with the predicted value.

Beam halo distribution dependence on beam intensity

The effect of beam intensity changes on beam halo distributions was studied by changing the total beam intensity. The total beam intensity can be controlled by changing the intensity of the laser which is injected onto the photo-cathode. In principle the laser intensity can be changed from 0% to 100% and the beam intensity can be changed from 0 to 10 10 , however, as the ICT, which was used for the beam intensity measurement, is not sensitive to a beam intensity below 10 9 e -, in this measurement we changed the beam intensity only from 1.1×10 9 to 2.5×10 9 and to 4.5×10 9 e -. The measurement results are shown in Fig. 8.13. As the measurements were done before fixing the cable, the "strange peak" on the HE side can still be observed. However, this doesn't affect the halo distribution before this peak. intensity in Fig. 8.13 (a) and (b). Besides, from Fig. 8.13 (c) and (d), it can be seen that after normalising the beam intensity to 10 9 for all the data, the shapes of the beam halo distributions are quite consistent for different intensities. Thus, we can conclude that for the intensity changes that we have applied, almost no change on the horizontal beam halo distribution was observed.

Beam halo distribution dependence on beam optics

The dependence of the beam halo distribution on the beam optics is quite important. Measurements of the effect of the beam optics on the horizontal beam halo distribution were performed during the Nov.-Dec. Run in 2014. During the run, three optics were used for different studies: BX10BY0.5 (ultra low β y ), BX10BY1 (nominal β y ) and BX100BY1000 (large β x,y ). The β x and β y values for different optics are shown in Table .8.3. From the table it can be seen that, at the DSv location, while there is no difference in β x value between the BX10BY0.5 and the BX10BY1 optics, in the BX100BY1000 optics the β x is much smaller than for the other two optics. Meanwhile, the β y value of the BX100BY1000 optics is much smaller than the other two optics after the IP. Therefore, we would expect less vertical beam halo to be intercepted by the BDUMP bending magnet for the BX100BY1000 optics. Consequently, less LE halo is expected as already shown in the BDSIM simulation described in Section 4.3 (see Fig. On the LE side, it can be seen that the distributions for BX10BY1 and BX10BY0.5 are quite consistent while for BX100BY1000 we observe less beam halo as expected, especially in the region from -10σ to -20σ. In the region with <-20σ, the signal is dominated by the pick-up signal. For the investigation of the possibility to detect the Compton recoil electrons on the LE side, we will only use the distribution measured on the LE side for further analysis in Chapter 9.

On the HE side, data for BX10BY1 was collected before relocating the cables, therefore, it has a higher beam halo level than BX10BY0.5 in the region >20σ. However, the signal level for BX100BY1000 is not much less than the other two optics as on the LE side. Comparing the signal level on the LE side with the HE side, larger signal level on the HE side was observed. Similar asymmetrical distributions were observed in the measurements using wire scanners. The results are compared to the wire scanner measured results in the next section.

Comparison of horizontal beam halo distributions

After the BDUMP bending magnet, at the DS location the horizontal beam size is dominated by dispersion:

σ 2 = σ 2 β + σ 2 p = x β x + (D x ∆E E ) 2 (8.3)
where the dispersion D x =1.294 m and the energy spread ∆E E =8×10 -4 , β x =436.74 m and x =2 nm as shown in Table 8.4. The calculated σ β = 934.6 µm and the σ p = 1035.2 µm, therefore, the expected beam size at the DSv location is 1.39 mm. The beam size measured by CH2 is 1.35 ± 0.03 mm (see Table 8.2). Since the dispersions are almost 0 and 0.0874m at MW2X and post-IPW positions, AT ATF2 respectively, which are both small comparing with the β function, the contribution of dispersion to the beam size and also on the horizontal beam halo distribution is negligible. Therefore, the fitted beam halo distribution with the parametrizations done in 2005 and 2013 can be considered as a fit for σ β and it can not be compared to the beam halo distribution measured at the DS location directly. However, as shown in Eq. 8.3, if we exclude the contribution from the dispersion function from the beam distribution and plot the measured beam distribution as a function of σ β , then it might be comparable with the WS measured distribution.

By excluding the σ p = 1035.2 µm from the beam size of 1.3496 mm measured by CH2, we can obtain the σ β as:

σ β = σ 2 -σ 2 p = 0.866mm (8.4)
Using this calculated σ β , we compared the measured beam halo distribution with the 2005 parametrisation (see Eq. 3.7). Fig. 8.15 shows the comparison of the DSv measured beam halo with the the 2005 parametrisation with and without the contribution from dispersion. Since a 30 dB attenuator was added for the beam core measurement, the signal in the beam core is divided by a factor of 0.0316. The curve from the 2005 parametrisation is normalised to the strength of the DSv signal using the "fitting model normalisation method" described in Section 5.3.1. The X axis in the upper plot is number of σ, where σ=1.3496 mm. And the lower plot is in number of σ β , where σ β =0.866 mm. The enlarged beam halo distribution measured by CH2 and CH3 is shown in Fig. 8.16. For CH3, the calculated σ β =0.804 mm.

It can be seen that by excluding the contribution from the dispersion, the beam halo distribution fits quite well on the HE side (right side on the plot), while on the LE side (left side on the plot) it is a little bit less than the 2005 model. This result is consistent with the post-IPW measurements shown in Fig. 8.17. It worth to mention here that the HE and LE sides of the halo are inverted after the BDUMP bending magnet, as illustrated in Fig. 8. [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF].

In Chapter 5 we have mentioned that the post-IPW measured distribution fits well with the 2005 parametrisation up to ∼6σ as shown in Fig. 8.17. From the 2005 measured result in the old ATF EXT line, we can also see an asymmetrical distribution between LE and HE sides 1 , which is consistent with the post-IPW result measured in 2013. The reason for this asymmetrical distribution is unknown. The old ATF EXT line and ATF2 beam line are shown in Fig. 8. [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF].

From the comparison of measurements done using the DSv and the wire scanners in the old ATF EXT line and in the new ATF2 EXT line, we can conclude that the beam halo horizontal distributions as a function of number of σ β are consistent. This 1 In the 2005 parametrisation, however, this asymmetrical distribution was not taken into account.

The parametrisation were done based on the measured beam halo distribution on the LE side [START_REF] Suehara | Design of a nanometer beam size monitor for ATF2[END_REF]. In Fig. 8.15 and Fig. 8.16 we used the same parametrisation for both LE and HE side. However, for more precise comparison, parametrisation should be done for LE and HE side separately. may indicate that the beam halo has the same level of energy spread as the beam core1 . Further measurements in high dispersion region can be performed to study the energy halo2 . Besides, investigating the reason for the asymmetrical horizontal beam distribution (more halo on the HE side than on the LE side) would also be important for the understanding of beam halo formation in the damping ring.

Compton recoil electrons measurements

A first trial of Compton recoil electron spectrum measurement was performed during the Dec. 2014 run. In this Chapter the measurement procedure is described, the measurement result is presented and compared with the expected signal level. Different ways to improve the visibility of Compton signals are proposed.

In Section 3.6.4 it was mentioned that for the Compton electron detection, large β x optics is preferred. Therefore during the Dec. 2014 Run, BX100BY1000 optics was applied for Compton measurements, which reduced the horizontal angular divergence to 1/10 of the nominal one at the IP.

Before the measurement, a timing scan and a fine alignment with respect to the laser wire scan were performed using the Shintake monitor as described in Section 3.4.2. These scans were performed with a crossing angle of 5.5 • . Both the timing and laser wire scans were fitted to the Gaussian distributions and after the scans the timing and laser position were set to the peak values obtained from the fitting (see Fig. 9.1).

After the adjustment of laser settings, a beam halo scan was first performed on the LE side of the beam with the IPBSM laser turned off. Then, the laser was turned on and the beam halo scan was done again. The measurement results are shown in Fig. 9.2.

Since 10 measurements were done at each point, the charge at each point is presented with errors calculated as the standard deviation of the mean:

Q = Q mean ± ∆Q mean with ∆Q mean = 1 √ N i=N i=1 (Q i -Q mean ) 2 N -1 (9.1)
However, as the measurements were done with a step of 0.5 mm and the signal fluctuation is too large, data binning is required. The mean value ( Q) and the error (∆ Q) after .3 shows the distributions after data binning, the vertical axis is normalised to the number of electrons assuming a gain of 2.88 fC/electron. The bin size is 2σ x where σ x =1.32 mm. Taking into account the large errors, no obvious change in the signal between laser on and off can be observed for this measurement.

The expected signal is also shown in Fig. 9.3 (in blue). The values are obtained by tracking using Mad-x with the Compton electrons generated in CAIN as explained in 4.3. Since the total number of electrons is N e =4.5×10 9 , estimation of the number of Compton electrons in Equation 9.3 is N c = 1.56 × 10 -7 × N e =702. Binning with a bin size equal to the width of CH1 strip (1.5 mm) was done for the Compton signal.

From Fig. 9.3 it can be seen that the signal from Compton electrons is quite small comparing with the signal from halo and its fluctuations. This may explain why no difference is observed between the laser on and laser off data.

The number of expected Compton electrons can be calculated from Equation 3.28 to be:

N c = N γ = f • N e • E l E γ 1 2π 1 σ yl σ tl σ (9.
3) From Equation 9.3 and Fig. 9.3, we can find several ways to improve the visibility of the Compton electrons signal:

• Increase the laser energy (E l ): since the number of Compton electrons (N γ ) is proportional to the laser energy as shown in Equation 9.3, by upgrading the laser energy from 0.2 J to 1.4 J, the number of Compton electrons can be increased by factor 7;

• Improve the sensitivity of the DSv by shielding the DSv to get rid of the signal pickup, and then amplifiers can be used for small signals;

• Put a collimator upstream to collimate the beam halo: if the horizontal beam halo can be collimated at the 10σ x level, then the Compton electrons deflected by the BDUMP magnet beyond 10σ x region can be visible.

It is worth mentioning that although the number of Compton electrons is also proportional to the beam intensity (N e ) as shown in Equation 9.3, the increase of beam halo is proportional to the increase of beam intensity as discussed in section 8.4.3, therefore increasing the beam intensity can not increase the visibility of the Compton signal.

Besides, although the number of Compton electrons in the BX10BY1 optics is almost twice that in the BX100BY1000 optics (see Table 4.1), the beam halo level is also higher for the BX10BY1 optics. Fig. 9.4 shows the comparison of the Compton signal visibility between the two optics. It can be seen that even with the design laser power (1.4 J), which is 7 times larger than the present one, the Compton signal is still completely covered by the beam halo in the BX10BY1 optics. However, with BX100BY1000, the edge of the Compton spectrum may be detectable if the sensitivity of the DS can be improved.

Conclusion and Prospects

Understanding of beam halo distributions is of great importance for the beam loss and background control of ATF2 and Future Linear Colliders. Measurements of beam halo distributions are a direct way of obtaining information on the beam halo. This thesis presents the research and development of a diamond sensor based scanner in vacuum (DSv) for beam Halo and Compton spectrum diagnostics after the IP of ATF2.

Beam halo and Compton recoil electron simulations have been performed using Mad-X and CAIN. The beam halo was generated using the parametrization based on the beam halo measurements using wire scanners (WS) done in 2005. The visibility of Compton recoil electrons in the presence of the beam halo was checked. The simulation results indicate that in order to measure the beam core, beam halo and Compton recoil electrons simultaneously, a dynamic range larger than 10 6 is needed.

A first attempt of beam halo measurements was performed in 2013 using the currently installed WS in the EXT Line and at post-IP sections. Measurement results were analysed and compared with the measurements performed in 2005 in the old EXT line of ATF. The dynamic range of the measurements in 2013 was ∼ 10 3 , which is less than the measurements done in 2005 (∼ 10 4 ) due to less favourable background conditions. Nevertheless, we have found that the post-IP WS measured horizontal beam halo distribution is consistent (up to ∼ 6σ x ) with the beam halo parametrization done in 2005. In addition we observed an asymmetrical vertical beam halo distribution in the post-IP WS measurements. This could be correlated with the tapered beam pipe installed between QD10BFF and QD10AFF magnets to reduce the background for the detectors in the vertical direction. However, more systematic measurements using the DSv are required in the future to confirm this.

Since the dynamic range of the WS is limited, the main goal of this thesis was to develop a diamond sensor with a large dynamic range (> 10 6 ) for simultaneous measurements of beam core, beam halo and Compton recoil electrons.

For the characterization of diamond sensors, tests using α and β radioactive sources were performed in a clean room. Charge collection efficiency and lifetime of the diamond sensors have been studied. These studies provided important information for the 10. CONCLUSION AND PROSPECTS understanding of the signal formation and saturation effect observed at very high beam intensity (10 9 e -). Further characterizations of diamond sensors were carried out using a ∼3 MeV electron beam at PHIL, where a linear response up to 10 7 electrons was confirmed using a diamond sensor in air.

In vacuum diamond sensor with four strips was developed to help cover the required large dynamic range. The first set of the DSv was tested at PHIL prior to the installation at ATF2 in November 2014. During the tests, signal correlations between different strips were observed. Large correlation (∼ 20%) was found between the wide strips while the narrow strips are much less affected. The reasons for these correlations are under investigation.

At ATF2, the first set of the DSv was installed horizontally in November 2014 and measurements were performed in December 2014. The main goals of these first measurements were to understand the limits of our measurement system based on DSv, and then also use the DSv to measure the horizontal beam halo distribution and investigate the possibility of probing the Compton recoil electrons.

The main achievements and results of this thesis are summarized as follow:

• We have mastered the diamond sensor technology through the R&D processes. The first in vacuum scanner based on a diamond strip sensor was successfully developed and implemented at ATF2. A dynamic range of ∼ 10 6 was obtained and confirmed for the first time, covering both beam core and beam halo measurements. The DSv has been tested with very high beam intensities (10 9 e -). Saturation effects of the DSv have been observed and investigated. These studies are very valuable for the development of the field of high-radiation diamond detectors.

• The horizontal beam halo distribution was measured up to ±20σ x by the DSv. The measurement results were compared to the beam halo distributions previously measured using the wire scanners. We found that by normalizing the beam halo distribution to the betatron beam size (σ β ), the distribution is quite consistent with the 2005 model and the post-IP WS measured distributions in 2013. This consistency may indicate that the beam halo has the same level of energy spread as the beam core.

• The possibility of probing the Compton recoil electrons has been studied by comparing the expected signal level with the measured beam halo and signal pick-up level. The comparison reveals that under the present conditions, the signal from Compton recoil electrons is quite small comparing with the signal from beam halo and signal pick-up.

Based on the results obtained from the first measurement campaign in 2014, we have also found the following remaining issues, possible ways to solve these issues are also listed below:

• With the present design the dynamic range of the DSv is limited by the signal pick-up at the level of 10 3 electrons and by the non-linearity starting from 10 7 electrons. For the signal pick-up, shielding of the PCB will be applied for the next set of DSv. The non-linear response of the DSv, due to large voltage drop on the 50 Ω resistor, may be avoided by adding a smaller resistor as voltage divider. With these solutions, the dynamic range of the DSv can be further improved.

• Concerning the horizontal beam halo distribution, further measurements in high dispersion regions are required to study the energy halo. Meanwhile, both in the WS and the DSv measurements, we observed more halo on the high energy side than on the low energy side. The reason for this asymmetry is still unknown.

• Under the present conditions, the signal from Compton recoil electrons is covered by the signal from beam halo and signal pick-up. The number of Compton recoil electrons can be increased by increasing the laser power. Nevertheless, in order to detect the Compton recoil electrons, shielding of the PCB of the DSv to get rid of the signal pick-up is essential. Besides, a collimator located upstream is planned to collimate the beam halo. Furthermore, an extra focusing quadrupole can be installed between the IP and the bending magnet to focus the beam halo and enable a clear measurement of the Compton spectrum.

A second set of DSv with shielding of the PCB has been installed vertically for vertical beam halo distribution measurement in April 2014. This vertical scanner will provide important information on the dependence of the beam halo distribution on the beam intensity for different beam optics, in particular for the ultra low β y optics study, which is important for both ILC and CLIC, where the L will be obtained with ultra low β y . Such ultra low β y will be tested at ATF2 and the background for these tests needs to be mastered. Besides, the asymmetrical distribution observed by the post-IP WS measurements can also be verified using this DSv. More systematic studies can be performed to understand the effect of the tapered beam pipe on the background.

3. 1 67 5. 1

 1671 Schematic layout of the ATF and ATF2 facility: components of the ATF2 beam line are shown on the top of the scheme . . . . . . . . . . . . . . . . 3.2 Comparison of ILC and ATF2 optics . . . . . . . . . . . . . . . . . . . . . 3.3 History of measured minimum beam size (left) and efficient beam tuning time after 3 days shutdown (right) . . . . . . . . . . . . . . . . . . . . . . ix LIST OF FIGURES 3.4 Example of consecutive beam size measurements: maximum measured modulation (left) and their corresponding minimum measured beam size (right) from 10 consecutive measurements performed on 12th June 2014 . 3.5 Schematic layout of IPBPM installed around the IP. . . . . . . . . . . . . 3.6 Upper left: schematic layout of the YAG:Ce screen system at ATF2, synchrotron radiation (SR) and coherent optical transition radiation (COTR) from the upstream are reflected to 90• ; Lower left: limitations on YAG optical resolution at large emission angles. Image from a point source is not sharp due to: finite crystal width and associated depth of focus problem (a) and light reflection from the back wall of a crystal (b) ; Right: an example of measured beam size using YAG:Ce screen . . . . . . . . . . . 3.7 Schematic layout of an OTR screen measurement (left) and the OTR system installed at ATF2 (right) . . . . . . . . . . . . . . . . . . . . . . . 3.8 Location of wire scanners at the old ATF EXT line (upper) and at ATF2 (lower) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Structure of wire scanners at ATF2 . . . . . . . . . . . . . . . . . . . . . . 3.10 Schematic layout of the laser wire interaction region installation. The laser beam enters the interaction chamber from one side, interact with the beam and exit from the other side, where it is absorbed by the laser power meter. The APD detector is used for timing purposes . . . . . . . 3.11 Shintake monitor for nanometer beam size measurement at the IP of ATF2 3.12 Example of a vertical beam size measurement using IPBSM (14th March 2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.13 Schematic layout of the gamma collimators used for the control of BG photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14 Horizontal(left) and vertical (right) beam distribution with different vacuum pressures (X and Y coordinate are normalized by RMS beam size) . 3.15 Top: Horizontal beam halo distribution measured with the MW2X WS in the old EXT line of ATF in 2005. Bottom: Measured beam halo distribution using different wire scanners for both vertical and horizontal directions as a function of number of sigmas. Vertical beam profiles are shown as squares and horizontal as circles and the difference of the Ion Pump (IP)-on data and the IP-off data is the vacuum level. For the IP-off data, some of the ion pumps in the ATF dumping ring were turned off to obtain data with degraded vacuum. The difference of the vacuum level is about 1:5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16 Beam halo measurement using YAG screen . . . . . . . . . . . . . . . . . 3.17 Beam halo measurement results using YAG:Ce screen . . . . . . . . . . . 3.18 Schematic drawing of the Compton scattering experiment at FFTB . . . 3.19 Compton scattering and inverse Compton scattering . . . . . . . . . . . . 3.20 Compton scattering in the electron rest frame . . . . . . . . . . . . . . . . 3.21 Lorentz transformation of Compton scattering from the electron rest frame to the Lab frame (modified from ) . . . . . . . . . . . . . . . . . . . . . . x LIST OF FIGURES 3.22 Schematic layout of using diamond sensor for beam halo and Compton spectrum measurements after the BDUMP bending magnet . . . . . . . . 52 3.23 Schematic for diamond sensor location calculation . . . . . . . . . . . . . 52 4.1 Beam core (N c = 10 5 ) and beam halo (N h = 10 4 ) distribution profile (upper) and histogram (lower) . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Energy spectrum of Compton recoil electrons (blue) and input electron beam (red) for BX1BY1 optics with 1.4 J laser energy . . . . . . . . . . . 63 4.3 Beam (green), halo (blue) and Comptons (red) transverse profile at the DS location for the BX10BY1 optics . . . . . . . . . . . . . . . . . . . . . 64 4.4 Horizontal beam halo and Compton distributions at the DS location simulated using Mad-X (upper) and BDSIM (lower) . . . . . . . . . . . . . . 65 4.5 Horizontal and vertical beam size along the ATF2 beamline for BX10BY1 optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.6 Normalised horizontal apertures as a function of positions for BX10BY1 optics (a); Normalised vertical apertures for BX10BY1 optics (b) and for BX10BY0.5 optics (c). Only positions with a normalised horizontal aperture of less than 30 or with a normalised vertical aperture of less than 50 are shown here. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Output signal of voltage as a function of time (green) and gate width in ns (blue) for the PMT at Post-IPW . . . . . . . . . . . . . . . . . . . . . 70 5.2 Post-IP wire scanner (photo taken in July 2013) . . . . . . . . . . . . . . 71 5.3 An example of scan from 0 to 80 mm using MW2X wire scanner with the corresponding wire positions . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4 Example of a beam core and beam halo scan applying different voltages to the PMT before (upper) and after (lower) voltage normalization. The rise of signal strength on the two edge of data taken at 1600V is caused by the background signal from the surrounding wires . . . . . . . . . . . . 73 5.5 Data without binning (left) and data binned (right) . . . . . . . . . . . . 75 5.6 MW2X WS measured beam halo horizontal distribution . . . . . . . . . . 78 5.7 MW2X WS measured beam halo vertical distribution . . . . . . . . . . . 79 5.8 post-IPW measured horizontal beam halo distribution . . . . . . . . . . . 81 5.9 post-IPW measured vertical beam halo distribution . . . . . . . . . . . . . 82 5.10 post-IPW measured vertical beam halo distribution in 17th April (left) and 12th June (right) 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.11 post-IPW measured beam halo distribution with different TBP positions (upper);Background level measured by the background monitor and Cherenkov detector at the Post-IP for different TBP position (lower): 0 mm represent the stay position of TBP, positive and negative positions represent moving the TBP up and down respectively . . . . . . . . . . . . . . . . . 86 xi LIST OF FIGURES 6.1 (a): Face-centered cubic structure of diamond; (b): CVD diamond growth conditions (picture from ); (c): A sCVD diamond pad sample (4.5mm×4.5mm× 500µm) with Al metallisation (4.11mm× 4.11 mm). . . . . . . . . . . . . . 6.2 Left: the mean energy loss of an electron in diamond; Right: Landau distribution simulated using Geant4 . . . . . . . . . . . . . . . . . . . . . 6.3 Charge generation and collection scheme . . . . . . . . . . . . . . . . . . . 6.4 I-V measurement circuit using FVMI method, where R is replaced by DS in our measurements (LO: low voltage side; HI: high voltage side). . . . . 6.5 DS sample No.1 (upper left) and sample No.2 (upper right) with the electronic circuit (lower left) and the Al box (lower right) . . . . . . . . . 6.6 I-V measurement results for DS sample No.1 and sample No.2 . . . . . . . 6.7 Capacitance measurement for DS sample No.1 . . . . . . . . . . . . . . . . 6.8 Left:Measurement set-up for test with radioactive sources and circuit diagram of diamond detector; Right: 40dB current amplifier used for the measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9 Averaged pulse of signal obtained from 90 Sr source with C2 amplifier (40 dB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10 Signal and noise amplitude distribution (a) and signal charge distribution (b) measured using current amplifier with self-trigger. . . . . . . . . . . . 6.11 Measurement setu-up for the detection of MIPs using an external trigger from a scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12 Signal waveforms of scintillator (blue) and DS (red) with trigger on scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13 Signal and noise distribution measured using charge amplifier with exter-

117 7. 1

 1171 (a): Histogram of charge collected from the alpha source; (b):Collected charge as a function of bias voltage for electrons (red) and holes (blue) . . 6.16 Upper: drift velocity as a function of electric field; Lower: Collected charge as a function of inverse drift velocity . . . . . . . . . . . . . . . . . 6.17 Layout of PHIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.18 Calibration for LANEX screen . . . . . . . . . . . . . . . . . . . . . . . . . 6.19 Experimental setup at PHIL. . . . . . . . . . . . . . . . . . . . . . . . . . 6.20 Structure of coaxial cables with braided flexible shield (left) and solid tube semi-rigid shield (right) . . . . . . . . . . . . . . . . . . . . . . . . . 6.21 Representation of inner conductor (skin effect), dielectric, and outer conductor (return-path) losses as a function of frequency . . . . . . . . . . . . 6.22 Left: Test of 50m RG58 cable with 2 ns input pulse (red) and output pulse after cable (blue); Right:Test of 1/4 inch Heliax coaxial cables with 10 ns input pulse w/o cable (gray) and output pulse after 1/4 inch cable (2 cables,50 m each) (pink and purple) . . . . . . . . . . . . . . . . . . . . 6.23 Signal pulse form for different injected beam intensity . . . . . . . . . . . xii LIST OF FIGURES 6.24 Signal amplitude as a function of number of input electrons. . . . . . . . . 115 6.25 Collected charge as a function of number of input electrons. . . . . . . . . 116 6.26 Beam size measurement using diamond sample No.1 (upper) and sample No.2 (bottom) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DSv with 4 strips:topside (left) and bottom side (right). . . . . . . . . . . 120 7.2 Layout of the PCB designed by CIVIDEC company and electronic circuit for DS (sample No.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.3 Left: Mechanical design; Middle: Fabricated mechanics; Right: Vacuum chamber layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.4 Photo of sample No.1 before adding 0.5Ω. CH1 and CH4 represent the wide strips, CH2 and CH3 represent the narrow strips. . . . . . . . . . . . 122 7.5 Settling of dark current after applying 10 V (blue) and 50 V (red) to CH1 of sample No.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.6 I-V measurement for CH1 of sample No.1 (left) and CH4 of sample No.2 (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.7 Tests of DSv sample No.1 using 90 Sr source. . . . . . . . . . . . . . . . . 125 7.8 Tests of DSv sample No.2 using 90 Sr source. . . . . . . . . . . . . . . . . 126 7.9 Pick-up signal from CH1 (red) and CH4 (green) at PHIL. . . . . . . . . . 127 7.10 Signal waveforms on each channel with reflections. . . . . . . . . . . . . . 128 7.11 Tests at PHIL using two diamond sensors simultaneously: DSv and in air DS pad (data taken on 9th Oct.2014). . . . . . . . . . . . . . . . . . . . . 129 7.12 Beam core scan using the 4 channels of the DSv at PHIL (data taken on 9th Oct.2014) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.13 Layout of data acquisition system . . . . . . . . . . . . . . . . . . . . . . . 131 7.14 ICT and BPM data reading from EPICS system during the scan . . . . . 131 7.15 Top: Layout of TDR measurement for DSv sample No.1;Bottom : TDR measurement result for DSv sample No.1. . . . . . . . . . . . . . . . . . . 133 7.16 Top: Layout of TDR measurement for DSv sample No.2; Bottom: TDR measurement result for DSv sample No.2. . . . . . . . . . . . . . . . . . . 133 7.17 TDR test result of 50Ωs terminators (left) and signal reflection observed on the signal waveforms (right). . . . . . . . . . . . . . . . . . . . . . . . . 134 7.18 Comparison of beam halo scan between manual and auto setting scope VR for CH1 and CH4. The auto setting made is only shown in the tails of the distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.19 VR distribution during the scan of beam halo on the left (a) and right (b) side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.20 Pick-up signal on each channels (left) and integrated charge during the pick-up scan (right) taken on 8th Dec. 2014. . . . . . . . . . . . . . . . . . 137 7.21 FFT of signal waveforms at different range of motor positions during the pick-up scan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7.22 Signal waveform before and after applying digital LPF. . . . . . . . . . . 139 xiii LIST OF FIGURES 7.23 The position chosen for the linearity measurements (stay position) (a) and the measurement results for the bias voltages of 40 V (b), 200 V (c) and 400 V (d) (data taken on 12-12-2014 with BX10BY0.5 Optics). . . . . 7.24 Correction for charge collected on CH4 for 400V of bias voltage. . . . . . 7.25 Signal waveforms of CH2 (a) and CH4 (b) in the beam center with V bias = 400V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.26 Scheme of measurement of CCE at different locations of beam core (a); Measurement results w/o correction (b), with 20% correction (c) and with 40% correction (d) (data taken on 20-12-2014 with BX100BY1000 Optics).144 8.1 Pedestal definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Pedestal level measured during the scan of the beam core (a) and beam halo (c); Beam core (b) and beam halo (d) distribution before and after pedestal subtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Beam halo distribution with (red) and without (blue) ICT correction . . . 8.4 Beam halo distribution without (a) and with (b) binning . . . . . . . . . . 8.5 Vertical alignment of beam by moving the AQD0FF mover vertically: (a) tilted beam (data taken on 18-12-2015 at -400 V with 30 dB attenuator) ; (b) not tilted beam (data taken on 05-12-2015 at -40 V without attenuator)154 8.6 Beam core scan before (left) and after (right) vertical alignment (data taken on 05-12-2014 at -40 V without attenuator) . . . . . . . . . . . . . . 8.7 Beam core signal strength comparison between CH1 and CH4 (left) and between CH2 and CH3 (right) after vertical alignment, CH4 and CH3 are moved by 2 mm and 0.2 mm to match the position of CH1 and CH2, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8 DSv bottom view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9 Example of beam core fit using Eq. 7.8 for CH2. . . . . . . . . . . . . . . 8.10 Left: photo taken before (upper) and after (lower) fixing the cable; Right: measured signal before and after fixing the cable. . . . . . . . . . . . . . . 8.11 Beam halo distribution before (upper) and after (lower) moving the beam horizontally at the QF9AFF location by 3mm . . . . . . . . . . . . . . . . 8.12 Beam halo distribution change on the HE side when the beam halo was moved toward the LE side by changing the BDUMP bending magnet strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.13 Horizontal beam halo distribution measured for different beam intensity before (top) and after (bottom) normalization . . . . . . . . . . . . . . . 8.14 Beam halo distribution measured using CH1 for different optics . . . . . . 8.15 Horizontal beam and beam halo distributions measured using DS CH2 with (upper, σ = 1.35mm) and without (lower, σ β = 0.866mm) contribution from dispersion (data taken on 18-12-2014) . . . . . . . . . . . . . . . 8.16 Enlarged horizontal beam halo distributions measured using DS CH2 (upper) and CH3 (lower) without contribution from dispersion (data taken on 18-12-2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv LIST OF FIGURES 8.17 Horizontal beam distributions measured by MW2X in 2005 (upper) and by post-IPW in 2013 (lower) . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.18 Old ATF EXT line (upper) and ATF2 beam line (lower) . . . . . . . . . . 169 9.1 Laser timing scan and position scan performed on 20th Dec. 2014 before the Compton recoil electrons measurement . . . . . . . . . . . . . . . . . . 172 9.2 Measured beam halo distribution with laser off (red) and laser on (black) (data taken on 20-12-2014) . . . . . . . . . . . . . . . . . . . . . . . . . . 173 9.3 Beam halo distribution with data binning with laser off (red) and laser on (black) and expected Compton recoil electrons signal (blue) . . . . . . 174 9.4 Comparison of Compton signal visibility between BX10BY1 (a) and BX100BY1000 (b) optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 A.1 Example of wire scanners scan using MW2X to measure the vertical and horizontal beam size at ATF2 . . . . . . . . . . . . . . . . . . . . . . . . . 183 B.1 Tapered beam pipe location (upper) and drawing (lower) . . . . . . . . . 186 B.2 Drawing of BDUMP Chamber . . . . . . . . . . . . . . . . . . . . . . . . 187 C.1 Horizontal beta function and dispersion function distribution along the ATF2 beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 xv LIST OF FIGURES xvi List of Tables 3.1 Design parameters of ATF2 and ILC Final Focus . . . . . . . . . . . . . 3.2 Beam parameters (10β * x × 1β * y ) . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Measurable range of IPBSM at different modes . . . . . . . . . . . . . . . 3.4 Laser and electron beam parameters at IP . . . . . . . . . . . . . . . . . . 4.1 Expected counts of Compton signal at DS location for different optics . . 4.2 Cut of beam halo by apertures at large beta locations and expected cut at DS location (in number of σ x,y ) . . . . . . . . . . . . . . . . . . . . . . 5.1 Summary of 2013 halo measurements . . . . . . . . . . . . . . . . . . . . . 5.2 MW2X-16A-H Modeling summary . . . . . . . . . . . . . . . . . . . . . . 5.3 MW2X-16A-V Modeling summary . . . . . . . . . . . . . . . . . . . . . . 5.4 PostIPW-17A-H Modeling summary . . . . . . . . . . . . . . . . . . . . . 5.5 PostIPW-17A-V Modeling summary . . . . . . . . . . . . . . . . . . . . . 6.1 General properties of sCVD diamond compared with silicon in normal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Charge transport parameters of DS sample No.2 comparing with the reported values (see Table.

  6.1) . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Cable test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Beam size measurement comparison . . . . . . . . . . . . . . . . . . . . . 7.1 title of table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Comparison of measured beam size for different optics by different channels of DSv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Comparison of simulated and measured beam size at the post-IPW and the DSv position for different optics (The errors of post-IPW measured beam sizes are negligible.). . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 β * x and β * y values for different optics . . . . . . . . . . . . . . . . . . . . . 8.4 β function and dispersion function values at different locations for BX10BY0.5 optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2 . 2 :

 22 Figure 2.2: Summary table of the 250-500 GeV baseline and luminosity and energy upgrade parameters [8].

Figure 2 . 3 :

 23 Figure 2.3: Schematic layout of the ILC, indicating all the major subsystems (not to scale) [8].

Figure 2 . 4 :

 24 Figure 2.4: Schematic view of the polarised electron source [8].

Figure 2 . 5 :

 25 Figure 2.5: Schematic view of positron source [8].

Figure 2 . 6 :

 26 Figure 2.6: Schematic view of the damping ring [8] and the achieved emittance [26].

Figure 2 . 7 :

 27 Figure 2.7: Schematic view of the electron RTML system (the positron system is a mirror image [8].

  2.8). Each crymodule is 12.65 m 2. INTERNATIONAL LINEAR COLLIDER long and there are two types: Type A with nine 1.3 GHz nine-cell cavities and Type B with eight nine-cell cavities and one superconducting quadrupole package located at the center of the module.

Figure 2

 2 Figure 2.8: A 1.3 GHz superconducting niobium nine-cell cavity with its schematic layout (upper) and longitudinal cross section of the ILC cryomodule (Type B) (lower) [8].

Figure 2 . 9 :

 29 Figure 2.9: BDS lattice layout, showing the major sub-systems. Shown is the electron BDS, which starts at the vertical dotted line. (Also shown is the positron system upstream of the electron BDS). The positron BDS is a mirror image.

Figure 2 . 10 :

 210 Figure2.10: Sketch of ILC collimation system (modified from[38]).

Figure 2 . 12 :

 212 Figure 2.12: Telescope optics for the FFS.

Figure 2 .

 2 Figure2.13: Chromaticity aberration from the strong final doublet for a particle with on and off-momentum respect to the nominal value (upper) and the correction of it by a sextupole magnet (lower) (modified from[START_REF] Kubo | Towards an International Linear Collider: Experiments at ATF2[END_REF]).

Figure 2 . 14 :

 214 Figure 2.14: Non-local (upper) and local (lower) chromaticity correction.

Figure 3 . 1 :

 31 Figure 3.1: Schematic layout of the ATF and ATF2 facility: components of the ATF2 beam line are shown on the top of the scheme [47].

Figure 3 . 3 :

 33 Figure 3.3: History of measured minimum beam size (left) and efficient beam tuning time after 3 days shutdown (right)[START_REF] Kubo | Towards an International Linear Collider: Experiments at ATF2[END_REF]

Figure 3 . 4 :

 34 Figure 3.4: Example of consecutive beam size measurements: maximum measured modulation (left) and their corresponding minimum measured beam size (right) from 10 consecutive measurements performed on 12th June 2014 [13].

Figure 3 . 5 :

 35 Figure 3.5: Schematic layout of IPBPM installed around the IP.

Figure 3 . 7 :

 37 Figure 3.7: Schematic layout of an OTR screen measurement (left) [59] and the OTR system installed at ATF2 (right)

Fig. 3 .

 3 Figure 3.8: Location of wire scanners at the old ATF EXT line (upper) and at ATF2 (lower)

Figure 3 . 9 :

 39 Figure 3.9: Structure of wire scanners at ATF2

Figure 3 . 11 :

 311 Figure 3.11: Shintake monitor for nanometer beam size measurement at the IP of ATF2

Figure 3 . 12 :

 312 Figure 3.12: Example of a vertical beam size measurement using IPBSM (14th March 2013)

Figure 3 . 13 :

 313 Figure3.13: Schematic layout of the gamma collimators used for the control of BG photons[START_REF] Yan | Precise measurement of nanometer scale electron beam size using laser interference by shintake monitor[END_REF]

Figure 3 . 14 :

 314 Figure 3.14: Horizontal(left) and vertical (right) beam distribution with different vacuum pressures (X and Y coordinate are normalized by RMS beam size)[START_REF] Wang | Analytical estimation of ATF beam halo distribution[END_REF]

Figure 3 . 15 :

 315 Figure 3.15: Top: Horizontal beam halo distribution measured with the MW2X WS in the old EXT line of ATF in 2005. Bottom: Measured beam halo distribution using different wire scanners for both vertical and horizontal directions as a function of number of sigmas. Vertical beam profiles are shown as squares and horizontal as circles and the difference of the Ion Pump (IP)-on data and the IP-off data is the vacuum level. For the IP-off data, some of the ion pumps in the ATF dumping ring were turned off to obtain data with degraded vacuum. The difference of the vacuum level is about 1:5.

Figure 3 .

 3 Figure3.16: Beam halo measurement using YAG screen[START_REF] Fuster-Martínez | Beam halo measurements and beam halo collimation at ATF2[END_REF]

Figure 3 . 17 :

 317 Figure3.17: Beam halo measurement results using YAG:Ce screen[START_REF] Fuster-Martínez | Beam halo measurements and beam halo collimation at ATF2[END_REF]

Figure 3 . 18 :

 318 Figure 3.18: Schematic drawing of the Compton scattering experiment at FFTB [80]

Figure 3 . 19 :

 319 Figure 3.19: Compton scattering and inverse Compton scattering

  3.20): p * γ c + m e c 2 = p * γ c + p * 2 e c 2 + m 2 e c 4 (3.14) and p * γ + p * e = p * γ + p * e (3.15)

Figure 3 . 20 :

 320 Figure 3.20: Compton scattering in the electron rest frame

Figure 3 . 21 :

 321 Figure 3.21: Lorentz transformation of Compton scattering from the electron rest frame to the Lab frame (modified from [86])

Figure 3 . 22 :

 322 Figure 3.22: Schematic layout of using diamond sensor for beam halo and Compton spectrum measurements after the BDUMP bending magnet

Figure 3 . 23 :

 323 Figure 3.23: Schematic for diamond sensor location calculation[START_REF] Combes | Etude de la separation du spectre des electrons de recul Compton d'ATF2[END_REF]

4. 3 Table 4 . 1 :

 341 Tracking of beam halo and Comptons BX1BY1 (E l =1.4 J) BX1BY1 (E l =0.2 J) BX10BY1 BX100BY1000 Expected counts of Compton signal at DS location for different optics

Figure 4 . 1 : 62 4. 4

 41624 Figure 4.1: Beam core (N c = 10 5 ) and beam halo (N h = 10 4 ) distribution profile (upper) and histogram (lower)

Figure 4 . 2 :

 42 Figure 4.2: Energy spectrum of Compton recoil electrons (blue) and input electron beam (red) for BX1BY1 optics with 1.4 J laser energy

Figure 4 . 3 :

 43 Figure 4.3: Beam (green), halo (blue) and Comptons (red) transverse profile at the DS location for the BX10BY1 optics

Figure 4 . 4 :Figure 4 . 5 :Figure 4 . 6 :

 444546 Figure 4.4: Horizontal beam halo and Compton distributions at the DS location simulated using Mad-X (upper) and BDSIM (lower)

Figure 5 . 1 :

 51 Figure 5.1: Output signal of voltage as a function of time (green) and gate width in ns (blue) for the PMT at Post-IPW

Figure 5 . 2 :

 52 Figure 5.2: Post-IP wire scanner (photo taken in July 2013)

Figure 5 . 3 :

 53 Figure 5.3: An example of scan from 0 to 80 mm using MW2X wire scanner with the corresponding wire positions

Figure 5 . 4 :

 54 Figure 5.4: Example of a beam core and beam halo scan applying different voltages to the PMT before (upper) and after (lower) voltage normalization. The rise of signal strength on the two edge of data taken at 1600V is caused by the background signal from the surrounding wires

Figure 5 . 5 :

 55 Figure 5.5: Data without binning (left) and data binned (right)

ρ

  H = aX -b and the Gaussian plus linear fit ρ H = me -(X-n) 2 2l 2 + p. Fig. 5.6 (lower) shows the fit for the right hand side halo tail. The beam halo model obtained with the fit (2013 model) is compared with the beam halo model from 2005 measurements (2005 model).

Figure 5 . 6 :

 56 Figure 5.6: MW2X WS measured beam halo horizontal distribution

Figure 5 . 7 :

 57 Figure 5.7: MW2X WS measured beam halo vertical distribution

Figure 5

 5 Figure 5.8: post-IPW measured horizontal beam halo distribution

Figure 5 . 9 :

 59 Figure 5.9: post-IPW measured vertical beam halo distribution

Figure 5 . 10 :

 510 Figure 5.10: post-IPW measured vertical beam halo distribution in 17th April (left) and 12th June (right) 2013

Figure 5 . 11 :

 511 Figure 5.11: post-IPW measured beam halo distribution with different TBP positions (upper);Background level measured by the background monitor and Cherenkov detector at the Post-IP for different TBP position (lower): 0 mm represent the stay position of TBP, positive and negative positions represent moving the TBP up and down respectively

Figure 6 . 1 :

 61 Figure 6.1: (a): Face-centered cubic structure of diamond; (b): CVD diamond growth conditions (picture from [102]); (c): A sCVD diamond pad sample (4.5mm×4.5mm×500µm) with Al metallisation (4.11mm× 4.11 mm).

Figure 6 . 2 :

 62 Figure 6.2: Left: the mean energy loss of an electron in diamond; Right: Landau distribution simulated using Geant4

Figure 6 . 3 :

 63 Figure 6.3: Charge generation and collection scheme

Figure 6 . 4 :

 64 Figure 6.4: I-V measurement circuit using FVMI method, where R is replaced by DS in our measurements (LO: low voltage side; HI: high voltage side).

Figure 6 . 5 :

 65 Figure 6.5: DS sample No.1 (upper left) and sample No.2 (upper right) with the electronic circuit (lower left) and the Al box (lower right)

Figure 6

 6 Figure 6.6: I-V measurement results for DS sample No.1 and sample No.2

Figure 6 . 8 :

 68 Figure 6.8: Left:Measurement set-up for test with radioactive sources and circuit diagram of diamond detector; Right: 40dB current amplifier used for the measurement.

Fig. 6 .

 6 Fig. 6.8 shows the experimental set-up for the test with the 90 Sr source and the 40 dB current amplifier (C2) used for the tests. The 90 Sr source was put on the top of the DS, and the DS was connected to the C2 amplifier via a SMA connector and then to the Agilent oscilloscope via a 1m RG58 coaxial cable. The C2 amplifier has a bandwidth of 2 GHz and a RMS output noise of 2.5 mV (3.5 dB).

Figure 6 . 10 :

 610 Figure 6.10: Signal and noise amplitude distribution (a) and signal charge distribution (b) measured using current amplifier with self-trigger.

Figure 6 . 11 :

 611 Figure 6.11: Measurement setu-up for the detection of MIPs using an external trigger from a scintillator

Figure 6

 6 Figure6.13: Signal and noise distribution measured using charge amplifier with external trigger given by the scintillator for all the recorded events (upper) and events above 10 mV fitted to Landau distribution (lower)

Figure 6 . 14 :

 614 Figure 6.14: Signal from collected electrons (negative pulse) and holes (positive pulse)

Figure 6 . 15 :

 615 Figure 6.15: (a): Histogram of charge collected from the alpha source; (b):Collected charge as a function of bias voltage for electrons (red) and holes (blue)

Figure 6 .

 6 Figure 6.16: Upper: drift velocity as a function of electric field; Lower: Collected charge as a function of inverse drift velocity

Figure 6 . 18 :

 618 Figure 6.18: Calibration for LANEX screen [57].

Fig. 6 .

 6 Fig. 6.19 shows the experimental setup for diamond detector testing at PHIL. A 4 cm long Al collimator with 2 mm diameter was used to collimate the beam after the exit window. The diamond detector was mounted next to the LANEX screen on a transverse movable stage after the collimator. The output signal was connected to a 100 m (50 m of 1/2 inch plus 50 m of 1/4 inch) long high quality LDF1-50 HELIAX RF low density foam coaxial cable to the control room, where we used an Agilent 6104 oscilloscope with 4 Gs/sec sampling rate and 1 GHz bandwidth to read the signal pulse. A 50 Ω feed through terminator was used to enable the 1 MΩ coupling on the scope, and the signals were viewed with the 50 Ω termination by the scope. The scope was controlled remotely using Labview installed on the laptop.

Figure 6 . 19 :

 619 Figure 6.19: Experimental setup at PHIL.

  6.20).

Figure 6 . 20 :

 620 Figure 6.20: Structure of coaxial cables with braided flexible shield (left) and solid tube semi-rigid shield (right)

Figure 6 . 21 :

 621 Figure 6.21: Representation of inner conductor (skin effect), dielectric, and outer conductor (return-path) losses as a function of frequency

Figure 6 . 22 :

 622 Figure 6.22: Left: Test of 50m RG58 cable with 2 ns input pulse (red) and output pulse after cable (blue); Right:Test of 1/4 inch Heliax coaxial cables with 10 ns input pulse w/o cable (gray) and output pulse after 1/4 inch cable (2 cables,50 m each) (pink and purple)

Figure 6 . 23 :

 623 Figure 6.23: Signal pulse form for different injected beam intensity

Figure 6 . 24 :

 624 Figure 6.24: Signal amplitude as a function of number of input electrons.

Figure 6 . 26 :

 626 Figure 6.26: Beam size measurement using diamond sample No.1 (upper) and sample No.2 (bottom)

Figure 7 . 1 :

 71 Figure 7.1: DSv with 4 strips:topside (left) and bottom side (right).

7. 1

 1 Design of the in vacuum diamond sensor

Figure 7 . 2 :

 72 Figure 7.2: Layout of the PCB designed by CIVIDEC company [123] and electronic circuit for DS (sample No.1).

Figure 7

 7 Figure 7.3: Left: Mechanical design; Middle: Fabricated mechanics; Right: Vacuum chamber layout.

Figure 7 . 4 :

 74 Figure 7.4: Photo of sample No.1 before adding 0.5Ω. CH1 and CH4 represent the wide strips, CH2 and CH3 represent the narrow strips.

Figure 7 . 5 :

 75 Figure 7.5: Settling of dark current after applying 10 V (blue) and 50 V (red) to CH1 of sample No.1.

Figure 7

 7 Figure 7.6: I-V measurement for CH1 of sample No.1 (left) and CH4 of sample No.2 (right).

2. 1 .

 1 The β source was put on the top of each channel of the DSv. The signal was triggered on the tested channel and the signals from the other channels were displayed simultaneously. Fig. 7.7 and Fig 7.8 show the signals triggered on different channels for sample No.1 and sample No.2 separately.

Figure 7 . 7 :

 77 Figure 7.7: Tests of DSv sample No.1 using 90 Sr source.

  Figure 7.8: Tests of DSv sample No.2 using 90 Sr source.

Figure 7 . 9 :

 79 Figure 7.9: Pick-up signal from CH1 (red) and CH4 (green) at PHIL.

Figure 7 . 10 :

 710 Figure 7.10: Signal waveforms on each channel with reflections.

Figure 7 . 11 :

 711 Figure 7.11: Tests at PHIL using two diamond sensors simultaneously: DSv and in air DS pad (data taken on 9th Oct.2014).

Figure 7 .

 7 Figure 7.13: Layout of data acquisition system

Figure 7 . 15 :

 715 Figure 7.15: Top: Layout of TDR measurement for DSv sample No.1;Bottom : TDR measurement result for DSv sample No.1.

Figure 7 .

 7 Figure 7.16: Top: Layout of TDR measurement for DSv sample No.2; Bottom: TDR measurement result for DSv sample No.2.

Figure 7 . 17 :

 717 Figure 7.17: TDR test result of 50Ωs terminators (left) and signal reflection observed on the signal waveforms (right).

Figure 7 . 18 :

 718 Figure 7.18: Comparison of beam halo scan between manual and auto setting scope VR for CH1 and CH4. The auto setting made is only shown in the tails of the distributions.

Figure 7 . 20 :

 720 Figure 7.20: Pick-up signal on each channels (left) and integrated charge during the pickup scan (right) taken on 8th Dec. 2014.

Figure 7 . 21 :

 721 Figure 7.21: FFT of signal waveforms at different range of motor positions during the pick-up scan.

Figure 7 . 23 :

 723 Figure 7.23: The position chosen for the linearity measurements (stay position) (a) and the measurement results for the bias voltages of 40 V (b), 200 V (c) and 400 V (d) (data taken on 12-12-2014 with BX10BY0.5 Optics).

  Figure 7.24: Correction for charge collected on CH4 for 400V of bias voltage.

  7.25 (b)).

Figure 7 . 25 :Figure 7 . 26 :

 725726 Figure 7.25: Signal waveforms of CH2 (a) and CH4 (b) in the beam center with V bias = 400V .

Figure 8 . 1 :

 81 Figure 8.1: Pedestal definition

Figure 8 . 2 :

 82 Figure 8.2: Pedestal level measured during the scan of the beam core (a) and beam halo (c); Beam core (b) and beam halo (d) distribution before and after pedestal subtraction.

Figure 8 . 3 :

 83 Figure 8.3: Beam halo distribution with (red) and without (blue) ICT correction

  Fig.8.4 shows an example of data taken for different optics without (a) and with (b) re-binning of the data. It can be seen that data binning has improved the visibility of the distribution.

Figure 8 . 4 :

 84 Figure 8.4: Beam halo distribution without (a) and with (b) binning

Figure 8 . 5 :

 85 Figure 8.5: Vertical alignment of beam by moving the AQD0FF mover vertically: (a) tilted beam (data taken on 18-12-2015 at -400 V with 30 dB attenuator) ; (b) not tilted beam (data taken on 05-12-2015 at -40 V without attenuator)

Figure 8 . 6 :

 86 Figure 8.6: Beam core scan before (left) and after (right) vertical alignment (data taken on 05-12-2014 at -40 V without attenuator)

Figure 8 . 8 :

 88 Figure 8.8: DSv bottom view

  8.2), CH4 measured the smallest σ y among all channels.

Figure 8 . 9 :

 89 Figure 8.9: Example of beam core fit using Eq. 7.8 for CH2.

Figure 8 . 10 :

 810 Figure 8.10: Left: photo taken before (upper) and after (lower) fixing the cable; Right: measured signal before and after fixing the cable.

Figure 8 . 12 :

 812 Figure 8.12: Beam halo distribution change on the HE side when the beam halo was moved toward the LE side by changing the BDUMP bending magnet strength.

Figure 8 . 13 :

 813 Figure 8.13: Horizontal beam halo distribution measured for different beam intensity before (top) and after (bottom) normalization

Fig. 8 .

 8 Fig.8.14 shows the measured horizontal beam halo distribution on the LE side (left) and HE side (right). Data binning was applied to reduce the fluctuations.On the LE side, it can be seen that the distributions for BX10BY1 and BX10BY0.5 are quite consistent while for BX100BY1000 we observe less beam halo as expected, especially in the region from -10σ to -20σ. In the region with <-20σ, the signal is dominated by the pick-up signal. For the investigation of the possibility to detect the Compton recoil electrons on the LE side, we will only use the distribution measured on the LE side for further analysis in Chapter 9.On the HE side, data for BX10BY1 was collected before relocating the cables, therefore, it has a higher beam halo level than BX10BY0.5 in the region >20σ. However, the signal level for BX100BY1000 is not much less than the other two optics as on the LE side.

Figure 8 . 14 :

 814 Figure 8.14: Beam halo distribution measured using CH1 for different optics

8. 5

 5 Figure 8.18: Old ATF EXT line (upper) and ATF2 beam line (lower)

Figure 9 . 1 :Fig. 9

 919 Figure 9.1: Laser timing scan and position scan performed on 20th Dec. 2014 before the Compton recoil electrons measurement

Figure 9 . 2 :Figure 9 . 4 :

 9294 Figure 9.2: Measured beam halo distribution with laser off (red) and laser on (black) (data taken on 20-12-2014)

  2.1 Three frontiers of high energy physics with the problems that can be solved by them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Summary table of the 250-500 GeV baseline and luminosity and energy upgrade parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Schematic layout of the ILC, indicating all the major subsystems (not to scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Schematic view of the polarised electron source . . . . . . . . . . . . . . . 2.5 Schematic view of positron source . . . . . . . . . . . . . . . . . . . . . . . 2.6 Schematic view of the damping ring and the achieved emittance . . . . . . 2.7 Schematic view of the electron RTML system (the positron system is a

mirror image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 A 1.

  .1 and compared with ILC. The comparison of the ATF2 and ILC BDS optics is shown in Fig.3.2.

		ATF2	ILC
	Beam energy [GeV]	1.3	250
	β * y [mm]	0.1	0.48
	y [pm•rad]	12	0.07
	σ * y [nm]	37	5.9
	l * (SiD/ILD detector) [m]	1.0	3.5/4.5
	Energy spread (e + /e -) [%]	0.06∼0.08 0.07/0.12
	Chromaticity l * /β * y (SiD/ILD detector) 10000	7300/9400

Table 3

 3

	.1: Design parameters of ATF2 and ILC Final Focus [8] [10]

Table 3

 3

	.2: Beam parameters (10β * x × 1β * y )

  • and 2 • to 8 • (continuously adjustable). The measurable range for different crossing angles is shown in Table3.3.

	Crossing angle θ	174 •	30 •	8 •	2 •
	Fringe pitch d	266 nm	1.028 µm	3.81 µm	15.3 µm
	Measurable σ *

y 20-100 nm 100-360 nm 360 nm -1.4 µm 1.4-6.0 µm

Table 3.3: Measurable range of IPBSM at different modes [49].

Table 4 .

 4 2, where several important locations of cut (large beta locations) are indicated.From the table we can see that the tightest horizontal cut is given by the C-Band BPMs (with radius of 8 mm) installed next to the sextupole SF5FF at 72.23 m from the 4.4 Cut of beam halo by apertures

		Horizontal Cut, [σ x ]		Vertical Cut, [σ y ]
		MSF5FF DS	TBP	BDUMP DS
		(72.23 m) (93.51 m) (61.39 m) (92.16 m) (93.51 m)
	BX10BY0.5 16.01	25.86	20.06	10.15	20.17
	BX10BY1	15.99	25.84	26.85	13.59	26.99

Table 4 .

 4 2: Cut of beam halo by apertures at large beta locations and expected cut at DS location (in number of σ x,y )

Table 5 . 1 :

 51 Summary of 2013 halo measurements

Table 5 .

 5

4: PostIPW-17A-H Modeling summary 5. BEAM HALO MEASUREMENTS USING WIRE SCANNERS

Table 6 .

 6 [START_REF] Aad | Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC[END_REF] shows the general properties of sCVD diamond compared with silicon in normal conditions.

	Property	Diamond	Silicon
	Atomic number	6	14
	Density, [g• cm -3 ]	3.5	2.32
	Band gap, [eV]	5.5	1.1
	Resistivity, [Ω•cm]	> 10 12	10 5
	Breakdown field, [V•µm -1 ]	1000 [110]	30 [111]
	Electron mobility, [cm 2

Table 6 .

 6

	104]	500

1: General properties of sCVD diamond compared with silicon in normal conditions

Table 6 .

 6 2: Charge transport parameters of DS sample No.2 comparing with the reported values (see Table.6.1) 6.4 Tests of in air diamond sensor at PHIL After the characterization of the diamond samples in the clean room, tests with an electron beam are needed to see the waveform shapes for different beam intensities, measure the linearity of the response of the diamond and to test the fast remote readout system. The first tests were done for sample No.1 starting in June 2013, and the tests for sample No.2 were started in Oct. 2013. In this section most of the results presented were obtained from the tests done with sample No.2.

	mm]

  .3.

		Length Input Width Output Width t rise	t f all	Atten.
	RG58	10m	2ns	2.163ns	1.073ns 1.487ns 1.16dB
		20m	2ns	2.256ns	1.202ns 2.457ns 2.50dB
		50m	2ns	2.783ns	1.358ns 4.211ns 9.63dB
	1/4 inch 50m	10ns	10.25ns	0.703ns 0.75ns	0.44dB
	1/2 inch 50m	10ns	10.1ns	0.733ns 0.5ns	0.37dB
				Table 6.3: Cable test results

  N Max. N/mm 2 Charge signal/mm 2

	Beam core	10 10	6.2× 10 8	1.7µC
	Beam halo	10 7	2.2× 10 4	61.4pC
	Compton	28340	5.2× 10 2	1.4pC

Table 7 . 1 :

 71 Expected signal at DSv location at ATF2

Table 8 . 1 :

 81 Comparison of measured beam size for different optics by different channels of DSv

Table 8

 8

.3: β * x and β * y values for different optics

Table 8 .

 8 4: β function and dispersion function values at different locations for BX10BY0.5 optics

A tapered beam pipe (TBP) has been installed at the upstream (between QD10AFF and QD10BFF) to shield background for the Shintake monitor.

The energy loss by synchrotron radiation emission ∆E is proportional to the fourth power of the particle energy E:∆E ∝ E 4 R , where R is the radius of the ring[START_REF] Kuriki | Lecture I2 -ILC[END_REF].

Beamstrahlung is the synchrotron radiation from a particle being deflected by the collective electromagnetic field of the opposing bunch.

The extraction line guide the beam and the bremsstrahlung from the IR to the beam dumps.

3.5 m for SiD detector and 4.5 m for ILD detector.

THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK Figure3.2: Comparison of ILC and ATF2 optics[START_REF] Seryi | Experimental and theoretical progress of linear collider final focus design and ATF2 facility[END_REF]

At larger intensities, the minimum beam size rapidly gets larger.

Switching between two detectors to allow operation of both at one single interaction region

In Suehara's parametrization, the ratio of the charge intensity between the central Gaussian and halo function is determined so that the density of the center is 500 times larger than the density at the 5 σ position, however, from Fig.3.15 it can be seen that the 1/500 of the peak intensity corresponds to the 4 σ position rather than 5 σ position, especially on the right side of the plot.

For simplicity, the Compton recoil electrons are called Comptons from now on.

The energies of Comptons are in principle more degreded than the beam halo.

THE ACCELERATOR TEST FACILITY (ATF) AND ATF2 AT KEK

In reality, N h is estimated to be 10 -3 of Nc.

The Breit-Wheeler process is the emission of positron-electron pairs off a probe photon propagating through a polarized short-pulsed electromagnetic field

The weight of the macro-particles is defined as the ratio between the numbers of real particles and number of macro-particles.

The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation.

In the simulation the radius of the beam pipe was set to 50 mm, however, in reality the beam pipe radius is 31.5 mm

The signal delay between the gate and the PMT

The 50 Ω terminators are used to enable 1 MΩ input resistance in the scope.

The estimated max. number of Compton recoil electrons at the DSv location is ∼ 5 × 10

/mm 2 (i.e ∼

× 10 3 for wide strips) for the design laser power of 1.4 J (see Table7.1 and Fig.

4.4).

In the beam core region, the waveform is similar to the signal waveform, rather than the pick-up signal, since small amount of charge is collected as shown in Fig.7.20 (right).

The simulated vertical beam size for BX100BY1000 optics is ∼0.04 mm, whereas for BX10BY1 and BX10BY0.5 it is ∼1.3 mm (see Table8.2).

Table 8.2: Comparison of simulated and measured beam size at the post-IPW and the DSv position for different optics (The errors of post-IPW measured beam sizes are negligible.).

Since the energy spread of halo is unknown, in our data analysis, we took the energy spread of the beam core ( δE E = 8 × 10 -4 ) for the beam halo dispersion correction. If the energy spread of halo is higher than the beam core, then the beam halo level should also be higher in the high dispersion region (DS location) than in the low dispersion region (or dispersion free region: MW2X and post-IPW location). However, from Fig.8.15 it can be seen that by excluding the dispersion contribution using the same energy spread for the beam core and beam halo, the beam halo distribution is consistent with the parametrisation at the MW2X location.

Energy halo is a tail in the energy distribution of the beam. It may or may not be correlated with the betatron halo.

Figure 8.15: Horizontal beam and beam halo distributions measured using DS CH2 with (upper, σ = 1.35mm) and without (lower, σ β = 0.866mm) contribution from dispersion (data taken on 18-12-2014)

Figure 8.17: Horizontal beam distributions measured by MW2X in 2005 (upper) and by post-IPW in 2013 (lower)

Acknowledgements

Scholarship Council for providing me the financial support and the opportunity to work in the Association of CSC fellows in Il-de-France.

It is my pleasure to thank N.

Dependence of collected charge on intensity

When electrons and holes recombine inside the DS, less charge is collected. This can result in the saturation of charge collection. A hint of such saturation in the collected charge (obtained by integrating the signal pulse above the pedestal) can actually be seen in Fig. 6. [START_REF] Hewett | Fundamental physics at the intensity frontier[END_REF] for input charges larger than 2 × 10 7 electrons (3.2 pC). Below such values, the response in terms of collected charge is linear. A factor two difference was observed with the expected signal as calculated multiplying the charge generated by 1 MIP (2.88 fC) by the number of electrons derived from the charge measurement using the LANEX. This may be due to systematic effects in the calibration procedure of the LANEX or some other unknown effects.

Beam size measurement

Beam size measurements were performed using the two diamond samples with a movable stage installed after the exit window. The measured beam size can be extrapolated from the signal amplitude distribution as far as the signal amplitude is not saturated (<100 V as can be seen from Fig. 6.24). Suppose the beam distribution after the exit window is Gaussian, then the measured distribution is a convolution of a Gaussian distribution and uniform distribution given by the strip width. Similar to the beam size measurement using wire scanners, by changing the variance of circular distribution (

Characterisations of the DSv at ATF2

Characterisation of the DSv was done at ATF2 to define the dynamic range. The lower limit of the dynamic range is defined by the noise level given by the pick-up signal and the higher limit will be impacted by the linearity of the DSv response.

Signal pick-up study

In Fig. 7.20 the pick-up signal on each channel is shown. The integrated charge of the pick-up signal during the scan is also shown. This scan was done without applying bias voltage to the DSv (by turning off the power supply). However, as the measurement was done after beam halo measurements with 400 V, and the bias voltage was ramped down from 400 V to 0 V in a relatively short time(∼ 30 s), the charging capacitors may not have been totally discharged. Therefore, when the beam went through the DSv a small amount of charge (∼ 10 nC) was still collected as shown in the distribution.

Meanwhile, the integrated charge from the pick-up signal is below 3 × 10 -3 nC which correspond to 10 3 electrons. This defines the lower limit (noise level) for beam halo measurements for our present set-up. This level of noise affects our measurements in the following two aspects: 1) Covers the signal from Compton recoil electrons 1 that we want to measure in the future.

2) Prevents us from seeing the tail of the waveform shape, where a small signal from backscattered particles from the DUMP may exist.

Summary

Summary

A DSv with large dynamic range was designed for beam halo measurements at ATF2. With the present design, the lower and upper dynamic ranges of the DSv are limited by the signal pick-up at the level of 10 3 electrons and by the non-linearity which starts from 10 7 electrons, respectively. With proper calibration for the signal in the non-linear region, the upper limit of the dynamic range of DSv can be further extended (to ∼ 10 9 in our experiment).

For the signal pick-up, a LPF in the data analysis was used to improve the signal shape. In addition, shielding of the PCB will be applied for the next set of the DSv. The non-linear response of the DSv, due to large voltage drop on the 50 Ω resistor, may be avoided by adding a smaller resistor as a voltage divider [START_REF] Griesmayer | [END_REF]. With these solutions, the dynamic range of the DSv can be further improved. check the effect of cuts by apertures downstream of QF9AFF. The QF9AFF quadrupole is located 64.12 m from the beginning of the EXT line. We found that the cut position stayed at around 30 mm on the left side (LE side) and at around 95 mm on the right side (HE side) (see Fig. 8.11). This confirms that the edges are due to the apertures downstream of QF9AFF. As mentioned in Section 4.4, we would expect the C-Band BPM installed after the SF5FF sextuple to be the main cause of interception of the beam halo. However, the cut at this position is at around 20σ x position (σ x measured 8.5 Comparison of horizontal beam halo distributions

Beam halo measurements

Appendices Wire scanner