ulant leurs réponses via l'utilisation des codes Geant4 et Silvaco TCAD. Par ailleurs, le détecteur CMOS (RadEye) de la société Teledyne a été étalonné sur l'accélérateur de protons conventionnel (AIFIRA). Ce détecteur associé à un spectromètre dispersif devrait permettre de caractériser les particules chargées accélérées par l'interaction laser-plasma. L'étude du détecteur CdTe a montré que son temps de réponse intrinsèque de l'ordre de la µs peut engendrer des problèmes de pile-up pour détecter des décroissances radioactives avec des demi-vies aussi courtes que 9 ns. La simulation TCAD du cristal CdTe a montré que le détecteur est aveugle pendant environ 14 µs après le flash X accompagnant un tir laser, interdisant toute spectroscopie gamma pendant cette période. Quant au scintillateur LaBr 3 couplé au détecteur HPD, nous avons modélisé la diode PIN à l'intérieur du photo-détecteur et montré que le signal de plusieurs dizaines de µs associé au flash X était principalement dû au phénomène d'afterglow du scintillateur. Par ailleurs, un traitement hors ligne approprié du signal issu du scintillateur couplé à l'HPD, a permis une réduction du temps mort de 200 à 15 µs. En outre, l'implémentation de l'algorithme de correction du pile-up a permis de réduire le temps mort entre deux impulsions consécutives de 60 ns à 4 ns. En ce qui concerne la détection de gammas de quelques keV à partir d'APD, l'exposition au flash X issu de l'interaction d'une intensité laser de 4.75 × 10 16 W/cm 2 avec une cible solide créé à ses bornes un signal de 90 V, 40 µs, ce qui rend impossible son utilisation pour faire de la spectroscopie gamma. Cependant, en associant 2 APD en mode différentiel, nous avons réduit ce signal à environ 30 mV, 1 µs, autorisant alors la possibilité de spectroscopie gamma. Enfin, l'étalonnage du détecteur RadEye a révélé que le détecteur nécessite au minimum ∼ 1000 protons de 3 MeV pour activer un pixel, ce qui est beaucoup. Ce travail a montré que les détecteurs CdTe et LaBr 3 couplés à des HPD ne peuvent pas être utilisés pour étudier la désexcitation du 84m Rb dans un plasma, mais pourront être utilisés pour caractériser des rayonnements créés par l'interaction laser-plasma. Les APD semblent quant à eux adaptés pour étudier l'excitation du 181m Ta dans un plasma.

ACKNOWLEDGMENTS

In all gladness, I am grateful to the Lord God Almighty for His many graces and favors supplied to me by His love, which have carried me through the period of this thesis work. Indeed, His love endures forever.

It is with great pleasure that I express my respect and deep sense of gratitude to my Ph.D. supervisor, Medhi Tarisien, for providing an enabling environment for the execution of this thesis through his expertise, thoughtfulness, patience, commitment, and understanding. Without your guidance, this thesis would not have been accomplished. Despite your busy schedules, you created time to follow the evolution of this work with the provision of very important insights that pushed me into further explorations. Personally, I learned a lot from you and I am grateful that you chose to share your precious knowledge and technical skills with me. You are really kind and I count myself fortunate to have had you as my Ph.D. supervisor. Thank you so much.

I sincerely want to thank Fazia Hannachi for the several stimulating discussions we had regarding my work. You are always ready to help. Thank you for taking the time to read my manuscript and giving constructive corrections, questions, and suggestions that contributed to improving the work. I would also like to express my gratitude to you for your kindness to my family, in particular for the love shown to my baby Esther on many occasions.

Many thanks to all the jury members of my thesis defense for reading the manuscript and sending contributions that helped to improve it, and for attending my Ph.D. defense, especially those who traveled a long distance.

I am grateful to the Université de Bordeaux for fully funding my Ph.D. program and for giving me the necessary aids needed for my research work.

To my family, 'ona too much. Wetin I for do if no be for ona wey dey my side gidigba'. I am indebted to my dear wife, Victoria, who has been my friend since we met during our high school days. Your love, understanding, and sacrifices have been indispensable during the course of this work. You stood in for me in very difficult circumstances and helped to make the journey less difficult. Your presence is such a relief. Thank you for always putting a smile on my face. I love you so much. Our daughter Esther is a joy and our biggest blessing in the last three years. Thank you, Esther, for bringing such a bundle of laughter that resonates from your innocence and pureness, and for keeping me awake for some late-night studies. I am also sending thanks to my parents for their prayers and kind words during the period of my thesis.

Contents

I wish to appreciate the members of the LP2iB laboratory and our collaborators.

Thanks to the director of the LP2iB laboratory, Fabrice Piquemal, for accepting and welcoming me to the lab to perform my research. Thanks to the technical and administrative departments of the lab for their support, and for Nadine whose kindness ensures that all trips for our experimental campaigns were properly sorted. Thank you to Aziz for always helping out whenever I had problems with my computers without feeling disturbed, and for your wise counsels given without asking. Thanks to Antoine, Arnaud, and Kristal, who are members of the ENL group for their show of love and support. Special thanks to our collaborators at LULI and CELIA for the opportunity to participate in experimental campaigns for my work. To my friend Michele, thank you for the beautiful moments we shared in the lab and outside: the jokes and laughs about Silvaco, and of course, the fun-moments beyond the walls of research with Giulia being so generous to host us with her flavors of creativity. Finally, I am grateful to everyone that I could not mention, including those who helped to ensure the cleanliness of our offices and the environment; thank you for the opportunity to share with you in the same laboratory.

Résumé

Les lasers de haute puissance avec des taux de répétition élevés présentent l'opportunité unique d'étudier dans un laboratoire les propriétés des états nucléaires à courte durée de vie (typiquement quelques dizaines de ns) lorsque le noyau est plongé dans un plasma chaud et dense. Dans ces plasmas de type astrophysique, les noyaux peuvent être très efficacement excités par le milieu environnant et peuvent même présenter des modifications des durées de vie apparentes de leurs niveaux. Les états isomères de noyaux tels que le 181 Ta et le 84 Rb conviennent à ces premières études car ils ont des niveaux qui peuvent être excités par les particules du plasma. Les observables de ces excitations sont des émissions gamma de 6,2 keV avec une demi-vie de 6,05 µs dans le cas du 181 Ta et des gammas d'environ 250 keV émis avec une demi-vie de 9 ns dans le cas du 84 Rb. Les détecteurs de ses rayonnements gammas doivent être capables de résister aux fortes perturbations créées lors de la formation du plasma par un tir laser de puissance car ils sont accompagnés de paquets très intenses d'électrons, de photons de Bremsstrahlung ainsi que de grandes impulsions électromagnétiques (EMP). Cette explosion soudaine d'énormes flux de rayons X peut déposer plusieurs GeV d'énergie dans les détecteurs, les saturant, tandis que les EMP peuvent endommager l'électronique connexe. De plus, l'éventuelle radioactivité associée aux durées de vie aussi courtes pourrait être très intense et présenter de l'empilement des signaux (pile-up). Les détecteurs doivent donc être adaptés pour survivre dans cet environnement difficile tout en permettant d'effectuer une spectroscopie gamma en quelques centaines de µs. L'objectif de ce travail de thèse est de développer ces détecteurs de spectrométrie gamma adaptés à l'environnement des lasers de haute puissance tirant à haute cadence (∼ un tir par seconde). Pour détecter les rayons gammas de quelques centaines de keV issus de la désexcitation du 84m Rb, nous avons étudié deux détecteurs semi-conducteurs à base de CdTe, l'un couplé à un amplificateur de charge et l'autre à un amplificateur de courant ; et un scintillateur LaBr 3 couplé à un photo détecteur hybride (HPD). Pour la détection des rayons gamma de faible énergie (6,2 keV) issus du 181m Ta, nous avons utilisé une photodiode à avalanche (APD) présentant une zone de déplétion épaisse. Ces détecteurs ont été étudiés expérimentalement en conditions normales d'utilisation et en environnement perturbé au voisinage du laser de haute intensité ECLIPSE du CELIA. Un traitement des données et une analyse hors ligne spécifique ont été développés pour minimiser le temps mort des détecteurs et la mise en oeuvre d'algorithmes ont permis de corriger des phénomènes de pile-up. Les détecteurs à semi-conducteurs ont également fait l'objet d'une étude théorique en sim-

Contents

Abstract

High-power lasers with high repetition rates present the unique opportunity to study in a laboratory the nuclear properties when the nucleus is in astrophysical hot and dense plasmas. In such plasmas the nuclei can be very efficiently excited by the surrounding medium and may even exhibit changes in the apparent lifetimes of levels.

Nuclei, such as 181 Ta and 84 Rb are suitable for these first studies because they have levels that can be excited by the plasma particles. The observables of these excitations are gamma emissions of 6.2 keV with a half-life of 6.05 µs in the case of 181 Ta and gammas of about 250 keV emitted with a half-life of 9 ns in the case of 84 Rb. Detectors capable of recording these gamma emissions (scintillators, semiconductors, etc.) must have the ability to produce fast signals well adapted to the lifetime of the nuclear state of interest. Furthermore, because the laser-matter interactions are promptly accompanied by bunches of ions, electrons and associated Bremsstrahlung photons, as well as large induced electromagnetic pulses (EMPs), these online detectors have to withstand the strong disturbance created during plasma formation by a power laser shot. The sudden burst of huge fluxes of x-rays can deposit more than GeV of energies and saturate the detectors, while EMPs can damage related electronics.

More so, possible high radioactivity within such short lifespan of the nuclear state could warrant an offline correction of pileup events. The detectors must therefore be adapted to survive in this harsh environment while delivering gamma spectroscopy within some tens of µs. The goal of this work is to develop online detectors to study short-lived nuclear states of 181m Ta and 84m Rb nuclei in astrophysical plasmas created by high power lasers with high repetition rates (∼ one shot per second).

To detect gammas of a few hundred keV in the context of the 84m Rb experiment, we studied two CdTe detectors, one coupled to charge amplifier and the other to a current amplifier; and a LaBr 3 coupled with Hybrid Photo Detector (HPD). For low energy gamma detection (6.2 keV) in 181m Ta, we studied Avalanche Photo Diode (APD) detectors. All of these detectors were exposed to X-rays from laser-plasma interactions in the ECLIPSE facility at CELIA laboratory. The laser-induced EMPs were minimized via a faraday cage and through proper grounding of utilised detectors. Processes of offline data treatment and analysis were carried out as well as the implementation of pileup correction algorithms. The semiconductor-based detectors were also theoretically studied using the X-ray flash data as inputs via Geant4 and Silvaco TCAD simulations.

For the purpose of characterizing laser-accelerated ions, which can be used to Contents induce the nuclear reaction for what is to be studied, CMOS-based detector (Rad-Eye) from Teledyne company, was calibrated from a conventional proton accelerator (AIFIRA).

In the results, CdTe coupled to a charge preamplifier was totally saturated while the other coupled to a current amplifier was not. The duration of a gamma photon current signal was at least 1 µs signalling the dangers of pileup issues for detections within a 9 ns half-life. The TCAD simulation of the CdTe crystal revealed that the earliest detection of a gamma photon after the X-ray flash is about 14 µs after the laser shot. In the case of the LaBr 3 coupled to HPD detector, we modelled the PIN diode inside the photodetector and showed that the tens of µs-duration signal of the X-flash was strictly due to the scintillator detector and not the HPD. Interactions from a 4.75 × 10 16 W/cm 2 laser showed that the X-ray signal could be as low as 2.5 µs from the LaBr 3 coupled to HPD detector. Furthermore, the offline treatment of scintillator-HPD signal during a previous experiment showed a reduction in dead time from about 200 to 15 µs. In addition, the implementation of pileup correction algorithm presented the possibility to reduce influences of pileup from less than 60 to 4 ns between consecutive pulses. Referring to the APDs, following the interaction of a 4.75 × 10 16 W/cm 2 laser, we succeeded to reduce the X-ray flash signal from 90 V and 40 µs from a single APD, to approximately 30 mV, 1 µs using two APDs in differential mode. Finally, the calibration of the RadEye detector for proton detection purpose revealed that a minimum of ∼1000 protons with 3 MeV, incident on a pixel can be detected. The work showed that the assembled CdTe and LaBr 3 coupled to HPD cannot be used to study 84m Rb in plasma, but can be used to characterise laser produced X-rays. The APDs have very good prospects for studying 181m Ta in plasma.

Introduction

Plasma is the most abundant state of matter that constitute the visible universe. It is 99.99 % in abundance, superseding all other states of matter. Nuclear astrophysics gives the possibility to study and understand how nuclear processes shape the cosmos through relationships between the properties of atomic nuclei and the properties of stars for example. Atomic nuclei do not exhibit the same features when in hotdense plasma such as in the stars, and when in neutral atoms like in solids and liquids. Properties such as the apparent lifetime of nuclear levels, nuclear crosssections amongst others are significantly different, thus the need to perform nuclear astrophysical studies in a stellar-like medium cannot be overemphasised. Thanks to a new generation of high power lasers (>10 16 W/cm 2 ) with high repetition rates ( ∼ 1 Hz), hot-dense astrophysical plasmas can be achieved in the laboratory, and nuclear properties can be studied in them. Nuclei, such as 181 Ta and 84 Rb are suitable for these first studies because they have short-lived levels (less than few µs) that can be excited by the plasma particles. The observables of these excitations are gamma emissions of 6.2 keV with a half-life of 6.05 µs in the case of 181 Ta and gammas of about 250 keV emitted with a half-life of 9 ns for 84 Rb. The gamma ray detectors to be deployed should have good detection efficiency and be able to deliver very fast signals well-adapted to the half life of the decaying state. Moreover, high-power laser interactions are promptly accompanied by bunches of ions, electrons and associated Bremsstrahlung photons, as well as large induced electromagnetic pulses (EMPs). The X-rays are emitted instantaneously and can exceed few GeV of deposition in a detector. Online detectors placed in such an environment will be saturated by this flash of X-rays, making them blind to detection for a relatively long period of time. On the other hand, associated electronics are greatly affected by EMPs and can be destroyed by them. Detection in such an environment is therefore not an easy task. The goal of this thesis is to develop online detectors capable of withstanding this harsh laser-induced plasma environment while performing gamma spectroscopy within few µs.

Thesis outline

The research work presented in this thesis are organised and structured in four chapters, which are briefly described as follows:

Contents

Chapter one is an introduction into the context of the research, the problems, aims and objectives. Chapter two details the study of two semiconductor detectors suited for 6 and 200 keV gamma rays in a laser-plasma environment. The detectors for the 6 and the 200 keV gamma rays are targeted towards the 181 Ta and 84 Rb experiments. Further in this chapter, semiconductors are explored for applications to the online imaging of laser-driven ion beams. Chapter three exposes studies using scintillators coupled with photodetectors for gamma energies of few hundreds keV in laser-plasma environment. In chapter four, the work focuses on the data analysis performed for scintillator detectors tested to detect 122 and 257 keV during a created nuclear reaction in a plasma environment, and pileup treatment processes.

Chapter 1

Context of work

The last two decades have witnessed several studies using high power lasers, with intensity (I) ≥ 10 16 W/cm 2 , for particle acceleration. Such studies have sparked innovative applications, for instance, in radioisotope productions [START_REF] Ledingham | Photonuclear physics when a multiterawatt laser pulse interacts with solid targets[END_REF][START_REF] Tayyab | Experimental investigation on nuclear reactions using a laser-accelerated proton and deuteron beam[END_REF], radiobiology [START_REF] Chaudhary | Radiobiology experiments with ultra-high dose rate laser-driven protons: Methodology and state-of-theart[END_REF], prompt heating of dense matter [START_REF] Tahir | Proposal for the study of thermophysical properties of high-energy-density matter using current and future heavy-ion accelerator facilities at gsi darmstadt[END_REF][START_REF] Malko | Proton stopping measurements at low velocity in warm dense carbon[END_REF] and ion sources for hadron therapy [START_REF] Murakami | Radiotherapy using a laser proton accelerator[END_REF][START_REF] Kroll | Tumour irradiation in mice with a laser-accelerated proton beam[END_REF].

The concept behind the existence of high-power lasers is enshrouded in the principle of chirped pulse amplification (CPA) that was developed by Strickland and Mourou in 1985 [START_REF] Strickland | Compression of amplified chirped optical pulses[END_REF], which eventually led to their Nobel price in 2018. The principle involves stretching a mJ laser pulse in time before amplification and compression, allowing to achieve a high intensity without any destruction of the amplification system. Today, the highest intensity reachable is of the order of 10 23 W/cm 2 that was achieved by the Center for Relativistic Laser Science (CoReLS) [START_REF] Yoon | Realization of laser intensity over 1023w/cm2[END_REF]. In addition to improvements in intensity, progress has been attained in the repetition rates with APOLLON (France) [START_REF] Zou | Design and current progress of the apollon 10 pw project[END_REF] and ELI 1 pillars (Europe) [START_REF] Gales | The extreme light infrastructure-nuclear physics (ELI-NP) facility: new horizons in physics with 10 PW ultra-intense lasers and 20 MeV brilliant gamma beams[END_REF] delivering 10 PW every minute, CLPU (Spain) 2 operating at 1 PW per second, and several other hundreds of TW lasers such as at LOA 3 shoot at 10 Hz. Thanks to these high repetition rates, more applications such as the experimental study of short-lived nuclei (few µs) in astrophysical plasmas can be explored. By detecting the emissions from such nuclei, relevant information about the behaviour of a nucleus in hot dense plasma may be obtained which could be used to enhance our understanding of nuclear processes in the stars.

However, the advent of high-power lasers with high repetition rates is proceeded by fresh challenges with concerns ranging from targets to particle diagnostics. Tape target systems [START_REF] Haney | Prototype high-speed tape target transport for a laser plasma soft-x-ray projection lithography source[END_REF][START_REF] Nishikino | Demonstration of a highly coherent 13.9 nm x-ray laser from a silver tape target[END_REF] have been designed for solid targets to fit the rate of the laser shot, nonetheless, the debris emerging from the destruction of a solid target after a shot impacts the optics making the subsequent shots of poor outcomes [START_REF] Humières | Investigation of laser ion acceleration in low-density targets using exploded foils[END_REF]. This is why some studies have embarked on alternatives like gas targets [START_REF] Puyuelo-Valdes | Laser driven ion acceler-ation in high-density gas jets[END_REF]. Also very important is the detection at a high repetition rate. In one-shot laser conditions, characterisation of laser-accelerated particles have, in most cases, adopted passive detectors like imaging plates (IPs) [START_REF] Bonnet | Response functions of fuji imaging plates to monoenergetic protons in the energy range 0.6-3.2 mev[END_REF], Californian resin 39 (CR39) [START_REF] Won | Cr-39 track detector for multi-mev ion spectroscopy[END_REF][START_REF] Kanasaki | The precise energy spectra measurement of laser-accelerated mev/n-class high-z ions and protons using cr-39 detectors[END_REF], radiochromic (RCF) films [START_REF] Pr Bolton | Instrumentation for diagnostics and control of laser-accelerated proton (ion) beams[END_REF], 1 Extreme Light Infrastructure 2 Centro de Láseres Pulsados Ultracortos Ultraintensos 3 Laboratoire d'optique appliquée and activation samples [START_REF] Tarisien | Natalie: A 32 detector integrated acquisition system to characterize laser produced energetic particles with nuclear techniques[END_REF]. While these have achieved satisfactory successes, they demand shot-to-shot treatments or replacements that are time-consuming, and therefore cannot be used under high repetition rate conditions. In today's generation of high power and repetition rate lasers, if maximum benefits are to be derived, on-shot detectors, otherwise known as active detectors, must be prioritized. In the context of this work, they are not only useful for the characterisation of laser-produced ion and electron beams, other dedicated online detectors are deployed for gamma spectroscopy studies in the case of short-lived nuclei in a laser-plasma environment. their usefulness transcends beyond the characterisation of laser-produced ion and electron beams, to other dedicated online detectors being deployed for gamma spectroscopy studies in the case of short-lived nuclei in a laser-plasma environment.

More so, these active detectors are not new and they have been successfully deployed for many applications in a conventional accelerator environment [START_REF] Bucciolini | Diamond detector versus silicon diode and ion chamber in photon beams of different energy and field size[END_REF][START_REF] Si Mulgin | Two-parametric method for silicon detector calibration in heavy ion and fission fragment spectrometry[END_REF][START_REF] Moszyński | Inorganic scintillation detectors in γ-ray spectrometry[END_REF].

Notwithstanding, the challenges faced in a laser environment are entirely different.

Laser-matter interactions are accompanied by strong electromagnetic pulses (EMPs) which could damage detector electronics, and high-intensity X-ray flash that saturates the detectors. As for EMPs, many successes have been achieved towards the mitigation of their influences on active detectors [START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF], but the effects of the X-ray flash on the detectors remain a major challenge. These detectors must therefore be chosen and prepared to fit properly in a laser-plasma environment for the purpose of the experimental venture. This work, therefore, concerns an exploratory study of online particle detectors for the characterisation of laser-produced particles and the study of short-lived nuclei in a laser-plasma environment.

In what follows, some of the fundamentals of laser-plasma acceleration will be briefly discussed. The application of laser plasmas for fundamental nuclear physics studies will be linked in, and the challenges of detection in the plasma environment will be stressed.

Laser-plasma interaction

Laser interactions with matter follow the path of plasma creation. When a highintensity laser with wavelength λ L comes in contact with matter, a plasma is first created from the intensity of the amplified spontaneous emission (ASE), at the pedestal, before the laser's main pulse (described from figure 1.1). Such an intensity typically exceeds 10 12 W/cm 2 and it is sufficient to overcome the binding energy of a valence electron mainly through the process of multi-photon absorption. The intensity I, of Laser-plasma interaction the laser is given by:

I = E ∆tA , (1.1.1)
where E (J) is the laser energy, ∆t (s) is the pulse duration, and A (cm 2 ) is the cross-sectional area of the laser beam at focus.

.1: Intensity of high power laser pulse normalised to one at the peak intensity. For a peak intensity greater or equal to 10 18 W/cm 2 , the pedestal can reach 10 12 W/cm 2 at a contrast of 10 -6 in the ns time domain. The inset shows the main laser pulse of the order of few ps.

A plasma is a gas of free electrons, ions and neutral particles. The electrons and ions are coupled with self-consistent electric and magnetic fields so that they exhibit a collective behaviour. This implies that the motion by a group of particles will be felt by the others due to their self-consistent electric field. Since the electrons are more mobile because of their higher charge-to-mass ratio compared to the ions, the plasma frequency ω p is related to the electron density by:

ω p = n e e 2 m e 0 1/2 , (1.1.2)
where e is the electron charge, n e is the plasma free electron density, m e is the electron mass, and 0 is the vacuum permittivity. In plasma, the electrons and ions screen the Coulomb potential created by an ion or electron inside it. The Debye length λ D defines the characteristic length above which the potential is screened; it is given by: where k B is the Boltzmann constant and T e is the plasma electronic temperature.

λ D [cm] = 0 k B T

Laser-plasma interaction

The propagation of the laser main pulse in the pre-created plasma is dominated by the presence of free electrons, and obeys the dispersion relation:

ω 2 L -ω 2 p = k 2 c 2 , (1.1.4)
where k is the wave number, ω L (2πc/λ L ) is the laser frequency and c is the speed of light. When ω L = ω p , the maximum plasma density is reached that allows the laser to propagate into a cold, linear, non-relativistic plasma. Therefore, the maximum electron density above which the laser cannot propagate further is defined by the critical density as:

n cr [cm -3 ] = 4π 2 m e c 2 λ 2 L e 2 = 1.113 × 10 21 1µm λ 2 L [µm]
(1.1.5)

From equation 1.1.5, it implies that for a near infrared laser (1.053 µm) the critical density is approximately 10 21 cm -3 . The plasma is underdense if n e < n cr , in this case the laser propagates through; it is reflected at the critical surface where n e = n cr ; and degenerates into an evanescent wave at n e > n cr .

High-power laser interaction with plasma leads to the acceleration of bunches of particles including ions, which can reach several tens of MeV; and electrons at GeV scales with their associated Bremsstrahlung photons of several tens of MeV. These emissions take place within a ns duration at relatively high intensities. For example, more than 10 11 protons and less than 10 12 carbon C 4+ ions per MeV per steradian solid angle have been measured [START_REF] Singh | Intensified proton and carbon ion flux from femtosecond laser driven plasma source[END_REF][START_REF] Carroll | Carbon ion acceleration from thin foil targets irradiated by ultrahigh-contrast, ultraintense laser pulses[END_REF] (see figure 1.4, and figure 1.2 ), and up to 10 9

photons/sr in a Boltzmann-like energy distribution with a 2.5-MeV temperature have been detected [START_REF] Courtois | Effect of plasma density scale length on the properties of bremsstrahlung x-ray sources created by picosecond laser pulses[END_REF] (see figure 1.8). In this section, the mechanisms of acceleration of ions, and the emission of photons will be discussed.

Ion acceleration

High-intensity laser interaction with plasma can be used for the acceleration of particle bunches. Compared to conventional accelerators, laser-plasma accelerators (LPA) can reach high electric fields of some TV/m (MV/µm), which is six orders of magnitude higher than conventional accelerators at MV/m. Amongst many applications, these ions can be used for radioisotope production and fundamental nuclear physics.

There are different mechanisms of laser-plasma acceleration, but two of them will be described as one applies more to one-shot lasers, while the other is well suited for high repetition rate ones.

Target Normal Sheath Acceleration (TNSA)

The most studied scheme of laser-plasma acceleration is the Target Normal Sheath Acceleration (TNSA) [START_REF] Wilks | Energetic proton generation in ultra-intense laser-solid interactions[END_REF][START_REF] Macchi | Ion acceleration by superintense laser-plasma interaction[END_REF]. In this case, relativistic electrons are generated as a high intensity laser interacts with the preplasma in front of a solid target. These relativistic hot electrons propagate through the target forming an electron sheath behind the target with the generation of a strong electric space charge (MV/µm).

This field then ionizes the surface and accelerates ions in the target normal direction (see figure 1.3).

Since electrons have a higher charge-to-mass ratio, they will be accelerated first, followed by proton and heavier ion bunches at relatively long time scales. Their high intensity and short duration give LPA a major advantage over conventional accelerator Laser-plasma interaction systems. For instance, 10 11 -10 13 protons are emitted in one ps laser shot, with energies > MeV, within a ps duration, correspond to a peak current in the range of hundreds kA at the source [START_REF] Borghesi | Laser-driven ion acceleration: State of the art and emerging mechanisms[END_REF][START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF]. This is more than a thousand times higher than what is obtainable from a continuous beam in 1 s. Furthermore, the beams are marked by low transverse emittance (0.004 mm-mrad [START_REF] Te Cowan | Ultralow emittance, multi-mev proton beams from a laser virtual-cathode plasma accelerator[END_REF]) and ultrashort duration (∼ ps) at the source [START_REF] Borghesi | Laser-driven ion acceleration: State of the art and emerging mechanisms[END_REF]. They are emitted in a cone-like fashion, and the half-opening angles follow a dependence in the ion energy. The opening angle increases with decreasing ion energy.

The energy spectra of the ion beams are typically broadband, and with an exponential distribution that reaches a cut-off at high energy, as showcased in figure 1.4.

The maximum proton energy denoted by the different cut-off, and their corresponding irradiance (I(W/cm 2 )λ 2 , λ D ∼ 1µm) have been reported by [START_REF] Borghesi | Laser-driven ion acceleration: State of the art and emerging mechanisms[END_REF] in figure 1.5, showing that increased laser intensities at ps duration, can deliver a high energy proton beam energy of the order of 60 MeV.

Collisionless Shock Acceleration

The mechanism of Collisionless Shock Acceleration (CSA) has been studied theoretically and experimentally by several authors [START_REF] Luís | Proton shock acceleration in laserplasma interactions[END_REF][START_REF] Humières | Investigation of high intensity laser proton acceleration with underdense targets[END_REF][START_REF] Palmer | Monoenergetic proton beams accelerated by a radiation pressure driven shock[END_REF][START_REF] Haberberger | Collisionless shocks in laser-produced plasma generate monoenergetic high-energy proton beams[END_REF]. The CSA with gas targets is interesting for high repetition rate lasers compared to the conventional target technologies and corresponding acceleration mechanisms. The principle relies on the creation of shock waves in a plasma characterised by an electrostatic potential at the shock front. Ions with mass m i can be accelerated from rest due to the reflection from the shock front with a velocity gain of twice the shock velocity V sh and energy

m i (2V sh ) 2 /2=2ZM 2 T e .
where Z is the ion charge, M the Mach number (>1), and T e is the electron temperature. M and V sh are related by V sh = M c s , with c s being the speed of sound defined by c s = ZT e /m i . More on CSA mechanism can be found in Fiuza et al. [START_REF] Fiuza | Ion acceleration from laser-driven electrostatic shocks[END_REF].

State-of-the-art high power laser pulse are capable of driving shocks at high speeds because of the generation of high-energy electrons, yielding effective values of T e of several MeVs [START_REF] Grassi | Vlasov simulation of laser-driven shock acceleration and ion turbulence[END_REF]. Using an overdense hydrogen target D. Haberberger et al., [START_REF] Haberberger | Collisionless shocks in laser-produced plasma generate monoenergetic high-energy proton beams[END_REF] demonstrated that protons can be accelerated via a CO 2 laser by CSA to 20 MeV.

Furthermore, other studies involving plasma shaping from gas jet targets are expected to reach optimal conditions for CSA mechanism [START_REF] Henares | Optimization of critical-density gas jet targets for laser ion acceleration in the collisionless shockwave acceleration regime[END_REF]. The mechanism is very promising as it has been predicted to accelerate ions up to hundreds of megaelectronvolt [START_REF] Luís | Proton shock acceleration in laserplasma interactions[END_REF].

Moreover, the ion energy profile has shown interesting structures in energy which could serve as a promising step closer to quasi-mono energetic beams. In figure 1.6, is the proton energy spectra obtained from a gas jet target collected from different detection angles relative to the laser direction. The spectrum at each angle shows some structures towards the energy tail, particularly at 0 0 .

Figure 1.6:

Typical spectrum obtained with a gas jet target for a laser intensity of 5 × 10 19 W cm -2 (taken from [START_REF] Puyuelo-Valdes | Laser driven ion acceler-ation in high-density gas jets[END_REF]).

New mechanisms for laser-plasma ion acceleration are being explored. An interesting advantage of these beams is that they can be used to create unstable nuclei in laser facilities.

Emission of huge X-ray flash

One of the consequences of high-power laser-plasma interactions are X-ray fluxes.

After the creation of laser pre-plasma due to the ASE, the expanding plasma strongly absorbs the remainder of the laser pulse, leading to its high temperature rise. A highly inhomogeneous plasma is produced with increasing density as the target is approached with a scalelength of the order of several micrometers. In principle, regions of the plasma combining both high temperature and high electron density will produce more X-rays. This is because the electrons can interact with the Coulomb potential of ions within the plasma leading to Bremsstrahlung emissions of X-rays. Meanwhile other sources of radiation emission are purely atomic and are due to rearrangement of electrons on their atomic orbitals.

While all the previously mentioned X-ray generation processes take place in the plasma, huge contributions from Bremsstrahlung processes also occur outside the plasma when laser accelerated electrons are stopped by objects in the experimental chamber [START_REF] Glinec | High-resolution γ-ray radiography produced by a laser-plasma driven electron source[END_REF][START_REF] Lemos | X-ray sources using a picosecond laser driven plasma accelerator[END_REF]. The typical energy distribution of the electrons is exponential, and for a high power laser, some hundreds of MeV can be reached. The different processes of X-ray generation for inside and outside the plasma, accompanying ion acceleration in laser plasma, have been graphically captured in figure 1.7a and b. The X-ray pulse duration is typically comparable with that of the laser pulse producing the plasma [START_REF] Giulietti | X-ray emission from laser-produced plasmas[END_REF]. Depending on the laser beam energy, duration, cross section, contrast, and target, the X-ray energies can reach some MeV. In ion acceleration with solid targets, the pre-formed plasma is best reduced to the minimum by an improved contrast for maximum transfer of energy to the plasma ions [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF]. An example of such is seen from a high power laser with 10 19 W/cm 2 intensity (25 J, 700-fs pulse duration, and 1:10 6 contrast) on a 125 µm aluminium solid yields 10 9 photons/sr in a distribution with a temperature of 805 keV [START_REF] Norreys | Observation of a highly directional -ray beam from ultrashort, ultraintense laser pulse interactions with solids[END_REF]. The spectrum which is displayed in figure 1.8, is from the contribution of Bremsstrahlung X-rays due to the deceleration of high energy electrons after a high power laser on a solid target. The distribution follows a Boltzmann form, similar to that of the accelerated electrons. With a gas target it is expected to observe lesser quantities of photons due to relatively lower density compared to solids.

While laser-plasma X-ray sources are relevant for purposes such as precision imaging of materials [START_REF] Glinec | High-resolution γ-ray radiography produced by a laser-plasma driven electron source[END_REF][START_REF] Courtois | Characterisation of a mev bremsstrahlung x-ray source produced from a high intensity laser for high areal density object radiography[END_REF], they are very limiting for active detectors as they can blind and saturate them [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF][START_REF] Negoita | Perspectives for neutron and gamma spectroscopy in high power laser driven experiments at ELI-NP[END_REF]. We will see in more details, during the course of this work, how laser-induced X-rays can affect online detection during nuclear physics studies in a laser-plasma environment. W cm -2 ) (adapted from [START_REF] Norreys | Observation of a highly directional -ray beam from ultrashort, ultraintense laser pulse interactions with solids[END_REF]).

Nuclear physics in a laser-plasma

In understanding the dynamics of nucleosynthesis, which concerns the origin of all elements in the periodic table, detailed knowledge of nuclear properties are required.

But so far, nuclear properties have only been studied in solid, liquid or gaseous state materials, however, if deeper understanding of the universe is to be achieved, they must be investigated in a plasma medium.

Plasma is considered the fourth state of matter and the most abundant in the visible universe (99.99%). It is the state of matter that defines the stellar environment. It is characterised by an interplay between ions, free electrons, and photons. It becomes pertinent to do nuclear physics in plasma because some of the decay modes of nuclear excited states are as a result of the coupling between the nucleus and its electronic cortege, and such couplings are expected to be greatly affected in a hot dense plasma leading to changes in nuclear properties. The large number of photons and free electrons in a plasma modifies the environment in which a nuclear excited level decays [START_REF] Gobet | Nuclear physics studies using high energy lasers[END_REF]. For instance, Klay and Gosselin et al., have hypothesized that the lifetime of a nuclear level in hot and dense plasma is expected to be significantly altered in comparison with the lifetime in a neutral target [START_REF] Klay | Nuclear structure of 176 Lu and its astrophysical consequences. ii. 176 Lu, a thermometer for stellar helium burning[END_REF][START_REF] Gosselin | Modified nuclear level lifetime in hot dense plasmas[END_REF]. Other authors have shown that decay rate of an isomeric level can be greatly enhanced if there is a short-lived nuclear level lying just above the isomer. Many of these investigations are theoretically founded and have not been experimentally observed. For example, the case of a modification in the apparent lifetime of 84m Rb in plasma, theoretically studied by Denis petit et al. [START_REF] Denis-Petit | Calculation of the rate of nuclear excitation by electron transition in an rb 84 m plasma under the hypothesis of local thermodynamic equilibrium using a multiconfiguration dirac-fock approach[END_REF].

From an experimental point of view, one will need to create astrophysical plasmas in the laboratory as a first step towards understanding nuclear processes in them. This is where high power lasers have an advantage. The figure 1.9 shows the density and temperature of different plasma sources. Laser plasmas are similar in temperature to what is obtainable in the solar corona at some hundreds of eV. This is interesting to experimentally study nuclear processes in stellar-like environment, which will be used to verify theoretical results in the same condition. Although few experimental studies have been performed but not many of them have succeeded to convince the scientific community about their findings. An example is a study about the excitation of 181m Ta in plasma; the estimated number of nuclear excitation per laser shot varies significantly by several orders of magnitude amongst different authors [START_REF] Vs Letokhov | Excitation of isomeric low-lying levels of heavynuclei in a laser-produced plasma[END_REF][START_REF] Av Andreev | Excitation of tantalum-181 nuclei in a high-temperature femtosecond laser plasma[END_REF][START_REF] Av Andreev | Excitation and decay of low-lying nuclear states in a dense plasma produced by a subpicosecond laser pulse[END_REF][START_REF] Gobet | Particle characterization for the evaluation of the 181mta excitation yield in millijoule laser induced plasmas[END_REF], and remains an open question.

In this part, nuclear excitation processes in plasma will be briefly discussed, and focus will be dedicated to two future experiments involving the direct nuclear excitation of 181m Ta, and the half-life-modification of 84m Rb nuclei in a laser-generated plasma.

Figure 1.9: Different plasma sources in their density and temperature. Compared to the solar core, lasers can deliver plasmas of similar temperature of some hundreds of eV at a higher electron density of 10 20 cm -3 (extracted from [START_REF] Anthony | Advances in numerical modeling of astrophysical and space plasmas[END_REF]).

Study of short-lived nuclear states in plasma

Mechanisms of nuclear (de-)excitation in plasma Nuclear excitation processes in plasma are tied to their interaction with charged particles and photons that are within the plasma. Some of the processes are briefly described below and can be found in more detail in [START_REF] Mr Harston | Mechanisms of nuclear excitation in plasmas[END_REF](with figures 1.10-1.12 describing the processes),

• Photoexcitation: In plasma, photons are created by the motion of charged particles, and their energies can be directly transferred to a nuclear level in a resonant process. This can then lead to the excitation of this nuclear level. The process has been studied for some selected nuclei such as 181 Ta in hot dense plasma (see table 1.1).

• Electron inelastic scattering: It is possible for plasma electrons with energies greater than the nuclear excitation energies to induce nuclear excitation by inelastic scattering. In this case, the hot plasma energetic electron transfers part or all its kinetic energy to the nucleus. The process is direct and the expected cross section is small ( e.g below 10 -30 cm 2 for 110 Ag and 201 Hg [START_REF] Gosselin | Nuclear transition induced by low-energy unscreened electron inelastic scattering[END_REF]) however, due to large number of free electrons in the plasma the transition rate is significant. The process requires that both the electronic and nuclear transitions carry the same amount of energy, angular momentum and parity, it is therefore a resonant process.

• Nuclear excitation by electron capture (NEEC): This is an indirect and a resonant process in which a free electron from the plasma is captured into a bound atomic state. The electron fills a vacancy within the ion atomic orbital and the released energy is transferred to the nucleus via a virtual photon. The de-excitation process can be due to internal conversion (IC) where an electron is emitted from the atomic shell to the continuum as a result of energy released through a virtual photon from a de-exciting nucleus. It is also possible for de-excitation to happen through a bound state internal conversion (BIC) [START_REF] Attallah | Charge state blocking of k-shell internal conversion in 125 te[END_REF], in which the nuclear photon is used to promote an orbital electron to another bound state. Finally, the nucleus could de-excite by directly emitting a gamma photon without being associated to any electron in the surrounding atomic shell. The figure 1.12 below summarises mechanisms of (de-)excitation.

Study of 181 Ta

The probability of observing the different nuclear excitation processes described above will increase when the nuclear excitation energy is of the order of the plasma temperature. Thanks to high power lasers, plasma temperature up to few keV could be realised. It is for this purpose that nuclei of excitation energy between 50 eV and 15 keV, and half-lives higher than 1ns, have been surveyed and reported [START_REF] Granja | Survey of nuclei for low-energy nuclear excitation in laser-produced plasma[END_REF] (table 1.1).

This survey is limited to low multipolarity transitions (E1-E3 and M1-M3), and only 10 nuclei (eight stable and two unstable with half-life higher than 10 7 years) respect these conditions [START_REF] Gobet | Nuclear physics studies using high energy lasers[END_REF]. 181 Ta is one of the nuclei captured in this survey. It is interesting for nuclear excitation studies due to the following information: the first excited isomeric state of I π = 9/2 -is 6.2 keV above the ground state, I π = 7/2 + and decays with a half life of 6.05 µs (figure 1.13). The 181 Ta nuclei can be excited in a plasma by at least two mechanisms: photoexcitation and electron inelastic scattering [START_REF] Gobet | Particle characterization for the evaluation of the 181mta excitation yield in millijoule laser induced plasmas[END_REF]. For example, in the results of Andreev et al., if correct, would be relevant for energy storage in nuclear levels [START_REF] Gobet | Particle characterization for the evaluation of the 181mta excitation yield in millijoule laser induced plasmas[END_REF].

A scheme of the typical experimental setup is revealed in figure 1.14. A high power laser with an intensity greater than 10 16 W/cm 2 interacts with 181 Ta to create a plasma. Due to the motion of charged particles in the plasma, photons of sufficient energy are produced, which are capable of directly exciting from the ground state of the nucleus I π = 7/2 + to the first excited isomeric state, I π = 9/2 -. Moreover, electron-electron scattering in the plasma also participate in the excitation to this first isomeric level. The de-excitation process can then be observed by the detection of the emitted gamma during the return back to the ground state, which takes 6.05 µs of decay time, in the midst of a high background of X-rays following the laser interaction.

Also, the majority of the emissions are conversion electrons with 1 photon for ∼ 44 electrons [START_REF] Meot | Nuclear excitation in plasma; excitation nucleaire dans les plasmas[END_REF].

Figure 1.13: Simplified level scheme of 181 Ta. The excitation process requires E 1 photons with an energy equal to that of the excited nuclear level.

Figure 1.14: Scheme of experimental Setup, from laser-plasma interaction to gamma detection. A shield is placed to block debris from laser-target interaction from reaching the optical setup. The detector is suited to detect gamma around 6 keV.

Study of 84 Rb

Laser-plasma has the capacity to induce the excitation of long-lived isomers to highlying levels. From figure 1.15, consider an existing isomeric level, with excitation energy E m , and another level just above it, with excitation energy E * . This higher nuclear level can be populated from the isomeric level from several mechanisms discussed above, and can then de-excite from its relatively high level to another lower state or ground state depending on its lifetime. The possibility of such processes occuring is also enhanced if the energy difference between both levels (E * -E m ) has the order of magnitude of the plasma temperature. 84 Rb was proposed as a good candidate to study the reduction in the apparent life time of a nucleus in plasma [START_REF] Gobet | Nuclear physics studies using high energy lasers[END_REF][START_REF] Denis-Petit | Calculation of the rate of nuclear excitation by electron transition in an rb 84 m plasma under the hypothesis of local thermodynamic equilibrium using a multiconfiguration dirac-fock approach[END_REF]. As can be seen in figure 1. [START_REF] Bonnet | Response functions of fuji imaging plates to monoenergetic protons in the energy range 0.6-3.2 mev[END_REF], it has a Nuclear physics in a laser-plasma eV. In other terms, at low plasma temperature, the half-life evolved from:

J π = 6 -isomeric
t 1/2 = ln 2 λ γ , (1.2.1)
when no nuclear excitation process was on, to

t 1/2 = ln 2 λ γ + λ excitation , (1.2.2)
when several nuclear excitation mechanisms were activated. The decay constant λ γ sets in normal condition of de-excitation with no plasma-induced excitation mechanisms in play. However, as the plasma temperature rises beyond 150 eV, the excitation processes are activated contributing an extra decay constant λ excitation to the decay time. The NEET process has been tipped to be the most dominant excitation process in 84 Rb for a plasma temperature around 400 eV (figure 1.17).

Figure 1.17: Probability of nuclear excitation mechanisms for 84 Rb in a 10 -2 g/cm 2 plasma under different temperatures(adpated from [START_REF] Gobet | Nuclear physics studies using high energy lasers[END_REF]).

Figure 1.18: Evolution of 84 Rb half-life in hot dense plasma (adpated from [START_REF] Denis-Petit | Applications of laser-driven particle acceleration[END_REF]).

The interest is also to perform this study on 84 Rb experimentally. To do this, we must first create 84 Rb, as it does not exist in nature. It can be created from 76 Ge in the following reaction 76 Ge( 12 C, p + 3n) 84 Rb. Thanks to high power lasers, all the stages from 84 Rb nuclei creation to their excitation in plasma can be realised. As depicted in figure 1.19, a high power laser of less than or equal 1 ps pulse duration, and some tens of Joules, interacts with a gas target adapted for high repetition rate experiment to accelerate carbon ions. These ions are made to interact with 76 Ge and to create 84 Rb nuclei. Then the nuclei is subjected to a relatively long duration and hot dense plasma created from a kJ, ns laser. The de-excitation processes can then be measured using appropriate detectors.

For both experiments of 181 Ta and 84 Rb, the main difficulty in the detection of the de-excitations lies in the high background due to the plasma emissions, and of course, high energy Bremsstrahlung X-rays. Some information about the detection challenges and procedures will be discussed in the next section. of the de-excitation mechanisms in both cases is in the gamma emissions. The aim is therefore to be able to perform gamma spectroscopy by the aid of relevant detectors in the laser-plasma environment. Not to forget that laser-created plasmas as well as accelerated electrons produce prompt fluxes of X-rays, which constitute an enormous background in the detection environment. Therefore, active detectors suitable in such background are necessary. Moreover, for the advantages of high repetition rate lasers to be fully maximised, both for this study and other applications, detec-Detection in laser-plasma environment tors that enable online characterisation of particles in the laser-plasma environment are imperative.

Since this section is about the detection in a laser-plasma environment, I will summarise the principle of radiation interaction with matter in the context of what we want to detect. The section will also contain the challenges facing detection, and method of data acquisition.

Interaction of radiation with matter

The focus of this work is in the domain of detection of photons and ions. The principle of radiation detection relies on the energy deposited by an interacting radiation.

Therefore, this part shall concern how radiation interacts with matter.

Photons

When photons of a certain number and energy traverse a material, there is an attenuation of the number of non-interacting photons. This is because of photon scattering or absorption processes in the material that contribute to the attenuation. The coefficient of attenuation µ ph (cm -1 ) from all these processes is used to estimate the number of photons I from an initial quantity I 0 exiting a material of thickness x(cm), in the following Beer-Lambert relation:

I = I 0 exp(-µ ph x) (1.3.1)
The constant term µ ph (cm -1 ), known as the photon attenuation coefficient takes into account all the different processes of photon interaction in the material, and the value for each process depends on the photon energy and material type. The main mechanisms of photon interaction are summarised, however more details can be found in popular text [START_REF] Glenn | Radiation detection and measurement[END_REF][START_REF] Spieler | Semiconductor detector systems[END_REF].

• Photoelectric absorption: In this process a photon interacts with an absorber atom and completely disappears. An energetic photoelectron is ejected by the atom from one of its bound shells. The photoelectron then has an energy expressed by:

E e -= hν -E b , (1.3.2)
where, h is the Planck's constant, ν is the frequency of the photon and E b is the binding energy of the photoelectron in its original shell. This process is dominant for gamma-ray energies less than or about a few hundred keV, where in this case, the photoelectron carries off most of the absorbed photon energy. It Detection in laser-plasma environment is also enhanced for higher atomic number (Z) (eqn. 1.3.1), absorber materials.

A rough estimate of the probability of photoelectric absorption per atom over all range of gamma-ray energy E γ , and Z, is given by [START_REF] Glenn | Radiation detection and measurement[END_REF]:

τ ≈ constant × Z n E 3.5 γ , (1.3.3)
where n varies between 4 and 5 over the E γ region of interest.

• Compton scattering: This process takes place between an incident gammaray photon and an electron in the material. On interaction, the gamma-ray is deflected from its initial direction by an angle θ and transfers part of its energy to the electron relatively initially at rest. The probability of the process increases linearly with Z since it essentially depends on the number of electrons present in the target. The energy of the scattered gamma ray hν , is derived in terms of the scattering angle θ, and the rest mass energy m 0 c 2 of the electron (0.511 MeV), given by:

hν = hν 1 + (hν/m 0 c 2 )(1 -cosθ) (1.3.4)
Two extreme cases can be deduced from the above equation: when the scattering angle θ ≈ 0, the incident photon is almost not deflected, and the scattered gamma ray is nearly the same as the incident gamma ray. Whereas, when θ ≈ π, the incident gamma ray is back-scattered in the direction of its origin, while the electron recoils along the direction of incidence. This represents the maximum energy, E e = hν -hν , that can be transferred to an electron in a single Compton interaction.

• Pair production: This process largely depend on the energy of the incoming photon. For energy greater than 1.02 MeV (twice the rest mass energy of an electron ), pair production starts. The gamma-ray interacts creating an electronpositron pair, and the excess energy above 1.02 MeV are shared as kinetic energy by the electron and positron.

• Rayleigh scattering: The gamma-ray photon neither excites nor ionizes the atom. Additionally, the photon maintains its original energy since it did not deposit its energy but the direction of the photon is changed. This is not relevant for radiation detection since no energy can be deposited in the detector material.

Heavy charged particles

Heavy charged particles including protons and carbon ions, interact with matter through Coulomb forces. The interaction is between the incoming ions and the electrons as well as the nuclei of the target medium.

When projectile ion collide inelastically with the atom, they deposit part of their energy to the electron δE. Part of this deposited energy is first used to overcome the ionisation I potential of the electron, and the remaining part is used to supply kinetic energy to the same electron. The projectile ion continues in the deposition process but with a lesser energy due to the previous energy deposition. This is explained in The stopping power is used to denote the mean energy loss of a charged particle within a distance dx, and it can be computed from the relativistic version of the Bethe-Block formula [START_REF] Fano | Penetration of protons, alpha particles, and mesons[END_REF] in eqn. 1.3.5, The stopping power is a sum of nuclear and electronic types. The electronic Detection in laser-plasma environment stopping power is due to the inelastic collisions of ions with the electronic environment of the target atoms (already explained above using figure 1.21). On the other hand, the nuclear stopping power refers to the elastic collisions between the projectile ion and the nuclei of the target. In the stopping power curves as a function of energy for proton in silicon (from figure 1.22), nuclei stopping power is orders of magnitude less than the electronic stopping power for the energies being considered.

dE dx = 4πe 4 Z t Z 2 p m e v 2 ln 2m e v 2 I -ln 1 -β 2 -β 2 - C Z t - δ 2 , (1.
The range R of an ion can be approximated as its total path length in the absorber medium (equation 1.3.6) from the stopping power.

R(E) = E 0 dE dx -1 dE (1.3.6)
The fact that ions have a definite range and deposit most of their energies in the end of their path, forming a Bragg peak, motivates their application to radiotherapy.

For light particles, such as electrons at very high energy of tens of MeV, they need to be considered differently from ions. The Bremsstrahlung emission represents their main energy loss mechanism. In this case, the deflection due to their relatively small mass, and the deceleration of the particle as they interact with the nuclei of the target cause the emission of photons. Additionally, the collisions are between identical particles, so that the calculation from the Bethe-Block formula must also take into account their indistinguishability. Rohrlich and Carlson [START_REF] Rohrlich | Positron-electron differences in energy loss and multiple scattering[END_REF] have refined the calculations in eqn. 1.3.5 to include energy losses via bremsstrahlung radiation, that is significant when high-energy electrons and beta particles interact with absorbers of high atomic number, which can be found in relevant texts such as [START_REF] Glenn | Radiation detection and measurement[END_REF].

Detection and acquisition in a laser-plasma environment

The challenges of detection are detailed here with reference to the 181 T a and 84 Rb short-lived nuclear state studies. The figures 1.14 and 1.19 serve as relevant schemes of the experiment.

X-ray flash

At the instant of a High power laser interaction, bunches of particles are produced as well as a huge flash of X-rays emerging at the time of the laser shot. The idea to study short-lived nuclear states ( few µs) in such an environment is, therefore, a very difficult task. The main problem concerns the enormous quantity of X-rays reaching the online detector at the same time as the gammas to be detected. These X-rays can blind the detector for a certain time, and depending on the duration of this blindness, Detection in laser-plasma environment and the half-life of the nuclear state to be observed, significant statistics may be lost.

To analyze the problem, the X-ray energy distribution in figure 1.8, will be used as a reference here. The distribution is summarised thus, 10 9 photons/sr are produced at mean energy (kT) of 805 keV, from a high power laser interacting with 125 µm thick Al foil. The X-ray spectrum can be modeled by a Boltzmann distribution,

A exp(-E/kT ) (A is related to the number of photons, and E, the photon energies) as shown in figure 1.23.

If we imagine a scintillator detector, for example, a 1.5 in (diameter) × 1.5 in (thickness) LaBr 3 , placed 20 cm away from the laser interaction point, the total energy deposited in the detector is at 1.4 ×10 13 eV , which is too much for it. One may attempt to reduce the background by using shielding materials, but as can be seen in figure 1.23, even after using a 10 cm lead shield, the total energy in the detector is about 40 GeV, that is again, too much a background to permit a prompt detection of a gamma photon. The situation is very complicated and even a 10 cm thick lead shield is not sufficient to allow for prompt gamma spectroscopy. This is why many online detectors have not succeeded for gamma detection applications in a laser plasma environment.

Moreover, the 10 cm lead shield completely attenuates all photons around 200 keV, which is the typical energy of the gammas we are interested in. Therefore, a shielding system that will well-minimise X-ray background and at the same time permit gamma spectroscopy of the order of some hundreds of keV cannot be devised.

ElectroMagnetic Pulses (EMPs)

Aside from X-rays, EMPs that destroy detector electronics also arise during a high power laser interaction with matter. This has been studied by several authors [START_REF] De | Electromagnetic pulse (emp) radiation by laser interaction with a solid h2 ribbon[END_REF][START_REF] Liao | Multimillijoule coherent terahertz bursts from picosecond laser-irradiated metal foils[END_REF][START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF][START_REF] Consoli | Sources and space-time distribution of the electromagnetic pulses in experiments on inertial confinement fusion and laser-plasma acceleration[END_REF].

EMPs mainly arise from charge separation and target polarization under the action of a laser pulse [START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF]. On the interaction of the laser's rising edge, strong fields ionize the atoms and create a plasma that expands from the target surface. When the main laser pulse eventually interact with the preplasma, the electrons are heated and accelerated to energies much above the ions. Relatively few of these electrons leave the target thus charging it positively.

During the electron ejection process and the return current in the target, high amplitude EMPs exceeding 1 MV/m with frequencies going down from 1THz can be produced which is in the domain most damaging for electronic circuits [START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF][START_REF] Bardon | Mitigation of strong electromagnetic pulses on the lmj-petal facility[END_REF].

Secondary electromagnetic emissions can also be created by the flash of hard X-rays emitted from the laser target interaction. Depending on the laser pulse duration, these secondary emissions could lie in a broad frequency range from THz for sub-ps laser pulses, but also in the GHz and MHz domains for longer, ns laser pulses [START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF].

An example of EMP signal is shown from LULI2000 laser facility in figure 1.24. EMPs should be avoided as much as possible because of the safety of online detectors. Bardon and Consoli et al. [START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF][START_REF] Bardon | Mitigation of strong electromagnetic pulses on the lmj-petal facility[END_REF] have shown several protection strategies against EMPs which will be briefly highlighted here. Some of the methods involve, the use of small targets as EMP energy increases with increasing target dimension; avoid physical connection between the target and the vacuum chamber; and use of a faraday cage to shield the involved electronics during high power laser experiments.

Also, in one of our experiments we were able to reduce EMP disturbances on detectors by ensuring that the detector supports were well grounded to allow the flow of electrons. In one case, the detector was placed on a non metallic support and electrons accelerated from laser interactions arriving on the detector had no passage to the ground, which affected the stability of our detectors. This was later mitigated with a ground link.

Pileups

In addition pileup issues are anticipated in high activity particularly for short-lived de-excitation in 181m T a and 84m Rb. For a nuclear lifetime around 6 µs, one can only manage a useful detection window of less than 60 µs. This may however be minimised by using very fast detectors that deliver pulses within few ns. Detectors could also be placed relatively far from the laser interaction point but this will lead to lesser solid angle and detection efficiency, which we want to avoid. Another approach to minimising pileup losses is to perform offline treatments that can extrapolate the "missing" pulses when a few gamma pulses are piled up together. For example, in

Data acquisition

During data acquisition for gamma spectroscopy, it is normal in the settings of conventional accelerators to collect a gamma signal from the detector, pass it to a preamlifier, then a shaping amplifier, and finally to a multichannel analyser (MCA) to build the histogram of number and energy of the detected gammas, as in figure 1.26. This process has proven to be very efficient and regularly implored. The time needed to pass Detection in laser-plasma environment from the preamplifier to the MCA for each gamma pulse could last few milliseconds, and in high radioactive source activity, several detected signal are lost when shaping a pulse for histogram. Nonetheless the matter of statistics is not an issue as most of these radiation sources are emitting continuously at more 1 MHz. To perform gamma spectroscopy of short-lived nuclei (few µs) in a laser plasma environment, the acquisition structure cannot follow the defined order in figure 1.26.

A typical high power laser shoots once in 1 second, which is at least 10 6 times less than conventional accelerators. Therefore each gamma pulse of a preamplifier, from a de-exciting nucleus in study, per laser shot, is very precious and cannot be wasted. We thus cannot afford to pass through the shaping stage to the MCA which can reach few millisecond compared to some µs for the decay time of interest. The detector signal will be collected from the preamplifier via an oscilloscope during a continuous time window that is at least 10 times the decay time τ of the nuclei, as in the figure 1.27.

The signal duration of interest can be as short as few ns depending on the detector and the preamplifier, and the rise time will be even less. This is nearly in the GHz domain. Clearly the sampling rate must be high enough to provide a faithful representation of the signal. Nyquist's theorem states that a periodic signal must be sampled at more than twice the highest frequency component of the signal [START_REF] Shannon | Communication in the presence of noise[END_REF]. This informs that the type of oscilloscope should be able to operate at giga samples per second (GSPS). Alternatively, fast digitizers operating at few GSPS can be adopted with vertical resolution up to 16 bits possible. In addition, all gamma signals of interest are to be collected at once from the preamplifier after every laser shot, and stored in the digitizer, which can weigh up to few Gigabytes of data. The digitizer must therefore have adequate memory for the storage of such sizes of data for offline retrieval. This is why we have purchased a 14 bit digitizer from SP devices company with a 4 GB memory, and it is capable of switching between 10 GSPS on one channel and 5 GSPS on the second channel. The collected oscillogram is a file containing all possible gamma signals for the set detection window. This is then passed in for offline analysis including treatments for pileup, pulse peak detection, pulse integration to obtain charge, and the final histogram depending on the pulse peak or the integrated charge. Furthermore, due to the huge flash of X-rays, a large detector pulse contribution is anticipated compared to the small pulses of gammas. This large signal represent the sum of X-ray photons arriving into the detector at the the same time. In principle, they would arrive at similar times as the gammas of the nuclei being study, and depending on their duration, the detector signal of the gamma pulses are on top of this long duration X-rays signal. Offline analysis therefore allows to subtract the background from the total signal and treat them before they are used to build the histogram. Part of the treatments also include a gain correction process. Because of the saturation of the detector due to the huge quantities of X-rays, the gamma pulses detected just at the recovery of the detector could be deformed in amplitude quality.

Search for Detectors

The aim of this work is to build or adapt detectors to be able to successfully operate in a laser-plasma environment in high repetition rate conditions while under the influence of a huge background of short duration X-ray flash. With focus to the de-excitation of 181m Ta and 84m Rb in plasma as have been described in this chapter, the detectors are in two categories: the first is for the detection of gamma rays from nuclear physics studies, and the second will be for the online characterisation of laser-accelerated particles such as electron, proton, and carbon beams which can be used to foster nuclear reaction processes in a laser-plasma.

Chapter 2

Semiconductor detectors in laser-plasma environment Semiconductors are well-known materials for photon detection. They are based on the motion of free charge carriers to induce current under the influence of an electric field. Compared to scintillators (discussed in chapter 3 ), they do not need a photodetector accessory. They are also not prone to long duration afterglow signal observed in many scintillators when there is a large deposition of radiation energy. This chapter will explore semiconductors for gamma detection in a laser-plasma environment.

The focus is on their application to the 84m Rb and 181 Ta typical example experiments discussed in chapter 1. In the 84m Rb experiment, the energy of the gamma photon to be detected is in the domain of few hundred keV with a lifetime of 9 ns. For this purpose we are considering CdTe material detector. In the 181 Ta experiment, the photon energy of interest is 6.2 keV, and decay time 6.05 µs. Silicon-based avalanche photodiode (APD) detector will be studied in this case.

In addition, for the purpose of the online characterisation of laser-driven particle beams, a CMOS detector will be studied in this chapter.

Basics of semiconductor detectors

Information about semiconductors can be found in several texts [START_REF] Glenn | Radiation detection and measurement[END_REF][START_REF] Spieler | Semiconductor detector systems[END_REF][START_REF] Colinge | Physics of semiconductor devices[END_REF][START_REF] Sm Sze | Physics of semiconductor devices[END_REF][START_REF] Safa | Principles of electronic materials and devices[END_REF][START_REF] Syed Naeem | Physics and engineering of radiation detection[END_REF]. Semiconductors are in a class of materials whose energy gap fall between zero and 4 eV [START_REF] Peter | Fundamentals of semiconductors: physics and materials properties[END_REF].

An exception to this is Diamond which is a semiconductor with a band gap of 5.47

eV [START_REF] Chris | Diamond as an electronic material[END_REF]. The energy gap E g is a forbidden energy range in which allowed states cannot exist unless below and above it [START_REF] Sm Sze | Physics of semiconductor devices[END_REF]. The energy bands with energy E v due to the

Charge carriers distribution

Free charge carriers (electrons and holes) in the bulk of a semiconductor crystal occupy different energy levels and their occupancy can be described by the Fermi-Dirac distribution function in eqn. 2.1.1.

f (E) = 1 1 + exp{E -E f }/k B T , (2.1.1)
where E is the energy of the electron, k B is the Boltzmann constant, T the absolute temperature, and E F is the Fermi level. f(E) is the probability that an available energy state E can be occupied by an electron. For an intrinsic semiconductor that ideally has equal number of positive and negative charge carriers, the probability is 0.5, so the Fermi level is in the middle of the band gap. The square of the intrinsic charge concentration, n 2 i , is with the assumption that the concentration of holes p is equal to that of electrons n, so that,

np = n 2 i = N c N v exp - E g k B T , (2.1.2)
where E g = E c -E v is the band gap energy, N c and N v are the effective density of states at the conduction and valence band edges. The equation 2.1.2 is called the mass action law which states that the product, np, is constant at a given temperature and only depends on the semiconductor material. The intrinsic concentration is therefore:

n i = (N c N v ) 1/2 exp - E g 2k B T , (2.1.3)
which is generally valid applying to both intrinsic (n = p) and non-intrinsic (n = p) semiconductors. However an intrinsic semiconductor does not exist in nature due to crystal defects and impurities that are usually present. There are therefore other energy states within the forbidden gap that significantly alter the electrical conduction properties of the material.

Doping

To use semiconductors as radiation detectors, some quantities of impurities are usually added to the material in a process called doping. Such semiconductors are referred to as extrinsic semiconductors. The aim is to increase the conductivity of the semiconductor by increasing the number of mobile electrons/holes. For example, in the case of silicon (group 4), a group 5 atom (donor) such as phosphorus or arsenic could be added in parts per million (ppm) (that is a donor atom for every 10 6 atoms of Si) to form four covalent bonds thus leaving behind a free electron whose energy is within the band gap, close to the conduction band. In this way, even at room temperature ). This difference will dictate the type of the semiconductor provided that it is much larger than n i (assuming all the acceptors and donors were ionized at room temperature):

• n-type, more donors:

N d -N a >> n i ; n = (N d -N a ) and p = n 2 i N d -Na • p-type, more acceptors: N a -N d >> n i ; p = (N a -N d ) and n = n 2 i Na-N d
Typically n i is about 10 10 cm -3 for silicon [START_REF] Martin A Green | Intrinsic concentration, effective densities of states, and effective mass in silicon[END_REF].

Conduction in semiconductors

Drift current

Under the influence of an electric field (V/cm), the current density J dr (A/cm 2 ) due to the drifting of electrons and holes can be expressed by:

J dr = eE(µ e n + µ p p). (2.1.4)
The effective conductivity σ(Ω -1 cm -1 ) of a semiconductor material takes into account the two charge carrier types present, electron n, and holes p

σ = e(µ e n + µ p p), (2.1.5)
where µ e and µ p are the mobility (in cm 2 /(V.s)) of electrons and holes respectively, and e is the elementary charge. The resistivity ρ(Ω.cm) is the inverse of the conductivity, and can therefore be obtained from eqn.2.1.5 as:

ρ = 1 σ = 1 e(µ e n + µ p p) , (2.1.6)

Diffusion current

In semiconductors the production of current can be due to a concentration gradient of carriers. This current is the diffusion current. It follows from the concept of the movement of gases from regions of higher to that of lower concentrations. The flux of electrons or holes F n,p is proportional to the n or p concentration gradient dn,p dx .

F n,p = -D n,p dn, p dx , (2.1.7)
where D n,p (cm 2 /s) is the diffusion coefficient for electrons or holes. Since the current moves against the direction of the flux for electrons, and in the same direction for the holes, the charge will be -e and +e for electrons and holes respectively. The total diffusion current J di (A/cm 2 ) due to electrons and holes is therefore,

J di = -eF n + eF p . (2.1.8)
The above equation is more clearly expressed as,

J di = eD n dn dx -eD p dp dx .
(2.1.9)

Drift-Diffusion current

The total current density is therefore the sum of the drift and diffusion current.

J n = eµ e nE + eD n dn dx , (2.1.10)
and

J p = eµ h pE -eD p dp dx . (2.1.11)
Total current J can be simply expressed as:

J = J n + J p .
(2.1.12)

Signal formation and preamplification

Signal formation is mediated by the motion of charge carriers in the semiconductor material. A case of a parallel plate detector geometry is used to describe the process with radiation interaction.

Ionisation Energy

When a photon interacts within a slab of semiconductor, sandwiched by two contact electrodes, the deposited energy E dep is used to excite electrons from the valence band into the conduction band; the electron leaves behind a hole. The energy needed to make this electron-hole pair is the ionisation energy i . The quantity of the electronhole pair(n pair ) created is proportional to the quantity of the deposited energy by eqn.

2.1.13,

n pair = E dep i . (2.1.13)

Induced current and charge

Under the influence of an electric field, supplied by a bias voltage, the electrons and holes drift toward the anode and cathode electrodes respectively. During their motion, they induce current until they are totally collected at the electrodes (schematically shown in figure 2.3). The induced instantaneous current of a moving charge is already studied by Shockley in 1938 [START_REF] Shockley | Currents to conductors induced by a moving point charge[END_REF] and Ramo in 1939 [START_REF] Ramo | Currents induced by electron motion[END_REF], expressed in terms of a

weighting field E Q in eqn. 2.1.14.

I = evE Q , (2.1.14)
where the velocity, v = µE, and the field E is related to the bias voltage V b and the distance between parallel electrodes by V b d . The weighting field E Q is not the same as the electric field and it is determined by applying a unit potential to the collection electrode and grounding the others [START_REF] Spieler | Semiconductor detector systems[END_REF]. Thus for a simple geometry detector as being described, E Q = 1 d . The induced current (eqn. 2.1.14) can now be re-expressed as:

I = e V b d 2 (µ e + µ h ). (2.1.15)
Subsequently, the induced charge Q = It tr can be derived from the relation between the charge transit time t tr and the current I depending on the different carriers (electrons e or holes h) and the position x 0 (from the cathode electrode) of the radiation interaction. The transit time t tr h/e , to the respective electrodes will take into account v e/h = µ e/h E, and become:

t tr h = x 0 v h = x 0 d µ h V b , and
t tre = d -x 0 v e = (d -x 0 )d µ e V b .
(2.1.17)

Following, the induced charge Q due to holes becomes,

Q h = eµ h V b d 2 . x 0 d µ h V b = e x 0 d . (2.1.18)
The induced charge due to electrons,

Q e = eµ e V b d 2 . (d -x 0 )d µ e V b = e(1 - x 0 d ). (2.1.19)
The measured charge will vary depending on the integration time used for the measurement. At a longer integration time, the measured charge should correspond to the total charge (Q e + Q h ). But this is not always the case due to the possibilities of traps and other defects.

Charge trapping

Typically, semiconductors suffer from certain imperfections that are introduced during the crystal growth, due to radiation damage or during device fabrication. States in the crystal that can trap charges can be introduced by defects in the form of structural irregularities, vacancies, and impurity atoms.

As the charge moves in the detector, the probability of encountering a trap is proportional to the elapsed time t (the time to traverse a specified distance in the detector by a specified carrier type). Thus charge trapping is characterised by a carrier lifetime τ , which is the time a charge carrier can stay in the crystal before trapping or recombination [START_REF] Spieler | Semiconductor detector systems[END_REF]. Trapping can lead to both a loss of charge or depending on the nature of the trap, externally applied electric field can release the carrier from the trap leading to delayed charge collection. Taking into account the carrier lifetime, the initial total charge Q 0 in the crystal can decay so that as a function of time, the remaining charge is:

Q(t) = Q 0 exp - t τ . (2.1.20)
For a time required to traverse a distance x in the detector by a charge with mobility µ, t = x µE , and equation 2.1.20 can be written as

Q(x) = Q 0 exp - x µEτ ≡ Q 0 exp - x λ , (2.1.21)
where λ(cm) in this case is the mobility-lifetime product(µτ ) multiplied by the electric field E. It defines the mean range of the carriers before they can encounter a trap.

The above equation can now be integrated for different positions x 0 within the full thickness of the detector d, and expressed for contributions concerning holes and electrons in eqn. 2.1.22. This is known as the famous Hecht equation [START_REF] Hecht | Zum mechanismus des lichtelektrischen primärstromes in isolierenden kristallen[END_REF] .

Q s Q 0 = λ e d 1 -exp x 0 -d λ e + λ h d 1 -exp -x 0 λ h , (2.1.22)
where Q s is the induced signal charge (total induced charge), λ e and λ h are the drift length for electrons (µ e τ e E) and holes (µ h τ h E) respectively, and x 0 is the position of charge deposition in the detector.

The quality of the signal depends on the properties of the semiconductor. For example, when considering a low energy photon in the case of gamma detection, a semiconductor detector with a low ionisation energy, is required for sufficient generation of charge carriers. High density materials are necessary for good detection efficiency. Properties such as the mobility of the electron and the hole influence the duration of the current signal. In table 2.1 some properties of selected semiconductor detectors are displayed.

Table 2.1: Some room temperature properties of Si, Ge and principal compound semiconductors [START_REF]Semiconductor materials and radiation detection[END_REF][START_REF] Eberth | From ge (li) detectors to gamma-ray tracking arrays-50 years of gamma spectroscopy with germanium detectors[END_REF].

Material Density (g/cm 3 ) Band gap (eV) i (eV) Resistivity (Ω cm) µτ (e) (cm 2 /V) µτ (h) (cm 2 /V) Si 2.

Signal amplification

In many cases, the signal from the detector is too small to be read directly, preamlifiers are therefore used to magnify them. Two of the well-known type of preamplifiers used in this work: Charge and current (transimpedance) preamplifiers.

• Charge-sensitive preamplifier: The charge accumulated on the detector capacitance C d is integrated on a feedback capacitor C f . The resulting potential on that capacitor is then directly proportional to the original charge on the detector (eqn. 2.1.23). In this configuration, a charge sensitive preamplifier serves as a charge integrator.

V out ∝ Q f C f (2.1.23)
where Q f is the charge integrated on C f , and it is proportional to the charge

Q d accumulated on C d .
In an ideal charge sensitive preamplifier circuit with only a feedback capacitor, the voltage output V out will increase until it reaches maximum where it does not change with time. This is not useful for gamma spectroscopy where several pulses are to be detected. Typically, a feedback resistor R f is added in parallel to the feedback capacitor to reset the amplifier. The pulse therefore decays exponentially with a time constant R f C f . One can express the time variation of the output pulse from an ideal resistive feedback charge sensitive preamplifier by

V out (t) = Q f C f exp -t/(R f C f ) . (2.1.24)
• Current-sensitive preamplifier (transimpedance amplifier): Converts the detector's instantaneous current I in into a measurable voltage V out (see figure 2.5).

Assuming an ideal preamlifier where no current flows into the positive or negative inputs, the current at the node N I is zero from Kirchhoff's Current Law (KCL):

V out = -RI in (2.1.25)
The resistance R, therefore dictates the value of the voltage output, and in this case its value is the gain of the preamplifier. If the gain and the output voltage is known, the detector's current can be deduced. The bandwidth represents the amount of frequencies or the band of frequencies that the amplifier can well amplify. This value is inversely proportional to the gain, and their product is a constant.

Specific semiconductor detectors

Most of the detectors used in this work are related to pn junctions. In this part, we will briefly describe the pn junction diode and PIN diode detectors.

PN junction diode

The n-and p-type semiconductors can be joined together to form a so called pnjunction. To compensate for the imbalance in charge concentration, the electrons in the n-type region of the semiconductor start to diffuse to the p-type region and vice versa. This continues until their Fermi levels coincide. In the process of diffusing, a region of neutrality called a space charge or depletion region is created between both type of the semiconductor. The field due to this space charge takes a direction to impede the flow of electrons and holes. This depletion region is interesting for semiconductor detectors as it is the part that is necessary for radiation interaction to create electron-hole pairs producing currents that can be measured. But it is too small and the generated electric field due to the junction is usually not sufficient to collect the created charge pairs. A reverse bias voltage across the junction is therefore applied to increase the depletion width and also contribute to the fast collection of the electrons and holes.

An electrostatic potential is created across the depletion region when n-and p-type semiconductors are brought together. The width of the depletion is

W = x p + x n = 2 V 0 e 1 N A + 1 N D 1/2 , (2.1.26)
where x p and x n are the depletion depths of the junction on p-and n-sides respectively, N A and N D are the acceptor and donor doping densities, e is the unit charge of electron, is the permitivity of the medium and V 0 is the potential difference. If for example, N D N A , the depletion region is greater on the p side than the n.

Considering the built-in reverse bias voltage V i due to the space charge, the depletion width on one side of the junction becomes:

W ≈ x p = 2 (V 0 + V i ) qN A 1/2 (2.1.27)
The depleted junction is free of mobile charge and thus takes the form a capacitor, bounded by the conducting p-and n-type semiconductor on each side. For a surface area A, the capacitance follows the relation:

C = A W = A qN A 2(V 0 + V i ) 1/2 (2.1.28)

PIN diode

The depletion region created in pn junction diodes is useful for radiation detection but can be too small (less than few µm). Increasing the voltage to augment the depletion region could lead to detector break down when the threshold voltage (breakdown voltage) is exceeded. Moreover, at such small depletion, the capacitance of the detector increases (as seen from eqn.2.1.28) which impedes applications for fast detection and reduces signal to noise ratio.

A method of increasing the depletion width involves introducing an intrinsic layer of a semiconductor material between the p-and n-type semiconductor materials. The emerging structure is a PIN diode. That is, p-type, intrinsic, and n-type semiconductor materials together. The width of the intrinsic semiconductor defines the depletion width. This is described simplistically in figure 2.7. In the electric field profile of the detector in figure 2.7b shows a peak electric field near the p-type region due to the pn junction.

Exploration of CdTe

In this part, we will combine experiments and simulations to study the application of CdTe for gamma spectroscopy of short-lived nuclei in a laser-plasma environment as well as via simulations.

Basics of CdTe semiconductor

For many decades, CdTe has been investigated for room-temperature gamma and X-ray detection [START_REF] Bell | Cadmium telluride, grown from tellurium solution, as a material for nuclear radiation detectors[END_REF][START_REF] Fiederle | Comparison of cdte, cd0. 9zn0. 1te and cdte0. 9se0. 1 crystals: application for γ-and x-ray detectors[END_REF][START_REF] Robert H Redus | Characterization of cdte detectors for quantitative x-ray spectroscopy[END_REF][START_REF] Gnatyuk | Cdte x/γ-ray detectors with different contact materials[END_REF]. The detector is a compound semiconductor that combines relatively high atomic numbers (48 and 52 for Cd and Te respectively). Compared to regular gamma ray detectors such as Silicon (Si) [START_REF] Fiorini | Silicon drift detectors for readout of scintillators in gamma-ray spectroscopy[END_REF] and Germanium (Ge) [START_REF] Uddin | High purity germanium detector in gamma-ray spectrometry: High-purity germanium detector[END_REF],

CdTe thrives on its relatively high density of 5.58 g/cm 3 good to stop X-rays at compact sizes of few mm; high resistivity of 10 9 Ω.cm and sufficient bandgap of 1.5 eV to minimise the influence of dark current, which are prevalent in low bandgap semiconductors. All of these qualities make it an option worth considering for gamma spectroscopy studies.

Description of bought CdTe crystal and associated electronics

Two CdTe detectors were bought from Eurorad (France) who is currently one of the leading producers of CdTe alongside the likes of Acrorad (Japan). The semiconductor crystals were grown by the travelling heater method (THM) from tellurium solution, under tellurium vapors [START_REF] Jeffrey H Peterson | Analysis of the traveling heater method for the growth of cadmium telluride[END_REF][START_REF] Shiraki | Improvement of the productivity in the thm growth of cdte single crystal as nuclear radiation detector[END_REF]. Moreover, the semiconductor is p-doped, and owing to its lower mobility of holes compared to electrons leads to increased detector resistance.

The detector has a specified resistivity of more than 10 9 Ωcm, which is helpful to minimise dark current occurrences and device noise [START_REF] Biswas | What causes high resistivity in cdte[END_REF]. Their areal dimension is 4.83 × 4.83 mm, with a thickness of 2 mm between both electrodes, and runs on a positive bias voltage of 70 V. The contact electrodes are Pt materials of few Angstrom in ohmic contact with both sides of the crystal. The significance of the ohmic contact is that current can be conducted in both directions of the metal-semiconductor contact.

It allows to deliver a linear and symmetric current-voltage relationship for positive and negative voltage [START_REF] Lisa | A critical review of ohmic and rectifying contacts for silicon carbide[END_REF]. This is the contrary when considering a Schottky barrier contact where the metal-semiconductor contact is constrained such that the device current flow is in one direction, following its rectifying character [START_REF] Raymond | Recent advances in schottky barrier concepts[END_REF]. Typically, Ohmic detectors can operate at ten times lesser bias voltage than Schottky ones, and for CdTe detectors, they have been studied to show relatively better signal stability over several hours of use [START_REF] Funaki | Development of cdte detectors in acrorad[END_REF].

Our CdTe detectors are designed such that the cathode side is the part exposed to radiation. This is because CdTe in general has very poor hole collection time compared to electrons [START_REF] Glenn | Radiation detection and measurement[END_REF] as dictated by their low mobility (table 2.2). If the most part of the radiation interaction take place near the cathode it makes it possible for the holes to take advantage of the short distance travel to this electrode. From figure 2.9, on the left is a sample of the CdTe with three pins indicating, the anode, cathode and ground; the right image reveals that the irradiation takes place from the cathode face of the detector. The charge amplifier has a gain of 6.6 V/pC, while the current preamplifier runs on a gain of 50 kV/A (and a bandwidth of 100MHz). For the sake of this work, we shall

Response to 122 keV gamma

To test the detectors, we tried to observe the spectrum of a 57 Co radioactive source using CdTe-C. 57 Co decays by electron capture into 57 The obtained spectrum shown in figure 2.12 is from CdTe-C. The first prominent peak at 3.7 mV is 14.4 keV, 13.5 mV corresponds to the 122 keV peak, while 136 keV is piled up near 14.7 mV. The peak at 90 keV (10.75 mV) is mainly due to the escape of the characteristic Cd and Te X-rays when photons with energies just above their K-edges (26.7 and 31.8 keV for Cd and Te respectively) interact by photoelectric process causing a reduction in the measured energy [START_REF] Redus | Cdte measurement of x-ray tube spectra: escape events[END_REF][START_REF] Robert H Redus | Characterization of cdte detectors for quantitative x-ray spectroscopy[END_REF]. In red is a Gaussian fit on the 122 keV peak, whose estimated resolution is 9 %. We have also illustrated by a Geant4 (GEometry ANd Tracking) [START_REF] Agostinelli | Geant4-a simulation toolkit[END_REF] simulation of 57 Co source on the CdTe, to show that the energy spectrum is as expected from the detector (see figure 2.13) and to understand the different peaks from the experimental result. Here we see the 14.4 and 122 keV lines clearly but due to the resolution, the 136 keV line is partially piled up near the 122 keV peak. The X-ray escape peak contributions are also marked out. So we can conclude that the assembled detector is in good condition for gamma spectroscopy.

Charge trapping

One can observe a low-energy tail contribution to the 122 keV photon peak in figure 2.12. This is a well understood phenomenon known as charge trapping (or hole tailing) in CdTe detectors (and many compound semiconductor detectors) and has been studied by several authors [START_REF] Abbene | 8.18 -cdte detectors[END_REF][START_REF] Iwańczyk | The effect of charge trapping on the spectrometric performance of n-type cdte surface-barrier detectors[END_REF][START_REF] Szeles | Cdznte and cdte materials for x-ray and gamma ray radiation detector applications[END_REF][START_REF] Redus | Charge trapping in xr-100t-cdte cadmium telluride detectors application note[END_REF]. Traps originate from chemical impurities and or crystal imperfections. Charge trapping affects the charge collection efficiency (CCE) in different regions of the detector. The charge collection efficiency is easily computed as the ratio between the total charge induced and the initial total charge. It is concisely expressed by the famous Hecht relation in eqn. 2.1.22. This is modelled for a constant electric field E to depend on the carrier mean free path length λ e/h = (µτ ) e/h E, which is the average distance that an excited carrier will travel before they encounter a trap or recombine.

To reduce the effect of charge trapping, the concerned detectors are normally configured such that λ e/h is greater than the detector distance d. In other words, that the lifetimes of holes(h) and electrons(e) are comparable or greater than their transit times t r e/h [START_REF] Szeles | Cdznte and cdte materials for x-ray and gamma ray radiation detector applications[END_REF]. For our detector, following the table 2.1, a bias of 70 V, and a detector thickness of 0.2 cm, λ e is ∼ 1 cm , while λ h is about 0.09 cm. So, the holes will suffer from more trapping effects before drifting through a 0.2 cm distance in the CdTe detector. In figure 2.14, we demonstrate the role of hole tailing by computing the fraction of collected charge for our CdTe detector using eqn. 2.1.22. This is estimated at the different depths of photon interaction from the cathode (at position x 0 = 0 µm) to anode (at position x 0 = 2000 µm) taking into account the mean carrier path length for holes and electrons respectively. One can observe that charge trapping increases with increasing distance of interaction from the cathode as reflected by the CCE.

Signal duration

The signal duration is very important for our quest. We normally would like a duration of some ns if we want to study the de-excitation of 9 ns state of 84m Rb nuclei in plasma. The current duration depends on where in the semiconductor the interaction takes place. Eqn. 2.1.17 shows a relationship between the rise time of the signal and the position of photon interaction away from the cathode. Considering that the holes are slower than the electrons in the detector, one can estimate the position of interaction by considering the drift time of the holes following eqn. 2.1.17, expressed in eqn 2.2.1,

x 0 = µ h t tr E = µ h t tr V d , (2.2.1)
where t tr is the transit time in seconds, µ h (cm 2 /V.s) is the mobility of holes, x 0 (cm) is the depth of interaction away from the cathode, and E (V/cm) is the electric field provided by the detector bias voltage V through a thickness d. For a hole mobility of 80 cm 2 /V.s, hole transition times of 1.2 and 4.2 µs (see figure 2.16a and c) and bias voltage 70 V, the depth of photon interaction is estimated at 336 and 1120 µm respectively. By taking one of the signals for a 122 keV gamma from the charge preamplifier (4.2 µs duration), and dividing by the preamplifier gain we obtain the charge in figure 2.17 (upper). Carrying out a low pass filter and performing a numerical derivation via scipy in python programming language [START_REF] Virtanen | SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python[END_REF], we are able to extract the current signal and obtain more information as revealed in red on figure 2.17. In the figure (in red), the amplitude of the current signal is about 3 nA, with a 4.2 µs duration. The electron-dominant part of the signal is in the first 0.7 µs, while the holes currents are more dominant after, until 4.2 µs.

For the purpose of comparison, we can calculate the current amplitude for a 122

keV photon energy deposition in the detector's thickness, d (0.2 cm), following Ramo's theorem, modified from eqn.2.1.15 and 2.1.13 as,

I = E dep i .e. V b d 2 µ e + µ h , (2.2.2)
where E dep is the energy deposited (122 keV), i is the ionisation energy (4.43 eV for CdTe), V b is the bias voltage on the detector (70 V), and e is the elementary charge, while mobility µ e and µ h were 1050 and 80 cm 2 /V s respectively [START_REF] Burmeister | On the preparation of cdte junction detectors for nuclear radiation spectrometry[END_REF]. The obtained current following this calculation is 9 nA, which is within the same order of magnitude with the derived current in figure 2.17.

In a similar test on CdTe-T no detected photons were observed due to the low induced current. More about this will be explained later in this section 2.2.3. For now, in the next phase of this work, we will explore charge carrier transport simulations as a means to better understand the processes taking place in the CdTe detector for a single photon, and the detector's response to a high radiation background such as a X-ray flash. In the simulation we will be able to verify the form and amplitude of the experimentally obtained signal.

Modelling electrical properties of CdTe

To verify some of the experimental results, and also to model other possible responses of X-ray or gamma interactions on the CdTe, we have considered Technology In this part the simulation will take two directions: the first would be to simulate the detector response to a 122 keV gamma, while the second is its response to a flash of X-rays from laser interactions (summarised information about Silvaco concerning this simulation can be found in the Appendix A 4.3)

CdTe Simulation

The main properties of the CdTe fed into the Silvaco simulation are summarised in the table below: In silvaco simulation, the first thing to setup is the geometry of the device to be simulated. This starts with defining the mesh of the device. Meshing in TCAD simulation is very important because if detector is poorly meshed, the result can be erroneous or the simulation may not even converge. In general, the finer the mesh, the better the simulation. However, depending on the size of the device, one may not be able to give fine meshes to all regions due to the cost in run-time and the limitations in the number of meshes possible in silvaco. An approximate method suggested in silvaco is to use fine meshes in regions where there will be higher density of carriers.

For example, in figure 2.18 (3D), also in figure 2.19 (2D), is the CdTe structure being designed, with a coarse mesh dimension of 50 µm and the finely meshed regions are between 0.5 and 2 µm. The meshes were refined until very minimal differences (less than 10 % difference) in the output of the simulated current were observed for different mesh adjustments.

Resistivity

The bought detector is slightly p-doped in ppm. For a CdTe atomic density of 10 22 atoms/cm 3 , this corresponds to an acceptor concentration of 10

Simulation of 122 keV photon events

To observe and study the behaviour of the current signal of a 122 keV gamma. Figure • Near the anode After charge creation by a 122 keV gamma near the anode (see figure 2.22), the electrons quickly drift to the anode electrode because of their relatively short distance from it. This speed, taking advantage of their high mobility, causes a sharp rise in the current. On the other hand, the holes, disadvantaged by their low mobility, will take a longer time drifting to the cathode electrode. In the process, they contribute a relatively low drift current and take a longer time to be collected at the cathode.

The duration of the overall signal is 6 µs, due to the long distance travelled by the holes for a mobility that is 10 times lesser than that of electrons. The fit function and parameters are then used as input in the silvaco simulation to generate the electron-hole pairs that correspond to the energy deposited in the different depths of the CdTe crystal. the electrons deliver a current density profile that is 10 times higher than the holes, which is in coherence with a mobility that is 10 times more than the holes. In the next part of this work, we shall explore experimental data from a laser interaction in which our CdTe detector is present to absorb X-rays. It will permit us to compare the experimental signal response from the CdTe to the simulated in that condition.

Edep(z) = A * exp{-b * z}, (2.2

Response to X-ray flash at CELIA

The experimental campaign at CELIA (CEntre Lasers Intenses et Applications) was aimed at studying the response of the CdTe detectors to flashes of low energy X-rays after a laser shot interacting on a solid target. This could provide relevant insights about the duration of the X-ray flash and the most probable time of observing the first gamma rays if performing a gamma spectroscopy of short-lived nuclei at about the same time. The experimental set-up and materials are briefly described in the following:

• Laser system: CELIA Ti:Saphire laser system operating at a 1 Hz repetition rate The result of the CdTe-C is an already saturated signal at -4V. There is first a fast rise in the charge collection, then an abrupt cut. The saturation is due to the charge preamplifier connected to the CdTe. The amplifier recovery time from the X flash is more than 1 ms. This configuration is therefore not suitable in a high power laser environment

X-ray flash from CdTe-T

Since we experienced a saturation using a charge preamplifier, we tried with a current preamplifier. Figure 2.33 is the current response of the CdTe detector coupled to a current amplifier after the arrival of a flash of X-rays from the interaction of a high-power laser. With a bias of 70V, the intensity of the signal is around 50 µA and the observable current duration is 1.75 µs. By integrating the current signal, the total charge created is some 21 pC, which corresponds to about 581 MeV of deposited energy. An interesting observation is related to the minimum observable current, which is in this case 1 µA. If we consider a drift time of 1µs, this corresponds to a charge of 1 pico Coulomb(C). It further goes to show the limitation of the chosen preamplifier for gamma detection within the energy domains of some hundreds of keV.

For example, it will be impossible to observe a current signal from a 200 keV gamma because the total charge that would be created in the CdTe detector is approximately 7 fC. For a drift time of 1 µs, this corresponds to 7 nA, and 3.5×10 -4 V (from our preamplifier gain of 50kV/A HCA-100M-50K-C from Femto company), which is too few to be seen on the scope for a gamma spectroscopy study with this current preamplifier.

Simulation of X-rays flash with gammas of interest

We have verified that our simulation is able to produce the X-ray signal from experiment. It is interesting to know if we can detect gammas just after the arrival of the X-ray flash. We will consider the X-ray energy deposition in the detector in figure 2.25, because it is obtained from the X-ray distribution after a high power laser interaction. The expected signal of the current has been simulated in figure 2.26 delivering a current amplitude of 10 -3 A and a duration of 14 µs. This phase of the simulation will now incorporate the instantaneous arrival of a huge bunch of X-rays and few gammas coming after the laser short in the CdTe, and to determine if the detector will be able to detect the earliest gammas if they come at different times. In figure Mean while, the gamma signal at 5 µs could be observed but with a deformation in the signal shape as presented in figure 2.47 because processes of recombination and electric field perturbation in the detector are enhanced as few of electrons and most of the holes created by the X flash are still being collected at this time which meets the arrival of the gamma. The gamma pulses arriving after could be detected without clear deformations in the signal form. The deformed signal is at almost twice the initial amplitude. In all, for gamma pulses built on top of the X-ray signal, offline analysis (more details in ch 4) will be required to extract their information from this relatively long exponential pulse. From figure 2.47, perturbation around 10 ns is due to the variation in the electric field at the instance of charge creation by the arriving gamma.

Figure 2.47: Result from subtracting the simulated flash X signal in the CdTe from the signal due to the simulated flash x and gammas.

Discussion and conclusion

The capability of CdTe detector to perform gamma spectroscopy of short-lived nuclei (few tens of µs) after a laser shot has been studied experimentally and by simulation with Silvaco. In experiments with high power lasers, the environment of detection is one perturbed with huge quantities of X-rays arriving at similar times as the gamma photons after a laser shot. A key parameter to therefore take into account is the duration of the current signal from the gamma and from the X-rays. Two CdTe detectors; one coupled to a charge sensitive preamplifier (CdTe-C) and the other to a transimpedance amplifier (CdTe-T) have been subjected to similar X-ray backgrounds after a laser shot. CdTe-C was completely saturated and enduring more than 1 ms, on the other hand CdTe-T experienced no saturation and lasted for about 1 µs for a voltage bias of 70V. To understand the obtained result, a Silvaco charge transport simulation was performed taking into account the depth profile of the deposited photon energies in the CdTe by . The result was fed into the charge transport simulator to see the resulting current signal, which showed an agreement with that emerging from the CdTe-T experimentally. We also saw from simulation that the tail contribution to the current is still due to the holes despite charge creation near the cathode. We have also studied the possibility to detect a gamma after the arrival of an X-ray flash on the CdTe. It was observed that gamma spectroscopy using a CdTe detector can only start after about 5 µs (via offline analysis) if we consider an X-ray flash energy deposition of about 10 GeV in the CdTe.

On the ability of both detector configurations to survive in a large background of X-rays after a laser shot, CdTe-T outperforms CdTe-C which is totally saturated at the same laser-produced background. Clearly, from an experimental perspective, CdTe coupled to a transimpedence amplifier passes for a good X-ray flash detector but the main problem is that a 122 keV gamma photon could not be observed as it could not distinguish a photon signal with amplitude less than 1 µA (a total energy deposition of about 20 MeV ) from the noise. From simulation, a few hundred keV gamma in CdTe can cause a current less than 1 ×10 -7 A. On the other hand, CdTe coupled to a charge sensitive preamplifier does well to detect few hundreds of keV but it peaks after the complete integration of induced charges which can last for more than 6 µs depending on the position of interaction. This long signal duration means a minimum of 6 µs spacing between arriving gammas is necessary against pile up effects on a signal rise time. In addition, the preamplifier used in this case contributes a signal fall time of nearly 200 µs.

The long time of the emerging signals shows that CdTe cannot satisfy applications in gamma spectroscopy for a 9 ns half life being considered in this work. It however,

shows that CdTe (coupled to transimpedance amplifier) can be used for online X-ray characterisation for each laser shot as shown in this work. Considering their good detection efficiency, very minimal thicknesses compared to Silicon will be required to detect the same energy and intensity of photons.

Experiment with APD

Avalanche Photo Diode (APD) detectors were studied for their application to detect nuclear level decays of low energy in a laser-plasma. The APDs we have used are semiconductors made of silicon, this is interesting in the perspective of obtaining fast signals for the detection of short lifetimes. One of the main advantages of silicon detector is the relatively high mobility of its charge carriers. The electrons have a mobility of 1350 cm 2 /(V.s) while the holes are approximately 500 cm 2 /(V.s) [START_REF] Ludwig | Drift and conductivity mobility in silicon[END_REF],

resulting in a fast signal that can be very useful against pileups during gamma spectroscopy with high activity. Unlike CdTe, for example, they do not suffer from a long current signal tail from poor hole mobility. In addition they posses relatively high carrier lifetime-mobility products typically > 10 -1 cm 2 /V reflecting good charge collection efficiency at relatively minimal voltage bias.

The detector response to an X-ray flash from a laser-plasma interaction will be measured and discussed in the following. As in the CdTe case, the signal duration and amplitude of the detected X-ray flash are important ingredients that can be used to determine how quickly the detection of a 6.2 keV gamma is possible after a laser shot.

Description and basic principle

Avalanche Photodiode (APD) exploits the process of impact ionization, in which the primarily created electrons in the detector material create more free electrons by imparting energy to atomic sites along their path under the influence of a high electric field. The gain of an APD can reach 10 8 but standard APDs are mostly operated between the gains of 10 and 1000 [START_REF] Syed Naeem | Physics and engineering of radiation detection[END_REF]. Due to its interesting features of internalmultiplication, high-quantum efficiency [START_REF] Mcclish | A reexamination of silicon avalanche photodiode gain and quantum efficiency[END_REF] and fast timing [START_REF] Kishimoto | A fast detector using stacked avalanche photodiodes for x-ray diffraction experiments with synchrotron radiation[END_REF][START_REF] Sola | Ultra-fast silicon detectors for 4d tracking[END_REF], APDs are very attractive for detecting low energy photons [START_REF] Ochi | Study of a large area avalanche photodiode as a fast photon and a soft x-ray detector[END_REF][START_REF] Baron | Time resolved detection of x-rays using large area avalanche photodiodes[END_REF]. An APD structure can be built by simply adding a p-doped layer to a regular p + -i-n + photodiode as shown in figure 2.48. When an incident photon is absorbed in the i-layer electron-hole pairs are created, and under the relatively low field in this region, the free carriers (in this case electrons) enter into the high electric field part called the avalanche region, where they experience a high velocity. They therefore accumulate sufficient energy to cause impact ionisation leading to the multiplication of free charge carriers as depicted in the figure 2.48. There are three types of APDs: Reach-through, Reverse-type and Beveled-edge.

The detector described above in figure 2.48 is a reach-through APD detector. The multiplication region is at one end of the detector such that the photon beam entrance is from the opposite end. Thus permitting the detection in a wide absorption region (∼ 100 µm). The advantage of such a reach-through structure is that only relatively low voltages (typically less than 500 V) are required to fully deplete the devices.

They are thus designed to permit efficient detection of low energy X-rays and have been studied by several authors for this purpose [START_REF] Kishimoto | A fast detector using stacked avalanche photodiodes for x-ray diffraction experiments with synchrotron radiation[END_REF][START_REF] Yatsu | Study of avalanche photodiodes for soft Bibliography x-ray detection below 20 kev[END_REF][START_REF] Ikagawa | Performance of large-area avalanche photodiode for low-energy x-rays and γ-rays scintillation detection[END_REF]. The reverse-type (see figure 2.49) is as the name implies; the narrow high field multiplication region has been moved to the photon entrance end typically 5 µm from the surface of the device. They are well adapted to be coupled with scintillators since typical scintillator emissions are less than 500 nm in wavelength and can be quickly absorbed within 3 µm before reaching the region of multiplication. They however cannot deliver efficient X-ray detection [START_REF] Yatsu | Study of avalanche photodiodes for soft Bibliography x-ray detection below 20 kev[END_REF]. In the case of the beveled-edge (see figure 2.49), this type of APD is a traditional p + n junction designed to require a very high breakdown voltage (typically 2 kV) [START_REF] Kataoka | Recent progress of avalanche photodiodes in high-resolution x-rays and γ-rays detection[END_REF]. They therefore have advantages of delivering a high gain and a low excess noise factor due to the broad multiplication region [START_REF] Yatsu | Study of avalanche photodiodes for soft Bibliography x-ray detection below 20 kev[END_REF]. Depending on the interaction position gain variations exist leading to corresponding variation in signal height [START_REF] Yatsu | Study of avalanche photodiodes for soft Bibliography x-ray detection below 20 kev[END_REF]. In this work, we are using two APD detectors (reach-through) bought from Hamamatsu company; their parameters are similar and have been summarised in the table 2.3.

Calibration and noise reduction

We started with APD31 because from the table 2.3, it is slightly better than APD30 from the perspective of the dark current contribution. To calibrate the APD31, we used a radioactive source of 55 Fe, which emits K α and K β X-rays of 5.9 and 6.4

keV respectively after electron capture to Mn-55 [START_REF] Cea | Table de radionucléides: Fe-55[END_REF]. These energies are similar to the 6.238 keV gamma photon anticipated from the decay of the first excited I π = 9/2 -isomeric state of 181 Ta in a high density plasma. The APD was connected to a transimpedance amplifier with a gain of 50 kV/A and a bandwidth of 100 MHz (see figure 2.50), and a voltage bias of -500 V was supplied to it. The signal line was connected to a 12 bit, 1 GHz bandwidth tektronix oscilloscope. The resulting signal of a 5.9 keV gamma is presented in figure 2.51, showing a duration of 4 ns FWHM.

This short duration of the signal is suitable for the 181 Ta studies. % following a 49 mV FWHM, which corresponds to 1.41 keV. The relatively large FWHM explains why the kα and kβ lines associated with the 55 Fe decay could not be distinguished. The poor resolution is attributed to the influence of dark currents on the actual signal of interest as well as noise contributions from the deployed preamplifier [START_REF] Ikagawa | Performance of large-area avalanche photodiode for low-energy x-rays and γ-rays scintillation detection[END_REF][START_REF] Kataoka | Recent progress of avalanche photodiodes in high-resolution x-rays and γ-rays detection[END_REF] due to its high gain ( 50 kV/A). In an attempt to improve the resolution of the APD, the detector was put in a climatic chamber, with the 55 Fe source, the temperature was varied from 25 to 1 • C.

We observed a reduction in the breakdown voltage as we lowered the temperature.

We therefore set our bias voltage below the breakdown voltage following the provided temperature coefficient of 3.5 V / 0 C from the data sheet (table2.3). The result of this test is shown in figure 2.53 with no significant improvement in resolution was observed at 1 • C. To allow for a better calibration with two known photon energies, we employed a 57 Co source. This source can give off K α and K β X-rays of 6.39 and 6.4 keV, and 7.05 and 7.01 keV respectively after electron capture to 57 Fe [START_REF] Cea | Table de radionucléides: Co-57[END_REF]. It also emits and 14.4, 122, and 136 keV gammas respectively [START_REF] Cea | Table de radionucléides: Co-57[END_REF]. The intensity of photons per 100 disintegration is 17.12 and 33.3 for the 6.39 and 6.4 keV X-rays, and 6.93 for the K β X-rays. While the intensities are 9.18, 85.9 and 10.7 for 14.4, 122, and 136 keV gammas respectively. Considering the detector resolution established above, the detector will be incapable of distinguishing the different photon energies; one will expect to observe a peak mostly around 6.4 keV. Moreover, the detection efficiency is largely dependent on the detector thickness. For a 145 µm thick silicon material, the efficiency of detection is 96 and 33 % for the considered x-and gamma ray energies respectively (see figure 2.54), therefore, the X-ray peak will have a more prominent intensity. We performed a calibration in this configuration putting the source on the APD31.

The result is presented in figure 2.59. We are able to reproduce the spectrum of the 57 Co source using this configuration. However, we noticed a reduction in amplitude , also for 55

CELIA X-ray flash signal from APD(s)

The detectors were tested in a laser-plasma environment, with a laser intensity of about 4.75 ×10 16 W/cm 2 at 1 Hz. The laser-pulse duration was 1ps, and energy of about 195 mJ with a beam focus of 12 µm (see section 2.2 for more details). The deployed targets were Mo and Ta having 25 and 70 µm thicknesses respectively. In all tests conditions, the detectors were wrapped in a 13 µm aluminium sheet to shield from external light emanating from the laser interaction.

Response from One APD

As a first attempt, one APD was placed in the chamber, about 30 cm from the target chamber centre (TCC), to be able to observe its signal response to a flash of X-rays after the laser shot. A sample of the APD detector is presented in figure 2.61 with the different cable connectors, while figure 2.62 shows the electronic circuit of the APD used. Furthermore, during this shot, we developed the detector to accommodate an LED light source (UV). The LED trigger was then synchronised with the instance of the laser beam delivery so that a few µs before each shot, a burst of 1 MHz LED pulses are released into the APD, spanning the full duration of the acquisition. We can see that the signal duration can last more than 40 µs, and the diode pulses are easily obvious beyond 20 µs. This implies that one-APD configuration will only be useful for gamma detection 40 µs after the laser shot, which is about 7 periods for the 6 µs first excited nuclear state of 181 Ta.

Response from two APDs

The one-APD test above revealed that the X-ray signal duration can be about 40 µs (see figure 2.64). This is limiting for short-lived nuclei studies. The circuit illustrating the connection between both APDs via the transformer to deliver an attenuated signal by subtraction is presented in figure 2.65. 90V from a single APD. We can also see from the raw oscillogram, the repetitive LED pulses. The zoomed view in figure 2.66b permits us to observe all the injected LED pulses starting from zero to 2 µs. The pulse before 0.25 µs is unaffected because it arrived earlier than the X-ray burst. After the X-ray burst, the first observed pulse was shot is at 1.1 µs. This is a large reduction from 40 µs in the single APD case to 1 µs in our developed configuration, 40 times better. The signal perturbations observed in-between zero and 1.5 µs are due to imperfect signal subtractions via the transformer device.

To see clearly the LED pulse it was set to achieve an amplitude of 5 mV. A 6 keV gamma pulse from this detector configuration is 180 mV when connected to a 50kV/A gain transimpedance preamplifier. Without this amplifier, the signal will correspond to 180 µV on a 50 Ω connector. This cannot be observed on the oscilloscope due to the electronic noise. It will therefore be necessary to perform this test with a preamplifier and maybe by setting the LED to deliver a 180 mV signal from the detector during an X-ray flash exposure. This way we can have a better representation of the detection of a 6 keV in an X-ray flash background.

Summary and perspective

Two APD detectors were bought for application to detect the gamma emissions from the de-excitation of the first excited state in 181 Ta in a laser-plasma with a short half-life of 6.05 µs. Calibration tests have been performed for one APD, and for a two-APDs configuration, which we developed in this work. The result of these calibrations are satisfactory for the purpose of our detector. In all conditions, the APDs were connected to a transimpedance amplifier to be able to observe a 6 keV gamma signal and to perform a gamma spectroscopy.

We also studied our APDs in an X-ray environment. After exposure to X-ray flash from laser interaction, the single APD produced an X-ray signal that lasted for 40 µs with a 90V amplitude, corresponding to 1.8 A over a 50 Ω. Such high current will destroy the amplifier. Moreover, the long duration presents a relatively large detection dead-time, and it is certainly too much for a simple detection of a 6.2

keV photon with a half life of 6.05 µs. With our developed detectors combining two APDs via an RF transformer, we succeeded to reduce this dead time from 40 to 1 µs.

Also, the amplitude went as low as 30 mV (600 µA). This is a very interesting result that presents great prospects for applications to study short-lived nuclei in such high radiation background environment.

It must be noted that during the tests with X-rays, the detectors were not con-nected to a preamplifier due to lack of beam-time to explore that option. In the future, it will be interesting to perform this test again using the transimpedance preamplifier.

Online proton detection

For the purpose of fundamental nuclear physics applications, laser-driven ion beams can be used to create short-lived nuclei to be studied in plasma (see chapter 1). The advantage of such beams lies in their short duration and corresponding high intensity when compared to what conventional accelerator systems can deliver. Several detectors exist for ions(mostly protons and alpha particles) detection in a laser environment, some of them are Radiochromic Films (RCFs), activation samples, and imaging plates (IPs). All of these are passive detectors, and cannot be used in highrepetition-rate laser systems due to the limitation that they need to be replaced after a laser shot and the experimental conditions re-set for the next shot. This can take a relatively long time from a few minutes to tens of minutes. Laser-ion beams delivered at a high repetition rate, thus require fast detection and characterisation to be performed online.

In this section, we shall study a silicon-based CMOS detector for online detection of laser-accelerated protons.

Principles of CMOS detectors

CMOS is essentially made up of N and P channel semiconductor devices known as transistors. The N and P channels are called NMOS and PMOS respectively, more explicitly meaning N and P channel MOSFETs (metallic oxide semiconductor fieldeffect transistors). The combination of both gave rise to the name, complementary MOSFET (called CMOS). The CMOS is simply an array of photodiode pixels that have an independent capacitor and amplifier assigned to each pixel, also known as active pixel sensors (APS), as illustrated in figure 2.67 [START_REF] Ay | Cmos active pixel sensor (aps) imager for scientific applications[END_REF].

When ionizing radiation comes in contact with a CMOS pixel, electron-hole pairs are produced depending on the total deposited energy and the ionisation energy of the semiconductor material (3.6 eV for silicon). As the CMOS detector has an independent amplifier in each pixel, the charges are collected, stored in a pixel-assigned capacitor, and converted to a voltage signal through its amplifier, as schematically illustrated in figure 2.67. All of these processes are independently performed for each pixel and finally converted to a digital output signal, called a digital number(DN). A look-alike of a CMOS detector is a charge-coupled detector (CCD). They are made up of an array of passive photodiodes; but created charges are transferred from pixel to pixel until they reach a shared amplifier where they are converted to voltage [START_REF] Hoffman | Cmos detector technology[END_REF]. Some of the main advantages of CMOS detectors over CCDs are lower power consumption, lower cost, high speed imaging etc. [START_REF] Bigas | Review of cmos image sensors[END_REF]. In addition, blooming is one one of the problems common to cameras, where there is vertical streaking/smearing due to excess charge spilling over into a vertical transfer register from a given pixel [130]. Because CMOS sensors convert the charges to voltage directly in each pixel before the read-out, they are inherently more immune to blooming [START_REF] Hillebrand | High speed camera system using a cmos image sensor[END_REF]. On the other hand, due to their active pixels, they contribute some noise during the reading process, which can lead to reduced signal to noise ratio [START_REF] Schildknecht | Improved space object observation techniques using cmos detectors[END_REF]133].

Apart from photon detection for which most CMOS detectors are fabricated to perform [START_REF] Farrier | Very large area cmos active-pixel sensor for digital radiography[END_REF][START_REF] Bai | Teledyne imaging sensors: silicon cmos imaging technologies for x-ray, uv, visible, and near infrared[END_REF], they can be used for charged particle detection [START_REF] Howard S Matis | Charged particle detection using a cmos active pixel sensor[END_REF][START_REF] Reinhardt | Test of pixel detectors for laser-driven accelerated particle beams[END_REF][START_REF] Reinhardt | Detection of laser-accelerated protons[END_REF]. In this work, we shall be studying a commercial CMOS detector originally built for photon detection purposes, for their adaptability to detect protons in a laser environment.

RadEye detector

The CMOS detector bought from Teledyne company is a remote RadEye HR X-ray detector The sensor is enclosed in a stainless steel with a carbon-fiber window to shield it against ambient light, and a black cable with a USB end that allows direct connection to a computer.

The CMOS detector is normally ready for acquisition within a time-window called the exposure time, during which all charges in the photodiodes are collected. This time is set by the user in the period of detection. The detector can be triggered by clicking from the computer user interface of the ShadoCam, in this case, the detector is in 'mode 0'. In another way, in 'mode 2', the detector is triggered automatically in the presence of a continuous light source. But for our purpose, we used an LED light source to trigger the detector to capture our desired image. After an image capture, each pixel delivers a value of grayscale level between 0 and 4095 (for a 12 bit digitisation) which is related to the amount of charges created within them.

As already stated, the detector was originally designed for X-ray measurement purposes, but we want to see if it can be adapted for use in charged particle detection.

Series of tests, and performed calibration will be discussed.

CMOS Tests

Exposure time test

One of the important control parameters of the CMOS detector is the exposure time.

It is an input parameter that determines how long the detector is time-exposed for acquisition. We therefore performed a test to verify that any set exposure time is the real one. To understand this, the detector was put in 'mode 2' and we used two LED pulses: one to trigger the detector, and the other to be captured. For each set exposure time, the second pulse was varied in time-width at constant amplitude until the set width exceeds the set exposure time. In this case, the width of the pulse corresponds to the irradiation time. If the width surpasses the exposure time, ideally, the mean gray value, which is the total gray value from a region of interest on the CMOS detector normalised by the total pixel number in that region, should be constant (see figure 2.69 for the setup of the LED pulse combinations). In the course of the test we realised that a minimum of 3 ms was required between the trigger light pulse and the image of interest. The real exposure time is therefore the set exposure time with a 921 ms increase. Given a gain of 155 e -/ADU , this corresponds to 64 keV of energy per pixel, which is huge and impossible to be caused by thermal processes (700 million kelvin). However, we will cool down the detector to see how it improves.

Temperature

In an attempt to improve the background condition of the detector, it was placed in a climatic chamber with no humidity. The chamber permitted us to regulate The 115 Gray value is therefore not due to dark currents in the detector but probably some contributions from the associated electronics in the reading of the detector. We can also notice that the recommended condition of use specified in the data sheet is from 0 to 50 o C (see table 2.4), which is the temperature range that ms before the beam on the detector. In the second part of the calibration, the Gd 2 O 2 S scintillator was placed in front of the sensitive CMOS surface (see figure 2.80), with detector operated in 'mode 0'. The set exposure time on the detector was slightly more than 1000 ms to enable easy synchronization between clicking on the computer to trigger the detector for aquisition and the arrival of the beam within the set time.

This value was also carefully chosen from being too high to avoid long accumulation of thermally stimulated charges in the detector. Moreover, to minimise background contributions from within the chamber, the detector was wrapped with a very light piece of aluminium foil (13 µm) to block external light from reaching the CMOS while the protons are able to pass through. and the areas that are proton-irradiated have been shown in zoom. The irradiation goes from right to left from pixel to pixel, moving downwards (s-shape) until the total target pixels are achieved. The duration of the beam in one pixel is the irradiation time t irr , and δ t is the time to move between two pixels (as low as 15 µs [START_REF] Barberet | First results obtained using the cenbg nanobeam line: Performances and applications[END_REF]). When these times are multiplied by the total number of pixels irradiated p irr , the total time should in reality be less than or equal to the real exposure time t exp of the detector, that is:

p irr (t irr + δ t ) ≤ t exp .
But we can see that 50 ms of exposure time and for a 3 ms irradiation time, should deliver only 16 irradiated pixels, but we observed 197 pixels. thus emphasising a mismatch between the set exposure time and the real one, which has been studied in figure 2.70. The response of the detector is not perfect during the proton irradiation (see figure 2.76). We have observed cases of charge sharing between pixels. This is a general challenge common to pixel detectors known as crosstalks [START_REF] Brouk | Characterization of crosstalk between cmos photodiodes[END_REF]. Considering that two consecutive irradiated points were spaced by 8 pixels, also that the pixel pitch is 20 µm and the beam focus at 1 µm, this manifestation of crosstalk could be due to the tails of the impinging beam's spread. It could also be due to low impedance of the CMOS detector allowing charges to easily spill to neighbouring pixels. The thickness of the detector is a very important quantity and it remains unknown.

Going by a Geant4 simulation, one will require about 90 µm of silicon to stop a 3 MeV proton beam. But the detector is not that thick, so if we assume a 2 µm thickness as in [START_REF] Reinhardt | Detection of laser-accelerated protons[END_REF], a 3 MeV proton will deposit 40 keV. About 0.44 µm of silicon is needed to deposit 8.7 keV of the proton energy. It is therefore highly possible that very little of the initial proton energy is deposited in the detector possibly owing to its small thickness.

CMOS with scintillator

The same test was performed but with a scintillator placed in front of the detector as shown in figure 2.80. Notice that the scintillator screen is facing the beam and not in direct contact with the photodiode array of the detector.

Summary and conclusion

Online particle detectors are imperative for experiments with high-power lasers at high repetition rates. A CMOS detector bought from Teledyne company has been tested

and calibrated for potential application in a high repetition rate laser environment.

The test revealed a background level of around 115 gray values in the detector that could not be minimised by cooling; this condition may have been constituted by the electronics of the detector. In addition, the test showed that the set exposure time on the detector is not the real exposure time. An offset of nearly 1000 ms is added to a set exposure time, and a 3ms delay is required before exposure.

In the calibration using 3 MeV proton beams, two configurations were tested, one in which only the CMOS sensitive area was irradiated by protons, and another where a scintillator screen was placed in contact with the CMOS sensitive area. In the first case, the minimum detectable number of protons was about 1000. In the second, the lowest detectable number of protons was 600. This is a slight improvement from the previous configuration, but it resulted in a very poor spatial resolution at an FWHM of 45 pixels compared to 1 pixel in the previous configuration.

While the scintillator configuration may not deliver the best resolution, it has the potential of detecting an even lower number of protons. In the previous calibration, we were limited to a maximum beam energy of 3 MeV, this energy cannot pass through the scintillator plastic support to reach the scintillator itself; this is the reason for setting the scintillator in the other direction. When the detector will be used with a Thompson parabola (separates accelerated particles by their mass, charge, and momentum [START_REF] Bellido | Design of a thomson parabola spectrometer for the detection of laser-accelerated protons and ions[END_REF]), we will well exceed 3 MeV and the scintillator can be set facing the CMOS surface. We will gain in the sensitivity but we may still have problems with spatial resolution. In any case, this will call for a calibration test at another proton beam facility.

Chapter 3

Scintillator-coupled photodetectors in laser-plasma environment

For many years, scintillators coupled to photodetectors have been used for gamma spectroscopy studies [START_REF] Sakai | Recent measurements on scintillator-photodetector systems[END_REF][START_REF] Pavlov | Gamma spectroscopy using a silicon photomultiplier and a scintillator[END_REF][START_REF] Grodzicka-Kobylka | Silicon photomultipliers in gamma spectroscopy with scintillators[END_REF]. These studies are in environments with minimal radiation background disturbances. In our quest to perform gamma spectroscopy in a laser-plasma environment, huge flash of x-rays from the laser interaction constitutes the main source of radiation background that limit prompt gamma detection. In this work, we want to detect gamma energies of the order of few hundreds of keV from a short-lived (few 9 ns) de-excitation of 84m Rb in a laser plasma while immersed in this huge X-ray background. One of the detectors we are considering is a Lanthanum bromide (LaBr 3 ) scintillator. In this chapter, their signal response within such radiation background will be examined from two different photodetectors; in one case, a regular photomultiplier tube (PMT), and in another a hybride photodetector (HPD).

LaBr 3 scintillator

Scintillators are materials that emit visible light when exposed to radiation. They are commonly classified into two types: organic and inorganic scintillators. Compared to organic scintillators, inorganic scintillators are typically high atomic number materials with a possibility to produce up to 60000 photons per MeV gamma radiation which makes them relevant for energetic radiation detection. The table 3.1 summarises some of the well-known scintillators. Amongst the most widely used scintillators for gamma radiation detection purpose is NaI due to its relatively high yield 41000 ph/MeV, and good resolution of 5.6 % at 662 keV. In addition to its low cost and ease of growth, it has become the most commercially successful scintillator [START_REF] Milbrath | Radiation detector materials: An overview[END_REF]. However, it has a relatively long decay time of 230 ns, which makes it unsuitable for very short-lived nuclei studies in the context of this work. Another attractive option is BaF 2 because of its excellently low mean decay time of 0.7 ns, fast signals can be produced for shortlived nuclei studies. Nonetheless, its very poor yield of 1500 ph/MeV and relatively low resolution discourages their application for gamma spectroscopy purpose. LaBr 3 deployed in this work is an inorganic scintillator with very special attributes: it gives a yield of 63000 ph/MeV; a fast decay time of 16 ns; a high density of 5.3 g/cm3, and 2.9 % high resolution at 662 keV [START_REF] Peter R Menge | Performance of large lanthanum bromide scintillators[END_REF][START_REF] Fga Quarati | Scintillation and detection characteristics of high-sensitivity cebr3 gamma-ray spectrometers[END_REF][START_REF] Quarati | High energy gamma-ray spectroscopy with labr3 scintillation detectors[END_REF].

Table 3.1: Survey of some inorganic scintillators with some of their important properties. [START_REF] Peter R Menge | Performance of large lanthanum bromide scintillators[END_REF][START_REF] Fga Quarati | Scintillation and detection characteristics of high-sensitivity cebr3 gamma-ray spectrometers[END_REF][START_REF] Rodnyi | Physical processes in inorganic scintillators[END_REF][START_REF] Carel | Inorganic scintillators in medical imaging[END_REF][START_REF] Nikl | Scintillation detectors for x-rays[END_REF][START_REF] Ackermann | Timeand energy-resolution measurements of baf2, bc-418, lyso and cebr3 scintillators[END_REF] Scintillator Density (g/cm

Mechanism of scintillation

LaBr 3 like other inorganic scintillators depends on the band structure and the energy states of the crystal lattice for its scintillation. In a pure inorganic scintillation crystal, the electrons are only allowed to occupy the valence or conduction energy bands.

The forbidden band or band gap existing between the valence and conduction bands cannot play host to an electron. High energy radiation can excite electrons from the valence band into the conduction band so that the return of the electrons leads to the emission of photons. But this process is inefficient as few photons are released per decay and their energies are too high above the visible range due to the energy gap. For the scintillator light to be detected by a photodetector, it should be in the visible range. Impurities, called activators, are thus added to the crystal to modify the band structure from a pure crystal, creating luminescence centers or recombination centers so that some energy states can be added in the band gap. These introduced energy states permit the de-excitation of an electron back to the valence band via a smaller energy distance. The emitted photon is now in the visible range serving as the basis of the scintillation process as can be seen for LaBr 3 doped with 5% Ce, and CeBr 3 scintillators, in figure3.1. In the figure, the shifting towards longer wavelength with increasing thicknesses of CeBr 3 is the result of scintillator self-absorption and re-emission processes as explained by the authors [START_REF] Fga Quarati | Scintillation and detection characteristics of high-sensitivity cebr3 gamma-ray spectrometers[END_REF].

L = L 0 exp(-t/t d ) -exp(-t/t r ) , (3.1.1)
where L is the light intensity, L 0 is the maximum height of the pulse, and τ d and τ r are the decay and rise time respectively. A fast decay time is useful against occurrences of pile-ups in high-activity radiation environments. Moreover, for purposes of gamma spectroscopy of short-lived nuclei in a laser environment, scintillators with few ns decay time, high radiation yield, and material density are desired for fast and efficient gamma detection.

Afterglow

From figure3.2, electron in the conduction band could easily locate a so-called electron trap. The traps are metastable energy states formed by the presence of impurities and defects in crystalline scintillators. While in the trap the electron can remain there for as long as more than an hour, and as short as a few nanoseconds. Due to thermal agitation, the electron could gain sufficient energy to enable a return, back to the conduction band, and later retrace a luminescence center for light emission. This delayed emission photons are responsible for the so called delayed light, phosphorescence or afterglow (these scintillation mechanisms are explained in [START_REF] Glenn | Radiation detection and measurement[END_REF][START_REF] Syed Naeem | Physics and engineering of radiation detection[END_REF]). It is an undesirable effect that is detrimental to short-lived nuclei studies in a laser-plasma environment.

Delayed emissions can saturate detectors for as long as they are emitted making early gamma detection a difficult task. Cases of significant afterglow have been observed

in several inorganic scintillators such as CsI, LSO and LaBr 3 [START_REF] Sergii Gridin | Scintillation properties of csi:in single crystals[END_REF][START_REF] Bizarri | Scintillation properties of o 11 inch3 labr3: 5Nuclear Science[END_REF].

In figure3.3, CsI scintillators doped with In and Tl respond to X-rays with the emission of afterglows lasting for several hundreds of milliseconds, which is about 100 times more than the scintillator's decay time.

LaBr 3 in high-power laser-induced X-ray environment

In this section we will study the X-ray flash signal output from a scintillator coupled with two photodetectors. The origin of this X-ray flash is due to the motion of charged particles in the laser-created plasma and the deceleration of high energy electrons as they interact within the experimental chamber, as already explained in chapter 1.

The LaBr 3 scintillator has been chosen for its high yield, high density, and relatively fast decay time of some ns. However, to make an energy histogram of the detected photons, they must be coupled to a photosensor, which is what we are examining in this part.

LaBr 3 with PMTs

Basics of PMTs

One of the photodetectors considered in this work to be coupled to a scintillator is a Photomultiplier tube (PMT). PMTs are the most common example of photosensors used to convert visible light into electrical signal for gamma spectroscopy purposes.

The basic building blocks of a traditional PMT are a photocathode, an electron multiplication structure in a vacuum tube, and a readout electrode. A single photon incident on the photocathode interacts by photoelectric effect ejecting an electron accelerated by a voltage drop towards the first dynode in the vacuum tube (illus-trated in figure3.4). The quantum efficiency QE of the photocathode is the fraction of incident photons that are converted to photoelectrons, and it typically does not exceed 40 % [START_REF] Mirzoyan | Very high quantum efficiency pmts with bialkali photo-cathode[END_REF][START_REF] Lei | Evaluation of new large area pmt with high quantum efficiency[END_REF] in PMTs. The dynode is composed of a metal plate containing a substance on the surface such as a bialkali compound, which gives off secondary electrons upon impact with accelerated electrons. The collision of the electron with the dynode releases secondary electrons, which are also accelerated to another dynode. Each subsequent dynode is given a higher positive potential to allow further acceleration of the secondary electrons and to produce a larger number of secondary electrons. The process is repeated several times until the anode is reached, producing a typical electron gain of ∼ 10 6 [START_REF] Oswald | 7 -amplifying and position sensitive detectors[END_REF]. In the end, the original photocathode current I c has been amplified to a final current equal to I c φ n , where φ is the secondary electron emission coefficient, and n is the number of dynodes. In this work, scintillators coupled with PMTs will be tested in the presence of a huge X-ray flash caused by a high power laser interaction.

Test with PMTs in laser-plasma environment

As a way to test the capacity of the PMT (coupled to LaBr 3 ) to detect gammas conveniently in a laser-plasma environment, a relatively long lifetime would be considered.

Such long lifetimes will permit us to know the dead time of the PMT in terms of detecting the first gamma in an X-ray flash background. For this purpose, 90m Nb is a good candidate. It can be created using laser-accelerated protons on a Zirconium(Zr) target ( 90 Zr(p,n) 90m Nb). Amongst other gamma photons emitted, 90m Nb emits 122 and 257 keV gammas with 63 and 6000 µs decay times respectively (schematic level structure). Moreover, the gamma energies are in the domain of interest of our main experiment ( 84m Rb experiment), also the decay times (in few µs and ms) are useful to determine the earliest time that a gamma photon can be detected after the laser shot.

In this part, we recount the performance of the PMT in this alternative experiment by examining the observed signal.

In 2014, in-situ gamma spectroscopy study was performed by F. Negoita et al. [START_REF] Negoita | Perspectives for neutron and gamma spectroscopy in high power laser driven experiments at ELI-NP[END_REF] to detect 122 (63 µs half-life) and 257 keV (6 ms half-life) from the decay of a 90m Nb source activated in a laser environment via the ELFIE laser beam (20 J and 350 fs) of LULI (Palaiseau, France) focused on a 25-µm-thick Mylar target. This experiment has also been partly reported by Tarisien et al. [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF]. The scheme of the setup is shown in figure 3.5. A high-power laser arrives on the solid target leading to the acceleration of protons with the production of X-rays. The protons arrive on a secondary target of Zirconium to create 90m Nb. A detector (PMT coupled to LaBr 3 ) connected to an oscilloscope and digitizer is positioned very close to the point of laser interaction for the detection of the emitted gammas. In 2020, we performed an experiment at GSI where a high power laser (intensity ∼ 10 20 W/cm 2 ) interacted with a laser-tailored gas target [START_REF] Bonvalet | Laser-driven collisionless shock acceleration of protons from gas jets tailored by one or two nanosecond beams[END_REF]. The LaBr 3 coupled to a PMT detector was placed on the roof of the experimental chamber. The PMT output revealed a detector recovery time of approximately 1 ms (figure 3.8). This time is relatively smaller compared to the previous case (illustrated in figure3.7) in which a laser on a solid target was considered, probably because lesser X-ray energies compared to that in solid target were produced. Also because the detector was placed outside the experimental chamber.

LaBr 3 with HPD-PIN

In a quest to improve the detection time from 3 ms with PMTs to the instant of the laser shot, a hybride photodiode (HPD) was tested together with the LaBr 3 scintillator in a laser-plasma environment. Some of the characteristics of the photodetector, and tests results with scintillators are detailed in this section.

Pin-based hybride photodiode

Structure and principle:

One may categorize the components of a hybrid photodiode into three parts: photocathode, vacuum tube, and semiconductor detector. As ionizing radiation interacts with the LaBr 3 scintillator, the deposited energy leads to luminescence light stimulated from activation centers within the scintillator. The light causes the production of photoelectrons as they interact with the photocathode of the HPD (QE of HPD photocathode in this work is 0.25 at 360 nm [START_REF] Da Orlova | High quantum efficiency s-20 photocathodes for photon counting applications[END_REF]). The created photoelectrons are then conveyed through the vacuum tube under the influence of an electric field (provided by a potential of several kV) to interact directly within the semiconductor detector (described by figure 3.9) and create electron-hole pairs. The signal response of the HPD is therefore governed by the motion of the created electrons and holes in the semiconductor material (silicon in this work) under the influence of an electric field inside it. Unlike PMTs, dynodes are completely left out in HPDs.

G = (∆V -E 0 )/W e/h , (3.2.1)
with W e/h =3.6 eV being the average energy needed for the creation of a single electron-hole pair in silicon. E 0 is the energy lost in the non-active material layers of the silicon detector (Aluminium contact layer, n+ layer), and ∆V is the potential difference of some kV between the photocathode and the sensor, which for a photoelectron corresponds to some keV. When relatively low energy electrons (around 15 keV or less) impinge on the silicon sensor, there is a probability of 0.2 that the electrons can be back-scattered into the vacuum [START_REF] Joram | Large area hybrid photodiodes[END_REF].

Properties of HPD pin photodiode:

The first conception of the HPD was in the fifties [START_REF] Sclar | Electron devices conf[END_REF], however, it was abandoned due to technical difficulties [START_REF] Arnaudon | Proximity focussed hybrid photo diode characteristics evaluations[END_REF]. The idea was later revived in the domain of particle physics by DeSalvo [START_REF] Desalvo | Hybrid photodiode tube[END_REF] near the early nineties. Since then, several studies have been performed on HPDs [START_REF] Joram | Large area hybrid photodiodes[END_REF][START_REF] Arnaudon | Proximity focussed hybrid photo diode characteristics evaluations[END_REF][START_REF] Desalvo | First results on the hybrid photodiode tube[END_REF][START_REF] Basa | Test results of the first proximity focused hybrid photodiode detector prototypes[END_REF][START_REF] Anzivino | Review of the hybrid photo diode tube (HPD) an advanced light detector for physics[END_REF][START_REF] Bellia | Performance of hybrid photodiodes with scintillator crystals[END_REF]. In particular, early studies by Desalvo et al. [START_REF] Desalvo | First results on the hybrid photodiode tube[END_REF], and Arnaudon et al. [START_REF] Arnaudon | Proximity focussed hybrid photo diode characteristics evaluations[END_REF], have shown that the rise and fall times for the case of a single bunch of electrons on the pin diode are within few ns. These studies were performed using very short duration LED pulses and the results show that the detector configuration is fast enough in the charge collection process to deliver a short duration signal for a bunch of single photoelectrons. Notably, both authors studied the linearity of HPD with respect to the input photoelectrons and output charge, and found the detector to maintain a linearity more than 10 4 pC (see figure 3.10).

For PMTs, they display a linearity that is three orders of magnitude less than that of a pin-HPD. A test was performed on a PMT to know the range of linearity obtainable [START_REF] Davis H Hartman | Pulse mode saturation properties of photomultiplier tubes[END_REF]. In figure3.11 is a plot of the the PMT response normalised by the expected. From the figure, we observe that the linearity of the PMT is constant until the photon intensity exceeds about 10 5 . This is four orders of magnitudes less than 10 8 photelectrons obtainable in HPD (from figure 3.10). Thus stressing that HPDs maintain a wider range of linearity than the conventionally adopted PMTs. No departure from linearity in pulse amplitude is found in the charge integral [START_REF] Arnaudon | Proximity focussed hybrid photo diode characteristics evaluations[END_REF].

Typical geometry of HPDs

There are basically three different categories of the HPD based on their electron optical design [START_REF] Joram | Large area hybrid photodiodes[END_REF] as follows, proximity focusing, cross focusing, and fountain focusing (see figure 3.12).

• Proximity focusing: This is very compact with a relatively close distance between the photocathode of the HPD and the pin diode which makes it tolerant to magnetic field. It however, has no demagnification thus the photosensitive area of the detector is limited to the size of the silicon sensor.

• Cross focusing: This is made of focusing electrodes that help to reduce the spread of the electron beam so that a small area focus is achieved on the silicon sensor. This demagnification is also made possible by allowing relatively large distance between the photocathode and the silicon sensor. The implication of this is a high response to magnetic field effects. However, this configuration permits good focusing of electrons on the sensor, thus small area PIN diodes can be used, implying lesser capacitance and noise.

• Fountain focusing: With a reduced spatial resolution compared to the cross focusing. The configuration also has a linear demagnification and it is sensitive to magnetic fields.

Description of HPD from Photonis

A HPD of type PP0475D was bought from Photonis company having a S20UV photocathode deposited on a quartz input window. The input window diameter is 40 mm and with operating voltage of up to -15 kV, a gain of 3500 can be achieved from the detector( figure 3.13) . The cathode sensitivity at 270 nm and 400 nm are averagely Inside the HPD is a T-type pin diode. T-type implies that the orientation of the diode in the HPD is such that the incoming electrons enter in the PIN through the surface far and opposite to the pn junction of the diode [START_REF] Desalvo | First results on the hybrid photodiode tube[END_REF]. The contrary case is an E-type orientation where the surface directly close to the pn junction is exposed to the electron beam (shown in figure 3.14). T type HPD was studied to have better gain loss recovery than E type [START_REF] Desalvo | First results on the hybrid photodiode tube[END_REF].

Experimental result from LULI-Elfie

In 2016 Tarisien et al. [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF] performed a follow-up experiment where the HPD was coupled to an LaBr 3 and tested in a similar condition as performed by F. Negoita et al. [START_REF] Negoita | Perspectives for neutron and gamma spectroscopy in high power laser driven experiments at ELI-NP[END_REF] in 2014. The aim was to see if the dead time could be improved from 3 ms (achieved with PMT) to some µs using this HPD. As part of this thesis, the obtained data have been treated and analysed.

The result is shown in figure 3.15 a-b for one of the oscillograms, a fast rising and slow falling exponential signal is clearly observed in 3.15b which indicates the detected large x-ray flash after the laser shot. The detector was developed with a LED source placed in between the scintillator and the HPD, so that a bunch of blinking light could be injected during the acquisition. The purpose of this is to serve as a correction tool against reduction in the amplitude of signals in potential cases of gain modification. These repetitive pulses are normally injected before the instant of the laser shot and extending several ms after. The LED pulse before the instant of the laser shot provides the expected amplitude of the light pulse and should not experience any gain modification, while the ones after could be prone to such effects.

These repetitive pulses can be clearly observed in figure 3.16, with one before the huge exponential signal and many others after. The other observed irregular pulses on the falling component of this signal are the detected gammas.The flash signal reached baseline around 200 µs after the laser shot. However, offline treatments can be deployed to extract gamma pulses piled on the falling part of the x-ray flash signal.

Considering cases of saturation, the pulses must be treated before being filled into histograms. As part of this work, I have treated and analysed data files as in figure 3.15, few of the procedure of analysis is displayed in figure 3. [START_REF] Bonnet | Response functions of fuji imaging plates to monoenergetic protons in the energy range 0.6-3.2 mev[END_REF] and more details can be found in chapter 4. One can see that the first detected gamma or LED pulse is around 15 µs. Compared to the case of a traditional PMT that lasted about 3 ms before a possible gamma detection, the dead time has been improved by a factor of 100. The detector was also calibrated using the same voltage parameters as used for the main experiment in a laser plasma environment(see figure 3.17).

Figure 3.17: Calibration of HPD with radioactive source: 22 Na (511 and 1274 keV), 137 Cs (662 keV).

A final result of the analysis is in the histogram of the detected gamma photons in figure 3.18 (from three laser shots). The figure reveals the formative stages of the expected photon peaks of 122 and 257 keV. The inset also shows the decay of the 122 keV fitted with a half life of 63 µs, which could not be observed with a traditional PMT [START_REF] Negoita | Perspectives for neutron and gamma spectroscopy in high power laser driven experiments at ELI-NP[END_REF] (figure 3.6). However, for more confident conclusions to be made, it is necessary to obtain more statistics, which also corresponds to more laser beam times. We observe the peak near 750 keV, which could be due to some activation in the chamber environment, but we are unable to identify the source due to insufficient statistics. Moreover, the acquisition was done with a poor resolution 8 bits oscilloscope. Subsequent experiments will use a 14 bits digitizer from SP Devices company This question on the origin of the long decay time of the signal from the HPD has been asked by Tarisien et al. [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF]. They attempted to provide an answer by subjecting the HPD to a laser pulse (220 mJ, 532 nm, 6 ns pulse duration, and 50 mm diameter spot). Before then, during an experiment on PICO2000 (at LULI) they coupled an APD to the LaBr 3 scintillator. In one shot, the LaBr 3 produced so much light that the APD delivered a large voltage signal V. Removing the scintillator in another shot, the signal induced in the APD by only X-rays was negligible. Some years after, they illuminated the same APD with a 532 nm wavelength laser (as they did not have a 380 nm laser) and they needed 38 µJ of light energy to get the same amplitude V from the APD. Then they irradiated the HPD with the 38 µJ that simulated the light exiting from the LaBr 3 during a laser shot. After releasing 38 µJ of laser energy in the HPD, the output signal lasted for about 3 µs. This value is a factor of hundred less than what was observed from the signal due to the X-ray flash (3.15). They therefore concluded that the main cause of this long duration X-ray signal is due to an afterglow from the LaBr 3 scintillator and not from the behaviour of the silicon detector in the HPD.

In this work, we would like to verify the origin of the long duration signal using Silvaco TCAD simulation. We will deposite a corresponding energy in the HPD due to the laser of 38 µJ and observe the signal duration. Also it gives us the opportunity to study the intrinsic behaviour of the PIN diode. Considering the parameters of the laser pulse as mentioned above with 38 µJ of laser energy deposited through the HPD photocathode, the estimated number of generated photoelectrons for a photocathode QE of 0.14 at 532 nm is 10 13 (from Photonis datasheet). Given an acceleration voltage of 11 kV, the gain factor is about 2500 from figure 3.13. The approximate energy deposited in the silicon sensor is nearly 90 PeV (when multiplied by 3.6 eV for silicon). Since the signal from the HPD is essentially due to electrons on the silicon sensor, the created electron-hole pair is 2.3 × 10 16 , which corresponds to a total charge of 3.6 mC. This simulation will come up a bit later.

Simulated signal response of HPD

The structure of the PIN diode has been presented in chapter 2 2.1.4. Here the PIN will be modelled using the information captured in table 3 The figure 3.22 shows the 1 D electric field distribution in the PIN diode (through a 150 µm thickness) for different combinations of n and p doping concentrations. We can see that for all considered concentrations, the electric field on the n side varies between 2900 and 3600 V/cm for 10 16 and 10 20 cm -3 donors respectively. The electric field varies between 6400 and 6700 V/cm for acceptor concentrations of 10 16 and 10 20 cm -3 . The differences in the electric field as we varied dopant concentrations was within 400 V/cm except for when n was 10 20 and p 10 19 . The electric field profile and value is not so sensitive to the dopant concentration. Therefore, even if we don't know the precise concentrations, we will be able to identify the behaviour of the detector. The detector was highly n-doped on the cathode side with 10 19 cm -3 , and highly p-doped near the anode at 10 17 cm -3 . The net doping profile from n on the cathode side ( from 0 µm), to p on the anode side (to 150 µm) is presented in figure 3.21b. One can observe the formation of a pn junction near the P side, which is responsible for the high field observed in figure 3.22. This high field is peaked at 6700 V/cm, a value relatively low compared to about 10 5 V/cm [START_REF] Piprek | Chapter 3 -carrier transport[END_REF], needed to cause impact ionisation in APDs (see Chapter 2 for APDs).

Simulated response of HPD from 511 keV deposited energy

As part of a verification of coherence between our simulation and experimental results, we simulated the current signal of a 511 keV photon from detection by a LaBr 3 scintillator to its eventual electrical output from the HPD PIN diode (see figure 3.20).

For a scintillator yield of 63 ph/keV in LaBr 3 , this corresponds to 32193 photons. The photon distribution in time is modelled after equation 3.1.1, and the generated photoelectron distribution when the photons are in contact with the HPD photocathode is described by the same equation.

For the HPD photocathode Quantum efficiency of 0.25 (at 400 nm according to the photonis datasheet), the total photoelectrons is 8048. Considering a HPD high voltage of 9 kV, the electrons will deliver a total of about 50 MeV in the PIN diode for a gain of about 1800/e (from figure 3.13). The vacuum structure of the bought HPD is a cross focusing one (from figure 3.12 ), so that the photoelectrons due to the interaction of one photon from the LaBr 3 , will focus into a relatively smaller region of the detector compared to the entire surface. For this we set a diameter of 100 µm. In figure 3.23, the electric field profile through the detector is shown for 15 ns into the simulation. We observe a screening of the electric field as the holes move towards the anode electrode. This is more clearly seen in the 1 D profile shown in figure 3.24, that the electric field is shifted to peak at 7800 V/cm as the holes approach the anode electrode compared to 6700 V/cm (see figure 3.22) before irradiation. This shows that the electric field could be shifted higher if more electrons interact on the PIN diode as we will see later. The result of the current signal after the simulation is captured in figure 3.26. With a duration of 1.5 µs, though larger than the duration of a detected single photon when coupled to a scintillator (see figure 3.25), it is 100 times shorter than the duration observed for a flash X-ray detected through the same scintillator in figure 3.16. This therefore confirms that the long duration signal after the absorption of an X-ray flash when coupled to a scintillator is not from the pin diode but mainly due to scintillation manifesting as an afterglow. Worth noting is the sudden high current amplitude of about 10 6 A that slowly decreases until baseline. Looking into the electric field profile 40 ns after shows that the electric field has been shifted on irradiation to a peak of 2 × 10 5 V/cm (figure 3.27 and 3.28). This field value is high enough to cause impact ionisation in silicon.

Thus holes on reaching this high field region create secondary electron-hole pairs that contribute to an increase in the current amplitude. The electric field in the bulk of the intrinsic region of the detector is relatively low at 18 V/cm (from figure 3.27 ).

This means the drifting of holes and electrons will be based on this field and will take relatively longer time than in the normal PIN diode condition. The secondary electrons will drift towards the cathode from the high field region drifting through this low field and experiencing relatively longer times for complete carrier collection.

It also implies that higher rates of recombination will be experienced in this bulk (as primary holes encounter secondary electrons). Towards the end of the current signal, there is an almost abrupt end in the current duration, this is due to the restoration to normal detector electric field profile, as can be obvious in the evolution of the electric field profile in figure 3.29.

Response to X-rays from moderately high intensity laser

LaBr 3 coupled with HPD in a high-power laser-plasma environment can detect gammas few tens of µs after the laser shot. The laser intensity in this condition exceeds 10 18 W/cm 2 , and the duration of the X-ray flash signal lasted for 200 µs. Another test was performed at CELIA using moderately high intensity lasers at 10 16 W/cm 2 , in this case, the intensity of the X-ray flash and the corresponding energy will be relatively less. It is therefore interesting to see how these influences the duration of the X-ray signal.

Experimental setup at CELIA

Results and discussion

Detector calibration

The detectors have been calibrated using a Na-22 source. The following energies are expected from its decay: 511, 1274 and 1785 keV. The output signal from the detectors were integrated to obtain the corresponding charge and plotted with the gamma energy they correspond to. The HPD was at an acceleration voltage of -11 kV, and bias of 70 V, while both PMTs ran at a high voltage of -500 V. The same condition is also set at each laser shot. The result of the calibration is in figure 3.34;

In the figure, unlike the PMTs, the HPD could not detect the 1785 keV due to its relatively lower gain. Response from LaBr 3 coupled to PMT

The PMTs coupled to LaBr 3 were used as monitors. Being outside the chamber, they were less exposed to high intensity of light and so less prone to saturation. Figure 3.35 shows the signal output for different shots from both PMT1 and PMT4. Same colours on both images represent same shots. The signals obtained from PMT1 and PMT4 were rather consistent from shot to shot. Also, one can observe that both PMTs did not deliver the same signal form. In particular, the signal from PMT1 seems to show that there is the presence of an extra signal component about 100 ns later. While PMT4 delivered the typical shape of an exponential signal. The form of the signal in PMT1 was never observed when detecting 1 MeV of gamma from a radioactive source with the same detector. This signal form could therefore be due to the creation of more electrons in the dynode as the quantity of instantaneous energy deposition increased from X-ray absorption. Compared to a laser intensity of 10 18 W/cm 2 for ion acceleration, the duration of the detected X-ray flash signal was 100 times lesser for an intensity of 10 16 W/cm 2 . This is because the electronic temperature of the plasma here is lesser than that used for ion acceleration, hence fewer x-xrays are produced. While this is interesting, the HPD-LaBr 3 detector is still very far from detecting gammas emitted with 9 ns half life.

Summary, challenges, and perspective

High power lasers are very promising for astronuclear studies but the large quantity of X-rays from their interactions makes prompt gamma detection within their environment a herculean task. The detectors can remain blind for a period of time before recovering to perform gamma spectroscopy. This dead time has been studied in the case of PMTs, and found to last for few ms. This is too large to permit the detection of emitted gammas from a 9 ns short-lived nuclear state in the 84m Rb experiment.

Further test with LaBr 3 coupled to an HPD based on a pin diode photosensor performed in similar conditions showed a long duration X-ray signal while minimising dead time to about 20 µs. Considering that the scintillator is a very fast one (16 ns decay time), it was studied by both experiment and simulation that the source of this long duration is due to the manifestation of an afterglow process inside the scintillator.

In addition, a further test with another high power laser at 10 16 W/cm 2 intensity was performed at CELIA. The result showed that the X-ray flash signal from the HPD could be as low as 2.5 µs. This is interesting for nuclear physics studies where such a laser intensity is good enough to deliver the needed astrophysical plasma. This dead time could be minimised if offline treatments are carried out to recover gamma signals that have suffered a loss of gain while being detected close to the instant of the laser shot and piled on the X-ray signal.

While we have seen that at lower absorbed X-ray energies the afterglow signal duration can be as low as 2.5 µs, our detector is yet to satisfy the demands for the detection of the 9 ns isomeric state due to this afterglow. Afterglows are due to delayed emissions from long-lived electron trapping in the lattice sites. However, if through optical stimulation (as have been done in some phosphors [START_REF] Van Der Heggen | Optically stimulated nanodosimeters with high storage capacity[END_REF]), we able to supply some energy to the trapped electrons to exit from these traps faster and to minimise this long time effects, we may be able to reduce the long signal in future studies of LaBr 3 in a laser environment.

Chapter 4

Data processing for gamma spectroscopy in a laser-perturbed environment

One of the objectives of this work is to set up tools in order to perform gamma spectroscopy in a laser-perturbed environment. In gamma spectroscopy, the aim is to do a quantitative study of the energies and intensity of gamma rays emitted from a radioactive source by the deployment of relevant radiation detectors. Amongst the commonly used detectors for gamma spectroscopy is the scintillator coupled to a photodetector, which is chosen for its fast decay time, good energy resolution, and high photon yield. For example, Lanthanum Bromide (LaBr 3 ), used in this work has a decay time of 16 ns, energy resolution of 3.2 % (at 662 keV) and a photon yield of about 60000/MeV [START_REF] Shah | Labr/sub 3: Ce scintillators for gamma-ray spectroscopy[END_REF], making it a very good choice for gamma ray studies.

Many gamma ray studies such as [START_REF] Quarati | High energy gamma-ray spectroscopy with labr3 scintillation detectors[END_REF] and [START_REF] Löher | High count rate -ray spectroscopy with labr3:ce scintillation detectors[END_REF] are done in accelerator environments in which the quasi-continuous particle beams allow for single photon counting with less background radiation disturbances compared to laser environments. Gamma spectroscopy in conventional cases commonly uses an acquisition system where the output electrical pulses are passed to an amplifier module, which shapes and filters the signal. The result is then passed to an analogue to digital converter (ADC) that measures the amplitude of the treated pulses and assigns a digit which is then histogrammed by a multichannel analyser (MCA). In this case, each gamma signal is sampled, treated and included in the histogram before the arrival of the next. Single photon counting during a laser shot or shortly after can be achieved on high repetition rate lasers by using very small detection solid angles [START_REF] Bonnet | Caractérisation et optimisation de sources d'électrons et de photons produites par laser dans les domaines du keV et du MeV[END_REF] and collecting data over several shots. However, this is not possible on single-shot lasers on which all the spectra have to be recorded on one shot. Furthermore, studies in a high-power laser environment are plagued by large background radiation arising mainly from huge quantities of low-energy X-rays [START_REF] Ak Norreys | Observation of a highly directional γ-ray beam from ultrashort, ultraintense laser pulse interactions with solids[END_REF], which are created during the interaction and reaching the detector within few hundred ps after a laser shot on a target. The deposited energy within such a short duration, overwhelms detectors and limits attempts to perform prompt gamma ray spectroscopy, for some ms in the case of LaBr 3 coupled to a Gated Photomultiplier tube (GMT) [START_REF] Negoita | Perspectives for neutron and gamma spectroscopy in high power laser driven experiments at ELI-NP[END_REF], and tens of µs when coupled to a Hybrid photodetector HPD [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF].

Moreover, the instantaneous deposition of large quantities of photons (more than 10 9 photons [START_REF] Ak Norreys | Observation of a highly directional γ-ray beam from ultrashort, ultraintense laser pulse interactions with solids[END_REF]) leads to variation in the gain of the photodetector which can last beyond 40 ms after the shot. Furthermore, electromagnetic pulses (EMPs), which are linked to the intensity of the laser [START_REF] Consoli | Laser produced electromagnetic pulses: generation, detection and mitigation[END_REF], distort the signals adding high frequency components that could be falsely interpreted as gamma pulses. Last but not the least, possibilities of many pileup occurrences are anticipated, thus emphasising a further need to treat each signal pulse after the laser shot. Taking all these into account, it is paramount to carry out signal treatment procedures on the entire collected signals after the laser shot before making a spectroscopy of the detected gamma ray energies.

In this chapter, I will detail the steps I have taken to process the data acquired for gamma spectroscopy in a laser-perturbed environment; ranging from cleaning the data from irrelevant and missing information, to the final histograms of the treated signal pulse. In the final session, emphasis will be on how to manage pileups that could possibly originate from such experiments. The pileup study will be done via a set of simulated pileup events taking into consideration the lifetime of one of the states of the metastable nuclei being considered. The programming and data analysis will be done adopting Python 3 programming language [START_REF] Van Rossum | Python 3 Reference Manual[END_REF]. The steps followed in the treatment are summarised in the flowchart in figure 4.1.

Exploring experimental Data

In this section, the data analysis and signal treatment procedures will concern data obtained in a typical experiment where gamma spectroscopy has been carried out near the instant of the laser shot, and under the influence of laser-based perturbations. The signal output is connected to an oscilloscope where they are digitized and the data collected and stored for offline analysis. at time t = 0, and the arrival of a large exponential-like signal called an afterglow [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF] (see chapter 3). The amplitude is cut due to the saturation of the oscilloscope that recorded the signals.

Data acquisition and pre-treatment

Description of Oscillogram from Activation experiment in laser environment

The repetitive LED pulses are expected to be detected with a relatively constant amplitude, but a variation in amplitude was observed that increased as signals arrived

Baseline correction

The large quantities of low energy X-rays emitted during the laser interaction deposit their energy at roughly the same time in the detector. The response of the overwhelmed scintillator manifest itself as a long duration afterglow signal of some tens of µs [START_REF] Tarisien | Scintillators in high-power laserdriven experiments[END_REF] before the protons arrive to cause some activation on the target in our case (see figure 4.2). It is important to correct the baseline due to this afterglow to be able to know the actual amplitude of each arriving gamma pulse. This is clearly depicted in figure 4.6. Just on the large signal are small irregular gamma signals due to the proton activation described in figure 4.2.

To correct for baseline, it is possible to make a fit with functions that well reproduce the shape of the afterglow, but the fit is only an approximate solution and is not always precise enough to address the problem, as we will see in this subsection. This means that if we have very small gamma pulses on the afterglow, though the fit seems good, these pulses can be cut by it because the fit is not exactly superimposed on the baseline of the signal. Another approach is to apply a low pass filter after a rough baseline from decoupled pulses on the afterglow, as used in subsection 4.1.1. The following subsections will discuss two simple methods applied to establish a reliable baseline as part of the correction procedures on the acquired data.

Rough baseline: Fitted baseline

To be able to define a baseline suitable to reveal the gamma signals, I wrote an a algorithm to first create a rough baseline which can then be fitted or filtered. This rough baseline was important because if one decides to make a fit or apply a low pass filter directly, it would be difficult to obtain the best fit parameters or perform a very good filtering because of the presence of the gamma and LED pulses. The essential idea of the rough baseline is to decouple the gammas and LED pulses from the whole data, not perfectly, but enough to carry out further treatment that will produce a qualitatively better baseline. In figure 4.7, a rough baseline in orange is plotted on the raw signal in blue. An approach that applies a low pass filter on the rough baseline is explored next.

V (t) = C + A × exp(-t/τ 1 ) + B × exp(-t/τ 2 ) ( 4

Smoothened baseline and removal

I have tried a set of exponential fit functions such as 4.1.2 but they are not good enough to reproduce the baseline. I applied a smoothing approach to the rough baseline using a Butterworth low-pass filter. An estimate of the decay time of the afterglow signal was used as a basis to establish the cut off frequency that was passed into the filter. The next phase of the analysis is to separate the LED pulses from the gammas.

LED and Gamma Identification

After baseline subtraction, the two types of signals present in the data are due to gamma photons and LED photons. It is important to separate these signals from each other before further treatments. First, a general pulse detection was done including all pulses present by using the signal class of the scipy library and calling the find_peaks function which is a peak finding algorithm. The peak finding algorithm takes the oscillogram data, a set threshold in amplitude, and a sample width as input. The output gives the position (with respect to the data points), of the peak of all the pulses present, which can then be used to identify the position in time and the amplitude of each pulse. In addition, if the gamma and LED signals have very distinct shapes, an alternative to this method could be to use pulse shape discrimination algorithms such as [START_REF] Nakhostin | A general-purpose digital pulse shape discrimination algorithm[END_REF] and [START_REF] Takaku | Development of neutron-gamma discrimination technique using pattern-recognition method with digital signal processing[END_REF], but they are completely unnecessary if we know the frequency of the LED pulses injected into the photodetector.

I coded a LED pulse detector algorithm by taking the frequency of the LED pulses and the indices of detected pulses as inputs. This functions with a 100 % efficiency as it easily identifies all LED pulses. For example, if we know the duration (t) of acquisition of the data and the period(T) of the injected LED pulse, one will expect that about a total of t/T LED pulses be identified, which is the case in the analysis.

When the LED pulses are identified, the gamma pulses can be obtained by separation from the overall detected pulses.

The next phase of the analysis is to treat possible pileup situations that occur when two or more signals arrive at close time intervals within the detector and the detector does not have the ability to properly separate them.

Pileup correction

After a baseline-correction of the data, a further treatment is to correct possible occurrences of pileups during the detection. Pileups occur at high count rates and large detector dead time to be able to separate two arriving gammas as distinct pulses.

For us, pileup treatment is important for two reasons: firstly because the pileups give wrong information about the amplitude of our gamma signals, and secondly because pileups could affect the input LED signals which are relevant for the calibration of all the gamma pulses present in the detection time. The overall effect is the deterioration of the energy spectrum. I have written a programme that detects pileups and corrects them by first verifying the pulses concerned in the pileup, and then extrapolating with a template pulse that concerns the pulse upon which another pulse is formed. For example, we could have a gamma-gamma, gamma-LED or LED-gamma pileup. The first case implies that a gamma pulse is formed on a gamma pulse and a gamma template pulse is to be used for the correction; the second implies that a LED pulse is formed on a gamma pulse so a gamma pulse template is to be used; and the last is a situation where a gamma pulse is formed on a LED pulse, and a LED pulse template is to be employed for the pileup correction. Figure 4.13 presents a pileup case involving gamma-LED pulses. The plot in green is the pileup case after the baseline subtraction, the LED pulse is built on the gamma signal before it. This gives an erroneous estimation of the LED pulse amplitude and further affects the calibration processes involved in the treatment procedure. There are different approaches applied to manage pileups such as method of rejecting pileups. As the name implies, this method means that when pileups are detected they should be pushed aside thus reducing the statistics of events. Another is the widely used method of shaping the pulse. This way, the tail of the signal is shortened using a shaping amplifier but this is done in the electronic configuration of the detector and does not match our situation.

A method that corrects pileup using two parameters of a simple exponential function voltage model, represented by equation 4.1.3, was implemented by [START_REF] Lee | Pulse pileup correction method for gamma-ray spectroscopy in high radiation fields[END_REF], such that the amplitude A, and the decay time τ can be calculated from:

V (t) = A exp (-t/τ ) . (4.1.3)
According to the author, it was a modification of the work of [START_REF] Wang | Advantages of digitally sampling scintillation pulses in pileup processing in pet[END_REF] who considered four parameters for a voltage model making the process computationally intensive.

The modified method relies on correcting only from the start point of the pileup by fitting an exponential curve to calculate the decay time between the peak point of a previous pulse (V (i-1) pk

) and the pileup start point (V (i) st ), the result of this is used to extrapolate the missing tail of the previous pulse, to derive the amplitude (V (i) ) of the current pulse, starting from the pileup start point as described by the figure 4.12. Such approach will only mean poor or good estimation of the decay time τ depending on the statistics of data between the pulse peak point and the pileup start point. A similar approach was earlier implemented in 2019 by [START_REF] Hammad | Pile-up correction algorithm[END_REF], paying attention to pileup correction by pulse tail extrapolation at the pulse pileup start point and calculation of τ . Here, instead of a fit, eqn 4.1.3 was manipulated to calculate τ for each pileup point as follows:

V (n) = A exp(-nT /τ ), (4.1.4)
where n is the number of points, and T is the inverse of the sampling frequency. If two points on the trailing edge of a pulse are known, for example, the peak point (V 1 , n 1 T ) and the pileup start point (V 2 , n 2 T ), then τ can be easily calculated as follows:

τ = n 1 -n 2 ln V 2 -ln V 1 T (4.1.5)
Similar to the fit estimation of τ , the calculation could be erroneous as V 1 and V 2 approach each other. This can be verified, if a fixed signal decay time is injected into a simulated set of signal pulses. In addition, an improved estimation of τ will also depend on the quality of the signal, dictated by the signal to noise ratio (SNR) of each pulse.

In this work, I have implemented a coded algorithm from the work of [START_REF] Hammad | Pile-up correction algorithm[END_REF] and [START_REF] Lee | Pulse pileup correction method for gamma-ray spectroscopy in high radiation fields[END_REF] where they applied a single exponential model to extrapolate from the start point of a pileup to the tail of the signal. This pileup correction method will be tested and compared with another proposed method where a template pulse is used from the knowledge that the signals anticipated due to the scintillator are homothetic and should have the same rise time and fall time. In this proposed method, I have used a template pulse normalised by its amplitude for the extrapolation process as in figure 4.14. In all these methods, pileups must first be detected before they are corrected.

Gain correction

There is a gain variation as depicted by the figure 4.3. The LED pulses are used as indicators of this variation, and are subsequently used as references for the restoration of the lost gain. The method employed here uses linear interpolation to deduce the output amplitude V interpolated L that a LED pulse would have if it were present on all the data points bounded by two LED pulses of known amplitudes V 1 L and V 2 L in the oscillogram. Thus, if the different points in the data have initial signal amplitudes

V 1
i , and the known:original input LED amplitude is V input L , one can apply the gain correction to obtain the corrected voltage V corrected i by using the following formula: showing that gamma spectroscopy at some µs after the laser shot is possible.

V corrected i = (V interpolated L /V input L ) * V initial i . ( 4

Summary

Offline analysis has been successfully applied on experimental data for gamma spectroscopy in a laser environment. More statistics are relevant to clearly distinguish the energies present but we can already see the formation of the 122 and possibly 257

keV. An inset showing the extracted signal decay fitted with an exponential with a known decay time shows that the 122 keV was detected but in need of more statistics to be properly formed.

After baseline correction, most of the pulses were treated for gain related deformities, with almost no pileup problems. However, the possibilities of more pileups are inevitable when faced with higher incident protons fluxes during nuclear activation, improved detection systems via optimised solid angle and detector configuration.

In the following section, a simulated oscillogram with more statistics and cases of pileups due to high activity will be studied to test the analysis tool.

Exploring simulated data

In the experimental data we did not encounter many pileups for us to test the pileup correction tool. In future nuclear physics experiments in a laser environment, a more optimised detection process is envisaged, so more gammas will be detected and thus more pileups are expected in the process. A simulated oscillogram with more events and pileup occurrences will be useful to understand the best ways they can be managed using the analysis tool. The focus here is on 90m Nb because it was used to test the detector in 4.1.1. In addition, two pileup correction algorithms are also tested in the process.

stages of simulation and components

The decay of 90m Nb nuclei can be simulated using the decay equation:

N (t) = N 0 exp(-λt), (4.2.1)
where N (t) is the number of particles at time t(s), N 0 intial number of nuclei particle, and λ (s -1 ) is the decay constant, which is related to the half life t

Treatment of simulated signal pulses

The simulated oscillogram is processed following the flowchart in figure 4.1 and procedures in section 4.1.

the next pulse, making it difficult to distinguish them. Peak detection is important because the pileup correction algorithms to be used, strictly depend on the estimation of the pulse amplitude to effect any necessary corrections.

Pileup correction by calculated decay time parameter: results and discussion

In this case, the work of [START_REF] Hammad | Pile-up correction algorithm[END_REF], similar to [START_REF] Lee | Pulse pileup correction method for gamma-ray spectroscopy in high radiation fields[END_REF] for pileup correction, has been explored.

The method involves calculating the decay time τ of each signal (using equation 4.1.5) in a pileup situation, and using the decay parameter for the tail extrapolation (see figure 4.12). In this method, pileup correction algorithm may produce very erroneous results when pileup points are approaching the peak of a previous pulse. This is intuitively seen from equation 4.1.5, that as the denominator term, ln V 2 -ln V 1 approaches zero when the separation between consecutive pulse is very small, the estimation of τ approaches a number larger than expected. able to reduce the deadtime from 60 ns in figure 4.24 to about 20 ns. This is a factor of 5 more than the previous method.

Summary and conclusion

The performance of gamma spectroscopy in a high-power laser environment is faced with unconventional challenges that are linked to large X-ray flashes, gain-related issues, and perturbations from EMPs. Offline analysis is necessary to correct their influences on the quality of the signal pulses before they are histogrammed for spectroscopy. Successful signal treatment procedures have been applied, from baseline and gain corrections, to pulse shape restoration by pileup correction. These procedures make it possible to deliver a spectroscopy of the detected gammas while preserving the original shape and amplitude of each gamma signal.

The analysis tool developed, based on python programming language, which in-corporates different stages of the signal treatment was first successfully applied to experimental data with nearly no pileups, but future experiments in laser facilities will have more improved detection processes, such as optimised solid angle to enhance reaction probabilities between ion projectiles and nuclear activation targets. This will lead to many signal pulse-pileups. The tool has therefore been tested on simulated data with many pileups present. In addition, two pileup algorithms have been compared, the first, based on a template pulse and the other based on the calculation of pulse decay time to be used for tail extrapolation. The template and the decay time methods perform relatively similarly when the delay between two pulses is greater than 20 ns but when this time-delay between pulses goes below 20 ns, the calculated decay time is overestimated and thus, the extrapolated pulse tail poorly affects the subsequent pulse leading to a reduction in the estimated pulse amplitude.

In addition, it is important to note that, the pileup study has been done with regards to a high power laser environment with a single shot per hour which provides little statistics and so necessitating an improvement in detection such as increasing the solid angle for more statistics. In this case, we expect challenges of pileup and should try to retrieve all detected signals. But for the same intensity of laser at higher repetition rate, we may afford to position the detector a bit far away from the laser-interaction point to reduce pileup effects at the cost of statistics.

Conclusions and perspectives

The aim of this work was to develop online detectors to study short-lived nuclei (few µs) in a laser-plasma. As already explained in previous chapters, the main difficulty of such study comes from the large flash of X-rays just after the lasermatter interaction which can make detectors blind and unable to observe gamma rays within the short time that interests us. This is why a major aspect of this work was focused on studying how our detectors respond in this huge and very short-lived (few ps) radiation perturbation that can manifest itself on the detectors as a long duration signal. The extent of this signal is a useful index to decide the applicability of our detectors for the studies. Because the nuclear reactions to be studied in a laserplasma environment can be initiated by laser-driven particle beams, we calibrated a CMOS detector for charged particle characterisation purposes. In all, the detectors considered and the domains they have been employed are summarised in the table 4.1. CdTe was chosen because of its very good detection efficiency for the considered domain of energy compared to other well-known semiconductor detectors such as Si and Ge. The nuclei lifetime of interest for which this detector is being deployed is 9 ns. From both simulation and experiment, a 122 keV gamma signal from the 2 mm thick CdTe can exceed 4 µs depending on where between the electrodes the gamma interaction is taking place. For a short-lived nuclei in high activity, this can lead to pileup conditions difficult to separate. Moreover, this signal could only be experimentally observed from a charge-sensitive preamplifier which contributed a long fall-time of about 200 µs to the global signal. Coupled to a current-sensitive preamplifier, the signal for a 122 keV gamma could not be observed because it was too small and was lost in the noise. Furthermore, the detectors were exposed to flash X-rays from a high power laser at CELIA, but, only the CdTe coupled to a current-sensitive amplifier gave a clear signal that lasted for about 2 µs representing 500 MeV of X-ray deposited energy. With the charge sensitive amplifier the signal was totally saturated at 4 V and accompanied by a long recovery time of more than 1 ms. This therefore means the CdTe-charge amplifier is not suitable for high power laser environment.

Using silvaco TCAD tool, we simulated the signal from a CdTe representing a flash X arrival on the detector (representing 10 GeV of deposited energy) with several other gamma rays coming at different intervals. The duration of the X-ray signal was 14 µs before a clear gamma detection was possible. We noticed that a gamma signal arriving at 10 ns after the laser flash could not be observed because the gamma-created electrons were collected with the electrons created after the absorption of X-rays. The earliest detectable gamma signal after subtracting the X-ray signal was at 5 µs after the arrival of the X-ray flash. If we consider the nuclei lifetime of interest being at 9 ns, the CdTe, though very efficient for gamma ray detection of a few hundred keV, it cannot deliver fast signals that suit our quest. More over, the long duration from each gamma signal from the CdTe implies that they will be very difficult to use near a high-activity nuclear radiation source such as anticipated in the de-excitation of 84m Rb nuclei in a laser-plasma. We cannot use CdTe to detect gammas emitted with a 9 ns life time, but the detector can be adapted for the online characterisation of laser-produced X-rays. Detectors for such purposes exist. One of them is a spectrometer designed at the Commissariat à l'énergie atomique et aux énergies alternatives (CEA) [START_REF] Bonnet | Caractérisation et optimisation de sources d'électrons et de photons produites par laser dans les domaines du keV et du MeV[END_REF]. This detector uses a stack of imaging plates (IPs) separated by different thicknesses of Tungsten filters. This means that after each shot, they have to extract the IPs for the information of the deposited energy before the next shot, which is not suitable during high repetition rate laser experiments. By replacing the IPs with CdTe, information about the energy deposited after a laser shot can be obtained online. The CdTe coupled to current-sensitive preamplifiers could also be used as shot-to-shot monitors during laser experiments.

APDs were studied to detect 6.2 keV gammas with a liftime of 6.8 µs from the decay of 181m Ta in laser-plasma. The detector is silicon-based, and relatively fast thanks to its high electron and hole mobility. A gamma signal from the APD can last 4 ns FWHM. But with the APD put in a laser-plasma environment, the X-ray signal was 90 V and could only reach baseline after about 40 µs. This is obviously too much for a 6.05 µs half-life. 90 V amplitude will be too much and damage the preamplifier. We succeeded to reduce this long duration in the X-ray background by combining two APDs in differential mode via a Balun RF transformer. This led to an eventual signal span of 1 µs and a 30 mV amplitude. The result is satisfactory and suitable for 181 Ta experiment. In the future we will test the APD in the presence of X-ray flash while coupled to a preamplifier.

LaBr 3 scintillator was studied using an HPD coupled to it. We had shown that PMTs saturate in high X-ray background due to a relatively poor linearity up to 10 4 photo electrons, and HPD is a more suitable option as it sustains a linearity up to 10 8 photoelectrons. The duration of the X-ray signal using Labr 3 and HPD gives a signal duration that reaches baseline after about 200 µs. A gamma signal from the detector typically lasts for 60 ns. Therefore we expected that the X-ray signal should be within a similar duration. We were wondering if the long duration comes from the scintillator or the HPD pin diode. We decided to study the origin of this long signal via a Silvaco atlas tool by modelling the PIN diode present in the HPD. The result showed that the long duration signal was mainly due to an afterglow process in the scintillator. We also subjected the detector to X-rays from a 4.75 × 10 16 W/cm 2 laser interacting with solid target. The X-ray flash signal lasted for about 3 µs. Though this result may be promising for studies with this kind of laser intensity, it is still a far cry from detecting gamma emitted at 9 ns half life where such moderate laser intensity will be used to create the plasma medium for 84 Rb.

The issue of signal treatment was also addressed for the scintillators. On subtracting the afterglow, the dead-time was reduced from 200 µs to 15 µs. Two pileup correction algorithms were implemented and compared. The first was based on a signal template pulse from the oscillogram and the other depended on the calculated decay time for each gamma signal. The template pulse could solve pileups between signals that are more than 4 ns apart, while the other method succeeded for pileups with pulses separated by more than 20 ns.

In the case of CMOS detector, it was calibrated with a 3 MeV proton beam for the purpose of characterising laser-accelerated protons. In one case the detector was directly exposed to the beam, and the least detectable number of protons was about 1000/pixel. In another hand, the detector was covered by a thin scintillator (100 µm thick), and supported by a plastic (200 µm thick). Because the proton beam cannot pass through the plastic support to reach the scintillator, we set the scintillator facing the beam. The result showed an improvement, with a minimum proton detection of 600/pixel, which is far from a minimum of about 10 protons desired. In both cases, the CMOS detector cannot be used for our purpose.

In the coming year(s) we hope we can have enough laser beam times dedicated to performing experiments on the APD detectors. Considering that the deadtime due to the X-ray flash can be as low as 1 µss and amplitude at 30 mV using the two APDs in differential mode with the RF Balun transformer, it would now be interesting to carry out the Tantalum experiment. • Material Models specification:

After setting up the detector structure for the simulation, the material and models statements allow us change the default material parameters in silvaco, modify the characteristics of electrodes, and choose which physical models Atlas will use during the device simulation. This is made possible using the MATERIAL, CONTACT, and MODEL statements respectively.

• Numerical Method Selection:

Numerical methods are necessary for atlas to calculate solutions to semiconductor device problems. The approach to solving the drift diffusion equations and other relevant equations are taken into account by the numerical method specified. This can be done with the METHOD statement. The numerical methods in Atlas are GUMMEL, NEWTON and BLOCK.

• Solution Specification:

Atlas solves DC, AC small signal, and gives transient solutions. When the voltage is defined on the electrode for example, It calculates the current through each electrode. Other information that can be calculated by atlas are internal quantities such as the carrier concentrations and electric fields through out the device which can be extremely difficult or sometimes impossible to measure. The result is saved in a file using the LOG or SAVE statements, and can be directly analysed after the simulation or during the simulation with TONYPLOT.

Basic equations for transient studies

In The continuity and the transport equations describe how the electron and hole densities evolve as a result of transport processes, generation processes, and recombination processes as shown in equations 4.3.3 and 4.3.4.

∂n ∂t = 1 q div J n + G n -R n (4.3.3) ∂p ∂t = 1 q div J p + G p -R p (4.3.4)
where n and p are the electron and hole concentration,q is the magnitude of the charge on an electron, J n and J p represent the electron and hole current densities, G n and G p are electron and hole generation rates, and R n and R n are the recombination rates for electrons and holes While the poisson equation and the carrier continuity equations combine to give the general framework for device simulation, further equations are to be specified in order to provide suitable models for J n , J p , G n , G p , R n , and R p .

The simplest and a useful model of charge transport or current density is the Driftdiffusion model, which is derived using Boltzmann's transport theory. This model has the attractive feature of not introducing any independent variables in addition to ψ, n and p. From the model, the current densities in the carrier continuity equations, can be approximated as: where k is the boltzmann's constant, and T L is the local temperature in the detector.

J n = qnµ n E n +
Charge transport models such as the Energy balance transport model, derive the current densities from higher order treatment of the Boltzmann's transport equation with couplings of the current density to the carrier temperature, or energy.

• Generation model Single Event Upset Model was used for the generation rate of electrons and holes in the semiconductor device. In the model, a single event function can be used to specify the entry and the exit of the single event particle such as a proton or a photon, including the radius, and the time of arrival of the event in the device. The expected quantity of energy to be deposited in the device is converted to equivalent charges of electron-hole pairs using the energy need to create one of the pairs for that material.

In addition, it is possible to define different functions that model the behaviour of the energy deposition in the device using a C-interpreter file. After running this file in the Simulator, it outputs the generation rates for defined regions of the material.

Time dependence in charge generation is taken into account using:

T (t) = 2 × e -( t-T 0 Tc ) 2 T c √ πerf c(-To Tc ) , (4.3.9)
where t, T 0 and T c , are run time, instant of charge creation, and time width of created charge, all in seconds. In another sense for an instant x-ray deposition, one can make a rough approximation that the charge deposition has taken place from an instant in time T 0 and within a time T c . The recombination rate was accounted for by specifying the Shockley-Read-Hall (SRH) model in Silvaco.

e n e e 2

 2

Figure 1 . 2 :

 12 Figure 1.2: Example of measured carbon ion energy spectra from laser interaction with intensity 6-7 × 10 20 W cm -2 on Al target. (from [26]).

Figure 1 . 3 :

 13 Figure 1.3: Schematic illustration of TNSA. The intensity f is normalised by the peak intensity f 0 . Dark blue shows the generated the electric field with E Z being the field in the target-normal direction (from [33]).

Figure 1 . 4 :

 14 Figure 1.4: Proton spectrum and conversion efficiency as reported by Snavely et al. [34].

Figure 1 . 5 :

 15 Figure 1.5: Survey of TNSA cut-off energies measured in experiments so far at different laser facilities; plotted vs. irradiance and labeled according to pulse duration (taken from [30]).

Figure 1 . 7 :

 17 Figure 1.7: Processes of X-ray generation: (a) summarising the processes in plasma [44] (b) the main contribution outside the plasma is when the accelerated high energy electrons are stopped by objects in the chamber of the experimental chamber wall [43].

Figure 1 . 8 :

 18 Figure 1.8: Bremsstrahlung spectrum of a 125-µm-thick Al target irradiated at 10 19W cm -2 ) (adapted from[START_REF] Norreys | Observation of a highly directional -ray beam from ultrashort, ultraintense laser pulse interactions with solids[END_REF]).

Figure 1 . 10 :

 110 Figure 1.10: Direct nuclear excitation processes in hot dense plasma (a) photoexcitation, and (b) electron inelastic scattering.

Figure 1 . 11 :

 111 Figure 1.11: Indirect nuclear excitation processes in hot dense plasma (a)nuclear excitation by electron transition, and (b) nuclear excitation by electron capture.

Figure 1 . 12 :

 112 Figure 1.12: Nuclear de-excitation processes in a hot dense plasma (a)internal conversion (b) bound state internal conversion and (c) direct gamma emission.

Figure 1 . 15 :

 115 Figure 1.15: Scheme describing the indirect de-excitation of an isomer.

  state with a 20.26 min half-life at an energy of 463.6 keV above the J π = 2 -ground state. The isomer then decays to the ground state by two gamma ray transitions 215.4 and 248.1 keV, or the emission of 463.62 keV gamma. The nucleus has also a J π = 5 -at an energy of 466.6 keV above the J π = 2 -ground state, having a much shorter half life of 9 ns lying just 3.498(6) keV above the J π = 6 -state . This isomeric state decays to the ground state through two γ-ray transitions at 218.5 and 248.1 keV respectively (figure 1.16).

Figure 1 . 16 :

 116 Figure 1.16: Partial level scheme of 84 Rb (adpated from [52]).

Figure 1 . 19 :

 119 Figure 1.19: Scheme of experimental Setup. The detector is one suited to detected few hundreds keV gamma

Figure 1 . 20 :

 120 Figure 1.20: Partial and total mass attenuation coefficients of lead as functions of the photon energy (taken from [66]).

Figure 1 .

 1 Figure 1.20 displays attenuation curves of the above discussed processes of photon interaction, in lead material, as functions of the photon energy. At energies less than 1 MeV, photoelectric effect is the most dominant, and as this energy is well exceeded, Compton and pair production are the leading processes.

the figure 1 Figure 1 . 21 :

 1121 Figure 1.21: Ion collision with electrons(adapted from D. Cussol [67])

3 . 5 )

 35 here, Z p and Z t are the nuclear charges of the projectile and target, m e and e are the mass and charge of the electron,v is the projectile velocity, β = v/c where c is the speed of light, C is the shell correction factor and δ is the density effect correction, while I is the mean ionization energy of the target atom or molecule.

Figure 1 . 22 :

 122 Figure 1.22: Proton stopping power in silicon

Figure 1 . 23 :

 123 Figure 1.23: Distribution of X-rays after laser interaction (blue), then attenuated by lead (orange), and finally absorbed by LaBr3 scintillator(red). About 40 GeV of X-rays was estimated to be deposited in the scintillator despite employing a 10 cm lead shield.

Figure 1 . 24 :

 124 Figure 1.24: A signal of detected EMP at the LULI2000 facility after a laser interaction.

figure 1 .

 1 figure 1.25, three gamma signals have arrived at very close intervals in the detector causing a pileup. One can implement pileup correction algorithms offline to enable the restoration of the signals.

Figure 1 . 25 :

 125 Figure 1.25: Simulated pileup of gamma pulses. The red line showing the region to be extrapolated to reconstruct each gamma signal of the detector.

Figure 1 . 26 :

 126 Figure 1.26: Schematic block diagram of a typical detection-acquisition system for γ-ray spectroscopy in a conventional accelerator. Typical pulse shapes produced by each element and the final result (from [75]).

Figure 1 . 27 :

 127 Figure 1.27: Schematic block diagram of a typical detection-acquisition system for γ-ray spectroscopy in a laser plasma environment.

  valence bands (VB), and E c due to the conduction bands (CB) respectively, are below and above the energy gap. Energised electrons leave off holes in the valence band as they migrate to the conduction band. Their motion in these bands is responsible for conduction in semiconductors. Other materials are insulators, which have very large band gaps typically more than 6 eV, or conductors that have no band gap (see figure2.1).

Figure 2 . 1 :

 21 Figure 2.1: Simplified energy band structure diagrams for insulators, semiconductors, and conductors.

  it has sufficient energy to jump to the conduction band for conduction purposes. The material is thus n-doped because of the addition of an extra electron. On the other hand if a group 3 atom (acceptor) like Boron or Aluminium is added, it makes only three covalent bonding with the silicon atom, thus creating a hole. This hole can have energy in the band gap very close to the valence band so that electrons in that valence band jump to this energy level leaving a hole behind. Consequently, the detector material is p-doped because of the extra hole added. Depending on the type of dopant the Fermi level is shifted either towards the valence or the conduction band (figure 2.2).

Figure 2 . 2 :

 22 Figure 2.2: Simplified energy band diagrams for (a) intrinsic, (b) n-type, and (c) p-type semiconductors.E F i , E F n and E F p are Fermi energy levels for intrinsic, n-type and p-type semiconductors respectively. In all cases, np = n 2 i .

Figure 2 . 3 :

 23 Figure 2.3: Schema showing charge creation to signal formation in semiconductor.

Figure 2 . 4 :

 24 Figure 2.4: Simple charge sensitive amplifier.

Figure 2 . 5 :

 25 Figure 2.5: Transimpedance amplifier (Chaniotakis and Cory. 6.071 Spring 2006).

Figure 2 . 6 :

 26 Figure 2.6: Semiconductors and their energy levels. (a) Separate n-and p-type crystals. (b) Formation of pn-junction. When n-and p-type crystals are brought in contact, flow of charges starts which continues till the Fermi levels E f of the two materials coincide.

Figure 2 . 7 :

 27 Figure 2.7: A simplified structure (a) of a reverse biased PIN diode and its idealized electric field profile (b)

Figure 2 . 8 :

 28 Figure 2.8: Total and photoelectric efficiency of 1-mm thick CdTe compared with Ge and Si (from [75]).

Figure 2 . 9 :

 29 Figure 2.9: CdTe in aluminium cylinder. Signal is read from the positive pin.

  code-name CdTe coupled to charge sensitive preamplifier as CdTe-C (configuration in figure 2.10), and CdTe-T, for being coupled to a current-sensitive preamplifier (configuration in figure 2.11).

Figure 2 . 10 :

 210 Figure 2.10: CdTe coupled to a charge amplifier, CdTe-C.

Figure 2 . 11 :

 211 Figure 2.11: CdTe coupled to a current amplifier, CdTe-T.

  Fe, and leading to 14.4, 122, and 136 keV probable gamma emissions with intensities per 100 disintegration of 9.162, 85.60 and 10.68 respectively[START_REF] Cea | Table de radionucléides: Co-57[END_REF]. The source is therefore important for us because it has a major energy peak at 122 keV, which is close to the photon energy of the de-exciting 84m Rb.

Figure 2 . 12 :

 212 Figure 2.12: Spectrum of 57 Co source from CdTe-C (in blue). A Gaussian fit is in red.

Figure 2 . 13 :

 213 Figure 2.13: Geant4-simulated Spectrum of 57 Co source from CdTe (in black), rescaled by a 9 % energy resolution (red) (from Arnaud Huber).

Figure 2 . 14 :

 214 Figure 2.14: Computed charge collection efficiency (CCE) vs. the interaction positions (from cathode) of incoming photon.

Figure 2 . 15 :

 215 Figure 2.15: CdTe-C typical signal of a 122 keV from a 57 Co source.

Figure 2 . 16 :

 216 Figure 2.16: Sampled signals of 122 keV from CdTe-C with focus on the rising part of the pulse. Depending on their distance of interaction from the cathode face, the peaking times will vary despite maintaining similar amplitudes. From a-d, blue and black have been used to denote the regions dominated by charge carrier type (e or h) as they drift to their electrodes.

Figure 2 . 17 :

 217 Figure 2.17: CdTe deduced charge from preamplifer(in cyan)-and derived current(red)-signal.

  Computer-Aided Design (TCAD) simulation tools. Technology Computer-Aided Design involves the use of computer and physics-based simulations for the development, optimisation, and understanding of semiconductor process technologies and devices. Such tools give insights into the electrical properties of semiconductor materials by solving the charge carrier transport equations. Some of the leading suppliers of TCAD software packages are Synopsis, Silvaco and Crosslight. In this work Silvaco TCAD has been deployed for device simulation of electrical properties of semiconductors irradiated by photons.

Figure 2 . 18 :

 218 Figure 2.18: Geometry of CdTe detector designed in Silvaco Atlas 4.83 × 4.83 × 2 mm 3 .

Figure 2 . 19 :

 219 Figure 2.19: 2D view of the simulated CdTe geometry showing the meshed regions.

Figure 2 . 20 :

 220 Figure 2.20: Structure of CdTe detector: in purple, on both sides of the crystal, are the cathode (left) and anode (right) electrodes.

  The current-voltage (I-V) characteristics of the detector was obtained experimentally via a picoammeter, and compared to that gotten from simulation as a means of calibrating the simulation and determining the resistivity of the detector(illustrated in figure2.21). We were able to estimate the detector's resistance at 4.7 × 10 9 ± 4 × 10 8 Ω. We can also see that both simulation and experimental results are in agreement.

Figure 2 . 21 :

 221 Figure 2.21: IV characteristics of CdTe : in blue experiment;in green, simulation

  2.22 is the simulation result of the current after a 122 keV gamma interaction in three different parts of the CdTe detector: near the cathode (15 µm away ), around the middle of the detector(1070 µm), and closer to the anode (10 µm away). The output current have been collected from the anode electrode and plotted with respect to the transient time. The amplitude of the signals are about 17 nA (on subtracting the baseline due to the bias current). This value is of the same order of magnitude with 9 nA obtained from Ramo's theorem. Also, two components of the current are clearly seen in the three cases of the simulation, and can be explained (below) by the interplay of the mobility of the charge carriers and the distances the charges must travel to reach their respective electrodes while inducing current.

Figure 2 . 22 :Figure 2 . 23 :

 222223 Figure 2.22: Current-time simulation result for 122 keV gamma interacting at three different points of the CdTe detector.In red, the point of interaction is close to the cathode; green, when interaction is around the middle; blue, when interaction is closer to the anode.

Figure 2 . 24 :

 224 Figure 2.24: Conduction current profile (a) 1 µs and (b) 4 µs into the simulation for a gamma interaction in the middle of the CdTe crystal.

  .4) where A = 4 × 10 5 keV, and b = 1.4 × 10 -4 /µm considering a distribution of 50 µm per bin.

Figure 2 . 25 :

 225 Figure 2.25: Simulated energy deposition distribution profile from X-ray flash in CdTe.

Figure 2 . 26 :

 226 Figure 2.26: Simulated X-ray flash signal from CdTe detector.

Figure 2 . 27 :

 227 Figure 2.27: Conduction current density profile (a) 10 ns and (b) 5 µs into the simulation for a gamma interaction in the middle of the CdTe crystal.

Figure 2 . 28 :

 228 Figure 2.28: Conduction current density profile (a) 10 µs and (b) 11 µs into the simulation for a gamma interaction in the middle of the CdTe crystal.

Figure 2 .

 2 Figure 2.29: 1 D current density profile (a) for electrons and (b) for holes.

  with pulse duration of few ps, energy of about 190 mJ. About 60 % of the laser energy is focused on a 12 µm diameter spot of Ta or Mo target with 70 and 25 µm thicknesses respectively. From shot to shot the x-rays energy and emission distributions were stable and reproducible. The estimated intensity of the laser is approximately 4.75 × 10 16 Wcm -2 . The typical spectrum from the X-ray spectrometer positioned in the chamber( in figure2.30, to be explained) about was obtained using a charge-coupled device (CCD). The different peaks on the spectrum are the characteristic X-ray lines related to the target materials.• Chamber, detector position and signal acquisition: The experimental chamber is as schematically shown in figure2.30. The CdTe detector is placed some 60 cm (including distance from the feed through) away from the point of interaction and about 80 degrees to the normal of the target. The output from the detector is connected directly to a 12 bits, and 1 GHz bandwidth tektronix oscilloscope.

Figure 2 . 30 :

 230 Figure 2.30: Deployed CdTe setup for exposure to laser-created X-rays.

Figure 2 . 31 :

 231 Figure 2.31: Typical X-ray spectrum after laser interaction with Molybdenum, Gadolinium, and Tantalum targets (private communication from Fabien DORCHIES).

Figure 2 . 32 :

 232 Figure 2.32: CdTe-C response to X-ray flash at a detector bias voltage of 70V.

Figure 2 . 33 :

 233 Figure 2.33: CdTe-T response to X-ray flash at a detector bias voltage of 70V.

Figure 2 . 34 :

 234 Figure 2.34: CdTe-T response to X-ray flash at different bias conditions: 10, 20, 50, 70 and 100V. The sharp spikes in the early part of the signal at low voltages, such as from 50 to 10 V are likely due to pronounced perturbation contributions.

Figure 2 . 35 :Figure 2 . 36 : 38 × 10 - 3 /

 23523638103 Figure 2.35: Scheme of geometrical setup to obtain the depth profile of photon energy deposited in the detector

Figure 2 . 37 :

 237 Figure 2.37: 3D structure of the CdTe biased at 70 V, irradiated from the Cathode face, showing the map of the total current density 10 ps after the energy deposition.

Figure 2 . 38 :Figure 2 . 39 :

 238239 Figure 2.38: Flash X-ray signal response from CdTe: (a) Experimental, (b) Simulation.

Figure 2 . 40 :

 240 Figure 2.40: CdTe 1D depth profile of the total current density at different times during the simulation. The cathode electrode is before zero µm of the x-axis while the anode is after 2000µm .

Figure 2 . 41 :

 241 Figure 2.41: Electron current density profile for a 70 V biased CdTe at different times in a simulation.

Figure 2 . 42 :

 242 Figure 2.42: Hole current density profile for a 70 V biased CdTe at different times in a simulation.

2. 43 ,

 43 the concept is summarised. The set arrival time for the gammas are 10 ns, 5 µs, 11 µs and 21 µs after the laser shot. These times were spaced to minimise the chances of signal pileup. For a detector volume of 4.67 ×10 -2 cm 3 , and an ionisation energy of 4.43 eV, this 10 GeV energy deposition corresponds to an electron-hole pair density of 5 × 10 10 /cm 3 . While the gammas of 122 keV, deposited in a 3.142 ×10 -12cm 3 volume corresponds to 10 16 /cm 3 of electron-hole pair density.

Figure 2 . 43 :Figure 2 . 44 :

 243244 Figure 2.43: Schematic illustration of the CdTe targeted by flash X-rays, then followed by gamma photons arriving at different times ∆t i after the laser shot (a). After irradiation, red (circle) is charge creation by one gamma, and in white (x symbol) are charges created by X-rays (b).

Figure 2 . 45 :

 245 Figure 2.45: Current-time simulation result for an X-ray flash, and four 122 keV gammas arriving 10 ns, 5 µs, 11 µs, and 21 µs after the flash.

Figure 2 . 46 :

 246 Figure 2.46: Current-time simulation result for an X-ray flash (green) and X-ray flash combined with gammas arriving at different times (red).

Figure 2 . 48 :

 248 Figure 2.48: Avalanche photodiode Operating principle of an avalanche photodiode based on a p + -i-p-n + doping profile. The left part is the electric field profile of the APD and the right part is the schematic of the avalanche process [122].

Figure 2 . 49 :

 249 Figure 2.49: APD structures and thier field distribution: Reversed (a) and Bevelededge (b) (from [125]).

Table 2 . 3 :

 23 Some properties of the two APDs (type: S12435-0305) at a gain M=100. Parameter APD30 APD31 Effective active area (mm 2 ) Vbr ( at 25 0 C) 601 596 Vbr temperature coefficient ( V/ 0 C) 3.5 3.5

Figure 2 . 50 :

 250 Figure 2.50: APD circuit with a transimpedance amplifier.

Figure 2 . 51 :

 251 Figure 2.51: APD-amplifier signal of 5.9 keV from 55 Fe source

Figure 2 .

 2 Figure 2.52: 5.9 keV peak of 55 Fe at room temperature in blue, in red is a Gaussian fit. The FWHM is 49 mV.

Figure 2 . 53 :

 253 Figure 2.53: Plot of resolution with different temperatures for 55 Fe source.

Figure 2 . 54 :

 254 Figure 2.54: Simulated photon detection efficiency for a 145 µm Silicon detector.

Figure 2 . 55 :

 255 Figure 2.55: 57 Co energy spectrum from APD31 (with 50kV/A preamplifier).

Figure 2 . 56 :

 256 Figure 2.56: Calibration of APD31 (with 50kV/A amplifier) only.

Figure 2 . 57 :

 257 Figure 2.57: Scheme showing two APDs combined to cancel-out signal as final output on exposure to radiation at the same time.

Figure 2 . 58 :

 258 Figure 2.58: Functional scheme of the bought Balun RF transformer(reference: TP104, from Macom company).

  Fe. Which is attributed to the insertion loss of the transformer on the input signals. For example, an amplitude drop from 230 to 191 mV corresponds to a 1.61 dB insertion loss. The calibration plot is captured in figure 2.60 for one APD and two APDs combined via the RF transformer and connected to the 50kV/A preamplifier.

Figure 2 . 59 :

 259 Figure 2.59: 57 Co energy spectrum from RF transformer with source placed on APD31 (with 50kV/A preamplifier).

Figure 2 . 60 :

 260 Figure 2.60: APD calibration: for APD31 combined with APD30 via a RF transformer(green), and APD31 only (blue). Both were with the HCA-100M-50k-C 50kV/A transimpedance preamplifier.

Figure 2 . 61 :Figure 2 . 62 :

 261262 Figure 2.61: An APD detector with bias, LED, and output cables

Figure 2 . 63 :

 263 Figure 2.63: Response from one APD detector (a) is the raw oscillogram and (b) a zoom showing the full amplitude of the signal in 0.4 µs (c) a zoom into the duration of the signal to reach baseline.

Figure 2 . 64 :

 264 Figure 2.64: Response from an APD detector to flash X-rays with successive LED pulses. The plateau in the figure is due to oscilloscope saturation for the chosen vertical scale.

Figure 2 . 65 :

 265 Figure 2.65: Two APDs circuit connection using the Balun RF transformer.

Figure 2 . 66 :

 266 Figure 2.66: Attenuated signal response from two APD detectors combined (a) Is the raw oscillogram and (b) a zoom showing the first detected LED near 1 µs.

Figure 2 . 67 :

 267 Figure 2.67: Scheme of CMOS readout architecture. C and A are pixel-assigned capacitors and amplifiers (from Teledyne princeton insruments)

Figure 2 . 69 :

 269 Figure 2.69: LED pulse combinations for a fixed exposure time. The first LED pulse triggers the detector for acquisition while the second is to be imaged.

Figure 2 . 70 :

 270 Figure 2.70: Exposure time test. (a) Mean gray values for different exposure times at increasing LED pulse width, where the first point of saturation indicates the real exposure time. (b) colorsracted real exposure times plotted with the set ones

Figure 2 . 71 :

 271 Figure 2.71: RadEye background response following different set exposure times in air (blue), and in vacuum (orange).

  the temperature between -40 to 40 o C. During these different temperatures, a fixed detector exposure time was set. The result of the test is plotted in figure 2.72, where at different exposure times, shown by the different colours, the detector was exposed to temperatures. For the different exposure times, the mean background seems to converge at 0 o C near a 115 mean gray value. It shows that this background could not be lowered by cooling.

Figure 2 . 72 :

 272 Figure 2.72: RadEye background response to varying temperatures at different exposure times. The colour-shaded portions correspond to the range of the error bar on each data point (show in appendix how to obtain the error bars).

Figure 2 . 74 :

 274 Figure 2.74: Response of RadEye detector on irradiation by a beam of protons. The numbers on the vertical and horizontal axes of the image reveal the positions of each pixel. The irradiated region is situated around pixel row 600 and column 600. A zoomed view has been added in the figure to try to show the irradiated pixels.

Figure 2 . 75 :

 275 Figure 2.75: Zoomed view of the normalised RadEye detector response to different quantities of protons per pixel at the same energy of 3 MeV.

Figure 2 . 76 :

 276 Figure 2.76: Charge sharing effects. A zoomed view on the right, revealing that some neighbouring pixels share charges from the targeted pixels.

Figure 2 . 77 :

 277 Figure 2.77: Taking region of interest from image after irradiation at 6281 ± 942 protons per pixel.

Figure 2 . 78 :

 278 Figure 2.78: Profile plot in steps from image irradiated at 6281 ± 942 protons per pixel.

Figure 2 . 79 :

 279 Figure 2.79: Calibration plot fitted with y = 0.0144x after background subtraction.

Figure 2 . 80 :

 280 Figure 2.80: Schematic view of CMOS-scintillator configuration.

Figure 2 . 81 :

 281 Figure 2.81: Proton energy deposition distribution in polypropylene plastic simulated in Geant4 for a 3 MeV proton beam, stopped at 140 µm.

(a)

  1200 protons (b) 600 protons (c) zoom view at 1200 protons (d) Zoom view at 600 protons

Figure 2 . 82 :

 282 Figure 2.82: CMOS-scintillator response to different quantities of protons at 3 MeV, with the circled regions showing areas irradiated by uv photons from the scintillator. The high intensities in the lower part of the image in a and b are due to non-uniformity in the detector gain.

Figure 2 . 83 :

 283 Figure 2.83: Profile plot in the scintillator-CMOS configuration (a) for 1200 protons, and (b) for 600 protons per spot irradiation.

Figure 2 . 84 :

 284 Figure 2.84: Simulated energy deposition distribution of 4 MeV protons in polypropylene (0-200 µm) and Gadolinium phosphor (200-250 µm).

Figure 3 . 1 :

 31 Figure 3.1: X-ray excited emission of CeBr3 and LaBr 3 :5% Ce with their different thicknesses [152].

Figure 3 . 2 :

 32 Figure 3.2: Production of prompt (path A) and delayed (path B) scintillation light by incident radiation. [80].

Figure 3 . 3 :

 33 Figure 3.3: Afterglow curves of CsI:In (curve 1) and CsI:Tl (curve 2), measured after 2 seconds of 130 kV X-ray irradiation [158].

Figure 3 . 4 :

 34 Figure 3.4: schema of PMT in the process of photo-electron generation, acceleration and multiplication.

Figure 3 . 5 :

 35 Figure 3.5: Scheme of experimental setup for gamma spectroscopy in laser environment [31].

Figure 3 . 6 :

 36 Figure 3.6: Energy of the detected gamma versus the arrival time in sync with the instant of the laser shot, showing detected 257 keV from 90m Nb using a PMT [48].

Figure 3 . 7 :

 37 Figure 3.7: Oscillogram from PMT at ELFIE (LULI, in France) laser facility, showing long detector recovery time of about 3 ms (pink-shaded region) after X-ray irradiation from a high power laser interaction on a solid target [31].

Figure 3 . 8 :

 38 Figure 3.8: Oscillogram from PMT at GSI showing long detector recovery time of about 1 ms after X-ray irradiation from a high power laser interaction on a gas target.

Figure 3 . 9 :

 39 Figure 3.9: Scheme of HPD coupled to a scintillator.

Figure 3 . 10 :

 310 Figure 3.10: Linearity measurement of HPD pulse amplitude (right scale, squares, bottom distribution) and pulse charge integral (left scale, triangles and circles, top and left distributions) versus light pulse amplitude. The two charge integral distributions do not line up because of different calibrations of two different measurement setups.No departure from linearity in pulse amplitude is found in the charge integral[START_REF] Arnaudon | Proximity focussed hybrid photo diode characteristics evaluations[END_REF].

Figure 3 . 11 :

 311 Figure 3.11: PMT saturation measurement: phototube response normalised by the expected response at +20 and -4 o C (from [175]).

Figure 3 . 12 :

 312 Figure 3.12: Designs of Hybrid Photodiodes: a) proximity focusing, b) cross focus-ing, c) fountain focusing.[START_REF] Joram | Large area hybrid photodiodes[END_REF]

Figure 3 . 13 :

 313 Figure 3.13: HPD gain with voltage (from Photonis).

Figure 3 . 14 :

 314 Figure 3.14: Scheme of PIN diode and electric field distribution of E and T type HPDs. ( [176])

Figure 3 . 15 :

 315 Figure 3.15: Recorded oscillogram after a laser shot: up to 2 ms (a) and up to 200 µs (b) showing the instant of the laser shot at 0s. The repetitive pulses (seen clearly in 'a') are LED pulses for calibration, while the smaller pulses are the detected gammas. The long exponential signal comes from the X-ray deposition.

Figure 3 . 16 :

 316 Figure 3.16: Oscillogram undergoing treatment: in blue is the original oscillogram; orange is the baseline on the long exponential signal x-ray pulse; and green is the extracted signal from the original pulse.

(

  comparative images of signals are shown in figure 3.19).

Figure 3 . 18 :

 318 Figure 3.18: Gamma spectrum.

Figure 3 . 19 :

 319 Figure 3.19: Two 122 keV signals: (left) obtained with an 8 bits oscilloscope, (right) with a 14 bit digitizer.

Figure 3 . 20 :

 320 Figure 3.20: experimental current signal of 511 keV from LaBr 3 coupled HPD.

Figure 3 . 21 :

 321 Figure 3.21: simulated 3D structure of PIN diode detector with Silicon (gold) and electrodes (purple) a) 1D view of the doping profile: n doped from left, slightly n doped in-between (150 µm layer), and p doped on the right b). The highly doped n and p sides were ∼ 1 µm thick.

Figure 3 .

 3 Figure 3.22: 1 D electric field distribution in PIN diode of thickness 150 µm, for different n and p dopant concentrations. The direction of the electric field is also shown by the arrow.

The penetration depth of a 9

 9 keV electron is about 1.1 µm in Silicon, this was used to determine the depth of irradiation in the diode. Since the PIN diode is a T-type structure, it implies that the irradiation is opposite and far from the pn junction ( from the n side, see figure 3.14), that is, irradiating from the low electric field side (from 0 µm).

Figure 3 .

 3 Figure 3.23: 2 D view of simulated electric field distribution (V/cm) on PIN diode after 511 keV photon detection from LaBr 3 scintillator, 15 ns later (right: expanded colour scale for the electric field).

Figure 3 . 24 :

 324 Figure 3.24: Projection of the electric field distribution, from axis y=0 µm (from figure 3.23).

Figure 3 . 25 :

 325 Figure 3.25: HPD current signal from 511 keV photon: experiment and simulation.

Figure 3 . 26 :

 326 Figure 3.26: HPD current signal from 90 PeV of total energy deposition (vertical axis in log).

Figure 3 . 27 :

 327 Figure 3.27: 2D electric field profile 40 ns after irradiation.

Figure 3 . 28 :

 328 Figure 3.28: 1D electric field profile 40 ns after irradiation.

Figure 3 . 29 :

 329 Figure 3.29: 1D evolution of the electric field in the PIN diode profile with elapsed time since the laser irradiation.

Figure 3 . 30 :

 330 Figure 3.30: HPD-pin diode signal at no bias voltage (vertical axis in log).

Figure 3 . 31 :

 331 Figure 3.31: 1D electric field profile at no PIN diode bias.

Figure 3 . 32 :

 332 Figure 3.32: HPD-pin diode signal at a photocathode voltage of 1 V (vertical axis in log).

Figure 3 .

 3 Figure 3.33 is a scheme of the experimental set-up showing the position and angle of photosensors coupled to LaBr 3 relative to the centre of the experimental chamber.The chamber is clindrical and so circular from the top view with a diameter of 100 cm. The walls of the chamber are made of Aluminium with a thickness of 1 cm. The laser arrives at about 45 0 to the target normal.PMTs coupled to LaBr 3 were placed outside the chamber to avoid saturation as previously discussed and to serve as monitors to judge the stability in the quantity and energy of the X-rays produced. The two PMTs were code-named PMT1 and PMT4. PMT1 is 40 0 right of the incoming laser, while PMT4 is 45 0 left of the laser.Both PMTs are about 51 cm distance from the TCC. The HPD was placed outside the chamber, and facing the TCC while in front of a 25 mm diameter opening blocked by a mylar material of 75 µm thickness. The output from all detectors are read and recorded from a 12 bits Tektronix oscilloscope over a 50 Ω terminator.

Figure 3 . 33 :

 333 Figure 3.33: Top view of the experimental chamber at CELIA, showing the different placement positions and angles of scintillator coupled photosensors.

Figure 3 . 34 :

 334 Figure 3.34: Photodetector calibration. Top,from left to right: PMT1 and PMT4. Bottom: HPD.

Figure 3 . 35 :

 335 Figure 3.35: X-ray flash signal from several shots a) PMT1 and b) PMT4, recorded at the same time.

Figure 3 . 36 :Figure 3 . 37 :

 336337 Figure 3.36: Response with HPD coupled to LaBr 3 (blue) and CeBr 3 (orange).

Figure 4 . 1 :

 41 Figure 4.1: Flowchart of the signal treatment procedure applied from when data was acquired to when histograms are generated.

Figure 4 .

 4 Figure 4.2 is a scheme of an experimental setup showing the laser-matter interaction that creates particles including protons and X-ray flashes. In the same figure, is a secondary Zirconium(Zr) target upon which the protons are used to initiate an activation for the creation of very short lived Niobium (Nb) radioisotopes. Some of

Figure 4 . 2 :

 42 Figure 4.2: Scheme of an experimental setup to perform nuclear activation: From the left, the laser(in red) interacts with the first target, generating many particles including protons and photons. Then the protons are used to initiate nuclear activation on a second target(Zr) producing nuclear isomers of 90m Nb whose gammas we want to detect. The scintillator detector is close to the second target and connected to an oscilloscope. Not only gammas are detected, large quantities of Xrays too. Modified from [31].

Figure 4 .

 4 Figure 4.3 is an example of a typical oscillogram taken after a laser shot ( from experiment in figure 4.2). The repetitive pulses are the injected LEDs, and the short irregular pulses the detected gamma photons. It shows the instant of the laser shot

Figure 4 . 4 :

 44 Figure 4.4: Bode diagram, with the black dot showing a cutoff frequency at 100MHz and a frequency response of about -3 dB, as filtering condition for noise reduction.

Figure 4 . 5 :

 45 Figure 4.5: (a) Example of a gamma signal before and after pre-treatment. Blue is the raw signal and orange is the de-noised signal: the filter parameters are chosen to preserve the shape of the gamma signal after filtering (b) EMP-perturbed signal.

Figure 4 . 6 :

 46 Figure 4.6: Part of oscillogram data showing random gamma and perodic LED pulses built on the large exponential-like afterglow signal. Signal correction by baseline subtraction must be done before estimating the energies that these pulses represent.

Figure 4 . 7 :

 47 Figure 4.7: (a)Part of an oscillogram in process of treatment in blue is the raw data, in Orange is the rough baseline obtained by extracting local minima around a pulse which can easily be fitted or smoothed(b) Shows a zoom into the few of the pulses in blue, roughly decoupled by a linearly fit between pulse minima(orange).

Figure 4 . 8 :

 48 Figure 4.8: Double exponential fit on data (a) is the fit on the raw data (b) shows the overlap of fit on pulses.

Figure 4 .

 4 Figure 4.9a shows the filtered baseline (orange) and the fitted baseline(green) on the raw signal(blue) and 4.9b shows a zoom into the overall signal within few µs into the data, showing that the filtered baseline extracts the baseline from the data better than the fit function used in equation 4.1.2.

Figure 4 . 9 :

 49 Figure 4.9: Comparing exponentially fitted afterglow and filtered one (a)In orange and green are the estimated baselines on afterglow after using low pass filter and exponential fit (b) A zoom showing the filtered baseline relatively well placed at the base of each pulse compared to the fit (in green).

Figure 4 . 10 :

 410 Figure 4.10: (a) Part of an Oscillogram data in process of treatment, blue is the raw data, orange is the baseline, green is the offset-free signals (b) Is a zoom into some of the pulses present (first detected gamma in red).

Figure 4 . 11 :

 411 Figure 4.11: Part of Oscillogram data showing pileup before baseline correction in blue, and in green, pileup after baseline correction.

Figure 4 . 12 :

 412 Figure 4.12: Method of pileup correction by[START_REF] Lee | Pulse pileup correction method for gamma-ray spectroscopy in high radiation fields[END_REF]

  a code that identifies the pileup start point t s using the times t p1 and t p2 by estimating the time where the lowest amplitude between the two peak times exits. Once the pileup start point is known corrections can commence (see figure4.13).

Figure 4 . 13 : 4 . 1 . 6 . 2

 4134162 Figure 4.13: Simulated pileup occurrence, showing conditions and processes of pileup detection and correction. When a Pileup is detected, the extrapolation is done only starting from the point (t s , V s ) in time and amplitude using a template pulse.

Figure 4 . 14 :

 414 Figure 4.14: Normalised template pulses spanning around 1µs of data (a) for a gamma pulse, of about 2 ns of rise time and 60 ns of decay time, and (b) for a LED pulse of about 10 ns rise time and 12 ns decay time.

.1. 7 )Figure 4 . 15 :

 7415 Figure 4.15: Zoom into oscillogram before and after correction by calibration LED, using equation 4.1.7. The orange lines are the raw data, with initial amplitudes marked by green stars, and the blue lines representing gain corrected data with new amplitudes marked in red.

Figure 4 . 16 :

 416 Figure 4.16: A gamma signal before and after correction by calibration LEDs, using equation 4.1.7.

4. 1 . 8

 18 Peak voltage to EnergyOur detectors were calibrated from amplitude in voltage to energy, using nuclear radiation sources. The obtained calibration function was used to get the energy equivalent from the amplitude of the signals obtained after every shot of the laser in the chamber.

Figure 4 .

 4 17 is a histogram of the amplitudes in volts of all the gamma pulses detected and figure 4.18 is a plot of the calibration from voltage V to energy in keV. Radioactive sources with energies within the range of energies to be measured in our experiment are suggested for calibration next time.

Figure 4 . 17 :

 417 Figure 4.17: Pulse voltage amplitude plot

Figure 4 . 18 :

 418 Figure 4.18: Pulse voltage amplitude to energy calibration

Figure 4 . 19 :

 419 Figure 4.19: Gamma spectrocopy of 90m Nb energies from laser accelerated protons on 90 Zr. The 122 keV line is in formation.The inset verifies the decay of 122 keV, thus showing that gamma spectroscopy at some µs after the laser shot is possible.

Figure 4 . 20 :

 420 Figure 4.20: Samples of input gamma pulses with noise. From (a) to (d) have pulse amplitudes about 0.14, 0.025, 0.020, and 0.36 V correspond to energies of 1067, 171.1, 122.3 and 257 keV respectively. Amplitudes of the input gamma pulses are proportional their energies in keV; increasing signal to noise ratios SNR in dB is also observed with increasing energy.

Figure 4 . 23 :

 423 Figure 4.23: Detection of 122 keV pulses in pileup condition: (a) all pulses are detected (b) a pulse is undetected.

Figure 4 . 24 :

 424 Figure 4.24: Amplitudes against the delay time separating two successive pulses.

Figure 4 . 25 :

 425 Figure 4.25: 122 keV pulses in two categories of signal pulse pileup: (a) Pulse pileup very close to the peak of a pre-pulse(black circles) and (b) pulse pileup towards the tail of a pre-pulse( green circle). The red dashed lines are markers for regions where tail extrapolation will take place.

Figure 4 . 26 :

 426 Figure 4.26: Amplitudes against the time-delay separating two successive pulse after pileup correction with a template pulse.

Figure 4 . 27 :

 427 Figure 4.27: Poor tail extrapolation indicated by the first pulse.

Figure 4 . 28 :

 428 Figure 4.28: Amplitudes against the time-delay separating two successive pulse after pileup correction with a template pulse. A zoom showing that effects are stronger at less than 20 ns apart between pulses.

  for high count rate gamma ray spectroscopy. Applied Radiation and Isotopes, 151:196-206, 2019. parts of the detector indicated by the REGION command. Other statements include ELECTRODE and DOPING which provide information on the electrode material, and the doping concentration respectively.

2 E

 2 Silvaco ATLAS mathematical models are used to obtain useful information about semiconductor devices. The models are based on a set of fundamental equations linking electrostatic potential and carrier densities in a simulation. These equations are the Poisson's equation, the continuity equation, and the transport equation, all of which have been derived from Maxwels' laws. Poisson's Equation associates variations in electrostatic potential to local charge densities. div( ∇ψ) = -ρ (4.3.1)ψ is the electrostatic potential, is the local permitivity, and ρ is the local space charge density. The local space charge density is obtained as the sum of contributions from all mobile and fixed charges, including electrons, holes, and ionized impurities.The electrostatic field E is deduced from the gradient of the potential as 4.3.= -∇ψ (4.3.2)

Table 1 . 1 :

 11 Stable and long-lived(T g.s 1/2 > 10 7 y) nuclei with isomeric state E m within 50eV-15 keV and half-life T m 1/2 > 1 ns. The Nuclei are ordered according to isotope abundance η (stable nuclei) or ground level half-life T g.s 1/2 (long-lived nuclei).Studies of the excitation of 181 Ta in plasma have been performed by some authors.

	Nucleus η or T g.s 1/2 (%) E m (keV )	T m 1/2
	45 Sc	100	12.4	318 ms
	169 T m	100	8.41	4.08 ns
	181 T a	99.988	6.2	6.05 µs
	201 Hg	13.2	1.56	81 ns
	83 Kr	11.49	9.41	154 ns
	73 Ge	7.76	13.28	2.92 µs
	57 F e	2.11	14.4	98 ns
	187 Os	1.6	9.75	2.38 ns
	235 U	7.04 x 10 8 y	0.0765	26 min
	205 P b	1.53 x 10 7 y	2.33	24.2 µs

The theoretical work of Letokhov et al. calculated 10 to 20 excitations per laser shot in a plasma created at an intensity of 10 18 W/cm 2 [53]. Andreev et al. presented experimental findings of 10 5 excitations per laser [55], while Gobet et al. estimated 10 -3 per laser shot [56] at a similar laser intensity around 10 16 W/cm 2 . This noncoherence in values amongst authors calls for experimental studies and validation.

Table 2 . 2 :

 22 Summary of CdTe properties used as inputs in the simulation at room temperature.

	Parameter	value
	Energy gap E g (eV)	∼ 1.5 [110-112]
	Ionisation energy i (eV)	4.43 [87, 113]
	electron mobility µ e (cm 2 /(V.s)) 1050 [109]
	hole mobility µ h (cm 2 /(V.s))	80 [109]
	electron mean-lifetime τ e (s)	3.10 -6 [113]
	hole mean-lifetime τ h (s)	2.10 -6 [113]
	relative permittivity	10.6 [114]

  One can estimate the net dopant concentration. Since the detector resistivity is dictated by the carrier type of the net dopant, which is in this case holes, we can re-write eqn. 2.2.3 as:

	ρ =	1 e.µ h .p net	,	(2.2.3)
	thus, the deduced net dopant concentration (p net ) of the CdTe is about 7.8×10 7 /cm 3 ,
	which is now fed into our silvaco simulation.

16

/cm 3 . From our communications with the manufacturer, the detector has a resistivity (ρ) that is more than 10 9 Ω.cm.

•

  Near the cathodeIf a 122 keV gamma is deposited near the cathode (see figure2.22), the poor hole mobility relative to the electrons is compensated for by this shorter distance. So they are quickly collected at the cathode electrode. On the other hand, while the electrons are 10 times faster, they have no problems reaching the anode electrode fast enough.In summary, this part of the work has been to study the signal of the CdTe detector from experimental data to simulations and calculations. We have seen that the simulated current signal of a 122 keV in CdTe has the same form, and is similar in amplitude with experimental results and calculations. The duration is more than 1 µs, which is too large for applications to detect a 9 ns isomeric state decay.

	Both charge carriers, while in this condition do well to deliver a global current that
	lasts for approximately 1 µs.

2.2.2.5 Simulation of X-ray flashes from a high power laser X-ray flash from high power laser (intensity > 10 18 W/cm 2 ) interaction will deposit its energy instantaneously in the detector. To be able to simulate this in Silvaco, we have taken the spectrum in figure

1

.23 with a mean energy of 805 keV, and made a simulation in Geant4. The Geant4 simulation gives us the energy deposited in the detector with depth (Edep(z)) from the cathode entrance of the 2 mm thick CdTe detector, this is shown in figure

2

.25. The total energy deposited is about 10 GeV from the simulation. An exponential fit in eqn. 2.2.4, is used to describe the distribution.

Table 2 . 4 :

 24 2 . It was fabricated for industrial inspection where images are taken in tight or difficult-to-reach places. The detector comes with a Gd 2 O by the manufacturers with which the detector can be controlled through a USB connection to a computer. The conversion gain is the number of electrons denoted by each digital number. For our CMOS detector it is 155 electrons per Analogue-Digital Unit (ADU), where 1 ADU corresponds to 1 Least Significant Bit (LSB). Additional information about the RadEye detector are shown in table 2.4. Some information about the CMOS detector from Teledyne company[139]

	Sensor specification	Value	Units
	P itch	20	µm
	T hickness	unknown	µm
	N umber of pixels	1650 × 1246
	Active area	33.0 × 24.9	mm
	Average dark current (23 o C)	6	ADU/s
	Digitization	12	bits
	Conversion gain	155	elec/ADU
	Operating temperature	0 to 50

2 S scintillator screen placed in direct contact with the photodiode array intended to convert incident Xrays to UV light to be detected by the photodiodes. An imaging software, ShadoCam, is also provided o C Figure 2.68: CMOS detector from Teledyne company.

Table 3 . 2 :

 32 Some properties of the HPD PIN

	parameters	minimal typical maximal	unit
	active area	3.14		mm 2
	depletion depth	150		microns
	operating voltage	100		V
	Silicon resistivity	3500	7000	Ωcm
	capacitance	2.24	2.49	pF
	Rise time (at 100 V)	4		ns
	Fall time (at 100 V)	4		ns

Table 3 . 3 :

 33 .2. The input parameters in the simulation captured in table 3.3, were taken from standard default values in Silvaco for a silicon material[115]. The simulated structure of the PIN diode is shown in figure3.21a, on the right is the doping profile in 1D. The intrinsic layer of the detector was lightly n-doped (10 12 cm -3 ) according to figure 3.14. The dopant concentration was deduced following the provided resistivity in table 3.2, and from equation 2.2.3. The detector is highly n and p doped on both sides but we do not have their values, so we made a simulation combining different doping concentration to see if there are significant variations in the electric field distribution in the detector. Summary of silicon properties used as inputs by Silvaco at room temperature (taken from default values for silicon in Silvaco).

	Parameter	value
	Band gap Energy (eV)	1.12
	Electron-hole pair creation energy (eV) 3.6
	Mobility of electrons (cm 2 /V.s)	1000
	Mobility of holes (cm 2 /V.s)	450
	lifetime of electrons (s)	10 -7
	lifetime of holes (s)	10 -7
	Permittivity	11.8

  After all gamma and LED pulses have been detected, the condition for pileup was established by setting a minimum time t pile between two consecutive pulses, below which is the existence of a pileup. The set minimum must be greater than the sum of the rise time and the decay time of a signal: t rise + t decay . The lower this value is the lesser the time it takes to run the programme. The rise time of our gamma signal is about 2 ns and decay time roughly 60 ns. So in our case, I set t pile = 0.1 µs, below this value separating two peaks is the occurrence of a pileup. The point where the second pulse is added to the first one is marked as the start of the pileup t s , the peak time of the first pulse is t p i and that of the second pulse is t p i+1 . Pileup is established

	4.1.6.1 Pileup detection

when:

t p i+1 -t p i < t pile

  The signal pulse was modelled in time t by combining two exponential functions for the rise time t rise and decay time t decay components with an amplitude weight A as shown in equation 4.2.3 and figure 4.20. This was deduced from the experimental data from the assumption that the LEDs pulses where decreasing in amplitudes logarithmically. B is a positive offset in the time axis,

	y(t) =	log 10 ((t) 2 + B) log 10 ((t max ) 2 + B)	,	(4.2.4)
				1/2 (s) by :
		λ =	ln 2 t 1/2		(4.2.2)
	V (t) = A(exp(-t/t decay ) -exp(-t/t rise )) + i	(4.2.3)
	Where i is related to a Gaussian noise contribution to the oscillogram. The equation
	4.2.3 is the same as 3.1.1, except for the noise parameter. Also, the equation 4.2.3

above, was used for the LEDs, but by the introduction of smaller values for the times t rise and t decay to enable us distinguish the LEDs from the gammas. The variation in the gain is modelled assuming a logarithmic effect y(t) on the enire oscillogram . and the denominator in equation 4.2.4 serves as a normalisation constant. The gain defect V 2 (t) can be introduced in the simulated oscillogram as shown in figure 4.21, by multiplying equation 4.2.3 and 4.2.4: V 2 (t) = V (t) * y(t) (4.2.5)

Table 4 . 1 :

 41 The main detectors in this work.

	Detectors	particle of interest energy domain
	CdTe	gamma	∼ 200 keV
	APD	gamma	some keV
	CMOS	protons/electrons	few MeV
	LaBr 3 (with HPD) gamma	∼ 200 keV

  qD n ∇n (4.3.5)J p = qpµ p E p -qD p ∇p (4.3.6)where µ n and µ p are the electron and hole mobility in (cm 2 /V.S),n and p corresponds to the quantity of electrons and holes respectively, and E n and E p are the local electric field due to electrons and holes respectively.With the assumption that the Einstein relationship holds, following Boltzmann's statistics, D n and D p correspond to:

	D n =	kT L q	µ n	(4.3.7)
	D p =	kT L q	µ p ,	(4.3.8)

https://physics.nist.gov/cgi-bin/Star/e_table.pl

https://www.teledynedalsa.com/en/home/

named after Stephen Butterworth https://en.wikipedia.org/wiki/Butterworth_filter

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit. html

delivers the optimum results.

Calibration at AIFIRA

The CMOS calibration was performed at the AIFIRA 3 beam facility in LP2i Bordeaux [START_REF] Sorieul | Aifira: An ion beam facility for multidisciplinary research[END_REF][START_REF] Barberet | Aifira: a light ion beam facility for ion beam analysis and irradiation[END_REF]. It is a 3.5 MeV singletron accelerator, equipped with a high resolution nanobeam line based on a two-stage double-triple configuration magnetic quadrupoles.

The beam is scanned over the target by the help of electrostatic scanning plates permitting to sweep the beam in the sample plane. The developed system allows to produce maps with a 256 x 256 pixels resolution and at a relatively high scanning speed, with the possibility to go down to 15 µs/pixel [START_REF] Barberet | First results obtained using the cenbg nanobeam line: Performances and applications[END_REF][START_REF] Daudin | Crionscan: A stand-alone real time controller designed to perform ion beam imaging, dose controlled irradiation and proton beam writing[END_REF].

The key parameters of the proton beam used for the calibration include: beam diameter of about 1.5 µm [START_REF] Barberet | First results obtained using the cenbg nanobeam line: Performances and applications[END_REF]; proton current up to 1 ± 0.15 pA; and energy of 3

MeV. At such high currents, a Faraday cup positioned in the chamber was used for the measurements, while for much lower intensity, a surface barrier was deployed for proton to proton counting. A holder was constructed to help fit the detector in the experimental chamber. In the figure 2.73 below, the RadEye detector is placed in the experimental chamber attached to a holder which is also attached to a motoring stem that moves vertically (back view) for proper alignment with the beam line. To minimise background contributions from within the chamber, black aluminium foils were used to shield radiation due to the infrared LEDs used for the motoring systems in the chamber. In the front view, the sensitive part of the detector is facing the beam. Quartz is placed on the holder for scintillation to be produced with which the beam diameter can be ascertained through a microscope objective.

The calibration modalities deployed on the CMOS are in two parts: one case where only the sensitive part of the CMOS detector was irradiated while working in 'mode 2'. An LED light source in the chamber was used to trigger the detector more than 3 3 Applications Interdisciplinaires des Faisceaux d'Ions en Région Aquitaine close to the time of the laser shot. This suggests that the gain of the detector is not constant during the laser shot.

Pre-treatment: Data cleaning and de-noising

The acquired data was cleaned from infinite (Inf) values that come from the saturation of the oscilloscope, which could lead to erroneous results if injected directly into the analysis. Python has useful functions that have been employed to handle Infs. In addition, the acquired data contains electronic noise which not only deforms the signal but could make further analysis erroneous. As a first-case treatment, the data was filtered from high frequency noise using the first order of a low pass Butterworth filter 1 (see figure 4.5a). The frequency response (gain) with a cut off frequency normalised to 1 radian per second is:

where, ω is the angular frequency in radian per second, and n is the filter order, which is related to the number of reactive components in the filter. The cut off frequency is the frequency at which the response is -3 decibel(dB) see figure 4.4. Above this frequency, all other frequencies are minimised from the data. Both log and solution files can be read directly using a dedicated visualization tool, • Structure:

Gain correction

The structure statements involve physical properties of the detector to be simulated such as the geometry which is formed by the MESH commands and different