Copyright

by

Joseph Michael Shaw

2019 The Thesis Committee for Joseph Michael Shaw certifies that this is the approved version of the following thesis:

Experimental Studies on High-Energy Radiation Sources from Laser Wakefield Accelerators

APPROVED BY

SUPERVISING COMMITTEE:

Michael C. Downer, Supervisor

Aaron C. Bernstein Experimental Studies on High-Energy Radiation Sources from Laser Wakefield Accelerators

by

Joseph Michael Shaw

Thesis

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Master of Arts

The University of Texas at Austin

May 2019 To my parents and the rest of my family for their unwavering support and love. Acknowledgments

My sincerest gratitude goes to my adviser, Professor Downer, for introducing me to the incredibly interesting world of laser-plasma physics and allowing me to play with his expensive laser. I would like to thank Xioaming Wang and Hai-En Tsai whose initial tutelage in laser maintenance and laser plasma diagnostics would prove invalu- able throughout my entire time at UT. I would like to thank Rafal Zgadzaj and Aaron Bernstein for the countless hours of time donated towards setting up experiments, proofreading publications and presentations, and providing general advice of all kinds. Thank you to Vincent Chang, Andrea Hannasch, Max LaBerge, Kathleen Weichman, Jake Welch, Xiantao Cheng, Ganesh Ti- wari, and Luc Lisi for all their help setting up and conducting experiments. And thanks for being great company during late-night data runs. I would like to thank Farbod Shafiei, Neil Fazel, and Loucas Loumakos for all the lively conversations and being great office mates. Thanks to Watson Henderson for all of his advice on a myriad of subjects. Finally, I would like to thank the entire Texas Petawatt staff for their hard work over several month- long experimental runs. The data and analysis in this thesis would never have been possible without the hard work and determination of everyone mentioned above.

v Abstract

Experimental Studies on High-Energy Radiation Sources from Laser Wakefield Accelerators

Joseph Michael Shaw, M.A. The University of Texas at Austin, 2019

Supervisor: Michael C. Downer

In this work I discuss a series of experiments on generating and characterizing a compact, ultrashort-duration source of Thomson backscatter γ-rays at the University of Texas, Austin. The γ-rays are created in a three-step process that begins with the Texas Petawatt laser-plasma accelerator producing GeV- scale electron beams. At the exit of the accelerator, the leading edge of the TPW laser pulse ionizes the surface of a glass or plastic substrate to form a plasma mirror. The plasma mirror retro-reflects a majority of the remaining laser energy back into the accelerated electrons to act as an optical undula- tor, which stimulates the production of γ-rays. By adjusting the separation between the plasma mirror and exit of the accelerator, we were able to simulta- neously confirm that the inherently self-aligning quality of the plasma mirror is maintained over a wide range of intensities and observe the transition from linear to nonlinear Thomson backscatter. Linear Thomson backscatter cal- culations inferred from accelerated electron spectra imply γ-ray spectra with peaked components ranging from 5 - 85 MeV.

vi Table of Contents

List of Tables x

List of Figures xi

Chapter 1 Introduction 1 1.1 Laser Plasma Accelerators ...... 1 1.2 Radiation Sources ...... 2 1.3 Thomson Scattering ...... 3 1.4 Laser Strength Parameter ...... 5 1.5 Thomson Backscatter of Relativistic Electrons ...... 5

Chapter 2 Relevant Laser-Plasma Dynamics 8 2.1 Light Propagation in Plasma ...... 9 2.2 Laser Wakefield Acceleration ...... 10 2.3 Plasma Mirrors ...... 12 2.4 Thomson Backscatter Experiments ...... 13

Chapter 3 Thomson Backscatter Experiments with the TPW 15 3.1 LPA Experimental Setup ...... 15 3.1.1 Plasma Mirror Performance ...... 16 3.1.2 Radiation Diagnostics ...... 18 3.2 Linear Thomson Backscatter ...... 20 3.2.1 Laser Intensity Approximation ...... 20 3.2.2 Bremsstrahlung Contributions ...... 22

vii 3.2.3 Linear Thomson Spectra ...... 25 3.3 Nonlinear Thomson Backscatter ...... 27 3.4 Future Work and Conclusions ...... 30 3.4.1 γ-ray Spectrometer Measurements ...... 30 3.4.2 Conclusions ...... 32

Bibliography 33

viii List of Tables

2.1 Neutral helium number densities by orders of magnitude and the approximate electron and He2+ ion oscillation periods for a fully-ionized plasma, respectively...... 9

3.1 Scaling of the γ-beam divergence (FWHM) along the laser po- larization axis with PM z-position...... 30

ix List of Figures

1.1 (a) A dipole radiation pattern in the rest frame of an electron

(i.e. γe =1). (b) A dipole radiation pattern for an electron

moving upward with total energy twice its rest energy (i.e. γe =2). 6

2.1 A computational simulation of electron injection and accelera- tion in the bubble regime for the TPW LPA, where the color scaling represents the electron density [cm−3]. (a) A laser wake- field bubble near the beginning of its formation and corresponds to the propagation distance z = 0.14 cm. (b) Corresponds to z = 0.336 cm. (c) Corresponds to z = 1.04 cm. [Image and caption are modified versions of a figure courtesy of Stefan Bedacht, University of Texas at Austin] [Original simulations/ figure courtesy of Serguei Kalmykov and Arnaud Beck] . . . . 11 2.2 The Texas Petawatt laser pulse temporal contrast measured via third-order autocorrelation [29]...... 13

3.1 A top-down schematic of the LWFA 5.5 experimental setup used for generating and characterizing the GeV-scale laser wakefield accelerator and PM-based Thomson γ-ray source at the Texas Petawatt...... 15

x 3.2 Probe beam reflectivity calibration: (a) The (null) probe beam profile imaged from the coverslip surface after scaling the gray values, accounting for reflection and transmission losses of the

imaging system, to the initial incident intensity (I0). (b),(c) A localized region of the coverslip surface is activated by the transmitted LPA-driving pulse, enabling a greater proportion of probe light to be reflected from the surface. The gray values

are then normalized to I0 to approximate the percent reflected. 17 3.3 (a) Electron spectrum (left) with peak at 2.2 GeV and corre- sponding betatron x-ray profile (upper right) recorded on IP. Secondary particles from γ-ray conversion produced a bright spot near center of metal disk (lower right) on a separate shot. (b) Scintillator signals with PM in place (top), showing Thom- son γ-ray profile, and with no PM (bottom)...... 18 3.4 Shot-to-shot pointing fluctuations. (a) Electron spectra (left), γ-ray profiles (right) for two shots showing equal but opposite vertical displacements and differing horizontal γ-ray displace- ments, with respect to the alignment axis. (b) Plot of vertical γ-ray vs. electron displacements...... 19 3.5 Side-scatter emission of the laser-induced plasma channel seen through a glass window in the helium gas cell. The laser prop- agates from left to right. A logarithmic function was applied to the image to dampen the strong scattering near the beginning of the gas cell and enhance the visibility of the channel near the end. The bright edge on the right is the exit aperture of the gas cell...... 21 3.6 Scaling of scintillator signal with position z and thickness L of PM: (a) z = 3.3 cm, L = 100µm; (b) z = 5.5 cm, L = 180 µm. Nearly identical laser pulses drove both shots; both yielded electrons with energy peaked at 0.92 GeV and corresponding charge (a) 50 or (b) 125 pC...... 23

xi 3.7 Scaling of the integrated fluence with fbrem at zPM = 3.3 cm. The blue, dashed curve has a slope of unity and illustrates the expected scaling if bremsstrahlung radiation were the only con- tributor of signal. The grey, dotted curve represents the best-fit for a linear relationship...... 25

3.8 Quasi-monochromatic Thomson γ-ray spectra generated as Ee tuned from 0.5 to 2.2 GeV. Spectra are labeled with multipliers that normalize true peak heights to the height of the two lowest energy curves...... 26 3.9 A typical electron dN/dE for LWFA 6.0 and 7.0...... 27 3.10 (a) The first three harmonics of a TBS spectrum calculated

from the above dN/dE, assuming a0 = 0.25. (b) The first three harmonics of a TBS spectrum calculated from the above dN/dE,

assuming a0 = 0.5...... 28 3.11 Scaling of the integrated fluence with the PM’s z-position. The blue trendline is a second-order polynomial fit for a total of 39 shots, represented by the light-orange boxes. The vertical red line represents the nominal exit plane of the gas cell. A statistical average and standard deviation is represented by the singular data point with error bars at each respective PM position. 29 3.12 Simulation of e− / e+ energy-angle distributions produced by a monoenergetic, 10 MeV photon beam in 2 cm of carbon. Image and simulations courtesy of Luc Lisi...... 31 3.13 (Left) A top-down view of the Compton & pair-production spec- trometer design. Higher energy electrons or positrons will de- posit their signal further down the length of the spectrometer. (Right) The design and specifications of the magnet housed within the spectrometer. Magnet drawing and specifications courtesy of Ganesh Tiwari...... 31

xii Chapter 1

Introduction

1.1 Laser Plasma Accelerators

Laser-plasma accelerators (LPAs) harness intense, ultrashort light pulses to drive charge-density waves in a plasma, ranging in electron density from 0.01 - 0.1 atm, to capture and accelerate electron bunches up to relativistic energies. Acceleration occurs within centimeters rather than the kilometers typical of conventional accelerators; this is because laser-driven plasma waves sustain internal electric fields on the order of GV/cm, thousands of times larger than the electric breakdown fields of ∼1 MV/cm to which conventional metallic accelerator structures are limited. LPAs of cm-scale now routinely produce high quality electrons up to GeV energies [25]. In recent years, LPAs [25] have produced 2 to 4 GeV quasi-monoenergetic electron bunches [84, 49, 50] within an acceleration distance of centimeters. In these LPAs, an ultrashort drive laser pulse of 0.3 to 0.6 PW peak power traversing cm-length tenuous plasmas blew out positively-charged, light-speed accelerating cavities of ∼ 50µm diameter, which captured ambient plasma elec- trons at their rear and accelerated them in their internal GV/cm electrostatic fields to GeV energy. The emergence of GeV LPAs raises the intriguing pos- sibility of developing small, easily accessible Thomson γ-sources that span a similar photon energy range (1 < Eγ < 80 MeV) of linac-based LTS facilities,

1 complementing their capabilities while more readily providing synchronized electron bunches and γ-ray pulses of fs duration [40]. Indeed the planned Ex- treme Light Infrastructure-Nuclear Physics (ELI-NP) facility is based on this possibility [36].

1.2 Radiation Sources

Bright fs x-/gamma ray pulses are difficult and costly to produce in a coherent and repeated manner. The source discussed here is a step towards extending the availability of x-/γ-rays to a wider spectrum of researchers, offering a compact tool to probe ultrafast atomic and nuclear dynamics across many scientific fields. Our developing understanding of high energy photons, and the sources from which they eminate, has vastly altered the way we view and manipu- late the world around us. Medical x-rays and computed tomography (CT) scans are perhaps the most obvious and commonly known examples of their use. However, dozens of Nobel Prizes have been awarded in physics, chem- istry, and medicine wherein x-rays have played a pivotal role. The advent of radio-frequency (RF) electron accelerators enabled many of those discover- ies by providing repeatable, highly-directional, high flux photon sources. For instance, intense directional beams of MeV photons have proven to be in- valuable tools for probing and manipulating the resonances of atomic nuclei. Indeed, intense beams of MeV photons have been applied to or considered for medical radioisotope production [35]; non-destructive detection and assay of fissile materials for nuclear waste management or cargo scanning [38, 37, 39]; isotope-selective transmutation of long-lived fission products [54, 24, 43]; and sterilization of food and medical equipment [39]. Additionally, γ-ray beams, with photon energy 4 < Eγ < 25 MeV, generated in high-Z targets by MeV electrons from small linacs are now standard tools in the treatment of deep cancers [52]. There is yet a greater set of nuclear applications that demands polar-

2 ized, quasi-monochromatic, and/or short-pulsed γ-ray beams — e.g. studies of astrophysical nucleosynthesis mechanisms [41]; pulsed radiolysis [76]; and efficient generation of ultrashort polarized positron bunches suitable for injec- tion into advanced accelerators [53, 57] — with some requiring photon energies up to ∼ 80 MeV. To meet this demand, several GeV-class electron accelerator facilities dedicated to generating intense γ-ray beams via pulsed laser Thom- son, or Compton, scatter (LTS) — e.g. the High-Intensity γ-ray Source (HIγS) [85], NewSUBARU [5] and others [19] — have been built and operated starting in the 1980s, while new linac-based γ-ray sources featuring e.g. exceptionally narrow bandwidth [3], high photon flux [38] and ultrashort pulse duration [76] continue to emerge. These facilities exploit the ability of linear Thomson scat- ter to map the polarization and spectral-temporal structure of the scattering laser pulse onto the γ-radiation.

1.3 Thomson Scattering

Thomson scattering is a phenomenon that occurs when unbound electrons experience periodic, laser-driven oscillations. The motion of a free electron under the influence of an electromagnetic field is, in general, dictated by the relativistic Lorentz force.

dp = −e (E + v × B), (1.1) dt where

p = γmev (1.2) and v · v − 1 γ = (1 − ) 2 . (1.3) c2 Consider the non-relativistic limit of an electron’s motion in a monochro- matic plane-wave arbitrarily polarized alongx ˆ. The electric field is described as,

3 E = E0 sin(ωt)ˆx, (1.4)

with amplitude E0 and laser frequency ωl. Since the magnetic field amplitude B0 = E0/c for a plane wave, the v × B component of the Lorentz force can be neglected for the non-relativistic limit where v/c << 1. The electron equation of motion is therefore,

d2x m = −eE sin(ωt), (1.5) e dt2 0 whose solution is,

eE0 x(t) = 2 sin(ωt) = dsin(ωt) (1.6) meω As a consequence of the laser-driven acceleration, the electron re-radiates/ scatters energy from the incident laser into a dipole distribution, where ed = p0 can be considered the dipole moment of the electron motion [34]. This is known as Thomson scattering and has a differential power radiated per solid angle,

4 2 4 2 dP ω p0 2 e E0 2 = 2 3 sin θ = 2 3 2 sin θ (1.7) dΩ 32π c 0 32π c me0 The ratio of the above quantity with the incident power per unit area 1 2 (i.e. time-averaged Poynting flux) of the laser < S >= 2 0cE0 yields the differential Thomson scattering cross-section,

2 !2 dσ dP/dΩ e 2 = = 2 sin θ, (1.8) dΩ < S > 4π0mec where the squared term in parentheses is recognized as the classical electron radius, re. Integrating the differential cross-section over all angles yields the total Thomson cross-section,

Z 2π Z π 2 2 8π 2 σT = re sin θ(sinθdθ)dφ = re (1.9) 0 0 3

4 1.4 Laser Strength Parameter

In the previous section, the non-relativistic limit of Thomson scattering was considered. As the intensity of incident light is increased, the possibility for electrons to interact with multiple photons in one oscillation cycle is also in- creased. Thomson scattering at near-relativistic intensities (∼ 1018 W/cm2) exhibit a more complicated energy and angular distribution. It is common to consider the importance of relativistic effects on the electron motion in terms of the so-called dimensionless laser strength parameter (or normalized vector potential)

q eE0 18 2 a0 = = 0.85λ[µm] I[10 W/cm ]. (1.10) meω0c

The first form of a0 indicates the onset of relativistic effects as the electron quiver momentum becomes relativistic, whereas the second equation involves quantities generally more relevant for experiments.

1.5 Thomson Backscatter of Relativistic Elec- trons

While section 1.3 dealt with the Thomson scattering distribution from a sta- tionary electron, the physics of the interaction remains the same with an electron that is moving, even near the speed of light. This is because the interaction must be transformed into the rest-frame of the electron such that the incoming and outgoing radiation fields are the objects that experience the relativistic distortion. In the laboratory-frame, the angular distribution and frequency spectrum of the scattered radiation begins to differ drastically from the stationary Thomson distribution as the electron energy is increased (see Fig. 1.1). Indeed, the great interest in Thomson backscatter (TBS) sources stems from the manner in which the radiated energy and spatial-distribution scales relative to the electron Lorentz-factor when γ >> 1.

5 Figure 1.1: (a) A dipole radiation pattern in the rest frame of an electron (i.e. γe =1). (b) A dipole radiation pattern for an electron moving upward with total energy twice its rest energy (i.e. γe =2).

6 2 Consider an electron with energy γemec and a photon moving toward a head-on collision. In the rest frame of the electron, the photon wavelength is compressed such that the photon energy is Doppler up-shifted,

hω¯ e ≈ 2γehω¯ l (1.11) assuming the electron recoil is neglected. The recoil can be neglected when the Doppler-shifted photon energy is not an appreciable proportion of the electron rest mass (i.e. 2γehω¯ l < 511 keV). The outgoing radiation experiences a similar Doppler-upshift, and, if the observation angle is small (i.e. θ << 1), the radiated photon energy in the laboratory frame can be described as

2 4γe hω¯ l Eγ = 2 2 2 (1.12) 1 + a0/2 + γe θ As seen in Fig. 1.1, the radiation is preferentially emitted near the electron’s primary axis of motion (θγ ∝ 1/γe), and the frequency of outgoing 2 radiation can be double-Doppler upshifted (Eγ ∝ 4γe hω¯ l) for θ = 0 and the a0 < 1. Considering the Lorentz factor for a 1 GeV electron (γe ≈ 2000), the final two results imply: the radiation from a single electron would be confined to a milliradian-scale divergence angle; and the TPW photons (¯hωl = 1.17 eV) double-Doppler upshifted yields ∼ 20 MeV photons. A rigorous description of the physics involved with relativistic Thomson scattering is provided in Refs. [26, 65].

7 Chapter 2

Relevant Laser-Plasma Dynamics

High energy density (HED) states of matter are commonly studied by ionizing and energizing – typically solid and/or gaseous – targets using high intensity laser pulses. Various regimes of laser-matter interactions can be accessed by delivering energy within certain timescales that are characteristic of the subse- quent laser-plasma. One of the most fundamental characteristics of a plasma is the electron plasma frequency (ωpe).

s 2 ve nee ωpe = = [SI], (2.1) λDe me0

where ve is the most probable electron velocity in a Maxwell-Boltzmann distribution; and λDe is the electron Debye radius, the length-scale associated with an electron’s electrostatic sphere of influence within the plasma. While the latter expression is simpler, requiring only the electron number density

(ne), the former expression is more intuitive in understanding ωpe as a re- ciprocal time-scale in which external electromagnetic perturbations propagate within the plasma. The table below provides a comparison between electron and ion time- scales over a range of densities relevant for LPA experiments. Typical electron

8 plasma densities for laser wakefield acceleration (LWFA) fall within the range of 1017 − 1019 cm−3. The LWFA experiments conducted at the TPW facility used pure helium, and the subsequent plasma was considered fully-ionized.

n0 τpe τpi [cm−3] [fs] [fs]

1017 250 15000 1018 80 4750 1019 25 1500 1020 8 480 1021 3 150 Table 2.1: Neutral helium number densities by orders of magnitude and the ap- proximate electron and He2+ ion oscillation periods for a fully-ionized plasma, respectively.

Generally the two-fluid theory of plasma physics requires a consider- ation of the ion plasma frequency. However the duration of pulses used for LWFA are on the order of tens to hundreds of femtoseconds (10−15 s). Indeed, the maximum laser pulse duration used for the TPW LPA was ∼ 200 fs and operated between ∼ 2 − 7 × 1017 cm−3. The duration of the laser pulses and the speed at which they propagate through the plasma implies that ions can be considered motionless throughout the LWFA process.

2.1 Light Propagation in Plasma

This last point conveniently reduces the complexity of describing a laser pulse’s propagation through a plasma because the optical response (i.e. dispersion relation) of the plasma becomes almost entirely dependent on the electrons. The TPW LPA is formed when the laser enters a uniformly pre-filled gas cell; therefore, the plasma can be considered uniform and non-magnetized. Under these assumptions, the linear response of a plasma from a laser pulse with frequency ωl can be described by the following equation.

9 2 2 2 2 ωl = c k + ωpe (2.2) If we consider a monochromatic gaussian laser pulse, its propagation in free-space (alongz ˆ) can be described with its electric field as,

i(ωt−kz) E(x, y, z, t) = E0u(x, y, z)e . (2.3)

The photon frequency determines what happens to the pulse when it encoun- ters a plasma. If ωl < ωpe, the linear dispersion relation indicates that the wavenumber (k) becomes imaginary at the boundary of the plasma, and the pulse’s propagation has two solutions – absorption or reflection. Transmis- sion of lower frequency light is impossible because the rapid oscillations of the plasma electrons will screen out the electromagnetic perturbations caused by the laser photons, and the pulse amplitude exponentially decays as a function of depth into the plasma. If ωl > ωpe, then the pulse propagates into the plasma. This can also be considered in terms of the plasma’s refractive index (η).

v u 2 s c k u ωpe ne η(ω) = = t1 − 2 = 1 − (2.4) ωl ωl nc(ωl)

In the last equality, the function nc(ωl) is the critical density and repre- sents the electron density for which ωpe = ωl. Plasmas with electron number densities above (below) the critical density are said to be over- (under-) dense.

2.2 Laser Wakefield Acceleration

Laser wakefield acceleration, first proposed by Tajima and Dawson in 1979, involves exciting high amplitude plasma waves using an intense laser pulse [77] to capture and accelerate electrons. While multiple schemes of laser plasma acceleration have been proposed, the focus of this work is on the so-called blow-out or ”bubble” regime. An intense enough gaussian laser pulse focused

10 Figure 2.1: A computational simulation of electron injection and acceleration in the bubble regime for the TPW LPA, where the color scaling represents the electron density [cm−3]. (a) A laser wakefield bubble near the beginning of its formation and corresponds to the propagation distance z = 0.14 cm. (b) Corresponds to z = 0.336 cm. (c) Corresponds to z = 1.04 cm. [Image and caption are modified versions of a figure courtesy of Stefan Bedacht, University of Texas at Austin] [Original simulations/ figure courtesy of Serguei Kalmykov and Arnaud Beck]

into a gas will begin to contract and expand (likely multiple times) because the front edge of the pulse is actively altering the nonlinear refractive index of the medium. If the contractions of the pulse allow the laser to reach a critical

11 2 power threshold (Pc [GW] = 17(ω/ωpe) ) the laser will begin to experience relativistic self-focusing and guiding. In the self-guided blow-out regime, the laser maintains a relatively stable beam profile with high enough intensity such that the laser ponderomotive force expels all of the electrons in a wake trailing immediately behind the pulse. This wake consists of an extremely positive plasma cavitation with an extremely negative electron sheath (see Fig. 2.1). Some of the electrons in the sheath are captured and accelerated toward the center of the bubble due to the strong electrostatic field of the electron-less region following the laser.

2.3 Plasma Mirrors

A major consequence of the chirped pulse amplification technique, used in many contemporary high power laser facilities, is the introduction of unwanted temporal structures that can experience amplification along with the main laser pulse. Amplified spontaneous emission contributes a ns-scale pedestal, while spectral clipping and other spectral phase aberrations can produce pre- pulses that exist on <100 ps time-scales [21]. A number of ultrahigh intensity experiments require very high contrast, prepulse-free laser pulses. These tem- poral structures can be particularly detrimental for applications that utilize fs-scale pulses and/ or experiments involving laser-solid interactions [83]. The ubiquity of femtosecond- and attosecond-scale lasers has spurred the development of a new class of active optical elements based on plasmas, known as plasma mirrors (PM). The PM acts as a self-induced optical shutter and is typically made of a cheap, transparent material such as glass or plastic. In an ideal situation, an ultrashort pulse’s pedestal and prepulses are com- pletely transmitted and the PM activates only on the rising edge of the main pulse. If the surface has not been degraded by these temporal artifacts, the laser will almost instantly ionize the surface via multiphoton absorption and optical field ionization. The high speed of ionization turns the surface to an over-dense plasma, making the once transparent surface into a highly reflec-

12 tive one. Indeed, this technique is now routinely used to temporally clean the leading edge of high intensity laser pulses prior to meeting its final target.

Figure 2.2: The Texas Petawatt laser pulse temporal contrast measured via third-order autocorrelation [29].

The limited time alloted for our experiments prevented a laser temporal contrast scan, however previous results [81] strongly suggest a recent TPW upgrade on the leading edge peak-to-pedestal contrast (105 at 20 ps, > 108 at 100 ps from the peak of each pulse) [29] improved the repeatability and consistency of PM activation. Without sufficient temporal contrast, amplified pre-pulses degrade the PM surface prior to the arrival of the main driving pulse, thereby affecting the reflection efficiency.

2.4 Thomson Backscatter Experiments

Contemporary research in LPA-based Thomson backscatter sources is primar- ily split between the two-pulse and PM methods. The two-pulse method re- quires a LPA driving-pulse to accelerate electrons and a counter-propagating pulse to stimulate TBS. In contrast, the PM method uses the LPA driving- pulse to accelerate electrons and stimulate TBS. This is achieved by placing a thin film at the LPA exit, which is ionized by the post-LPA-driving pulse, caus-

13 ing an over-dense plasma to form on the surface of the film that retro-reflects most of the remaining light. The simpler of the two methods generated broadband [60] or tunable quasi- monochromatic [82, 23, 88] Thomson backscatter x-rays with measured photon energy up to 2 MeV [88] by inserting a reflective film just after the exit of a < 450 MeV TW-laser-driven LPA. The film acted as a PM [32] that retro-reflected the intense part of the drive pulse onto trailing accelerated electrons, without alignment difficulty, while the generation of background bremsstrahlung x-rays from LPA electrons was suppressed by using a thin low- Z PM material [82, 88]. However, this simple technique has not been scaled to GeV LPAs because their PW drive pulses possess stronger pre-pulses (requir- ing more stringent suppression techniques than TW pulses) that pre-expand the PM surface, degrading its reflectivity and the efficiency and reliability of Thomson backscatter. Instead Thomson photons above 2 MeV have been generated from LPAs by the more technically challenging approach of colliding the micrometer-sized LPA electron bunch with a separate pulse created either by splitting off a major fraction of the fully amplified LPA drive pulse [13] (thus limiting the achievable

γe) [61, 55, 87], or by splitting it from the drive pulse oscillator and separately amplifying it to multi-TW power [67]. In either case, the backscatter pulse was focused at the LPA exit through a separate optical path that had to be carefully aligned and compensated for pointing jitter. Some researchers successfully met these challenges, generating quasi-monochromatic LTS photons up to 9 MeV

[55] with a backscattering pulse focused to a0 < 1. Sarri et al. and Yan et al. extended the high-energy tail of the LTS photon spectrum up to 18 MeV [67] and beyond 20 MeV [87], respectively, by focusing the backscatter pulse to a0 > 1, accessing a nonlinear Thomson scatter regime for which 2 the mean Eγ ∼ 4γe hω¯ La0. Since, however, the nonlinear TBS spectrum is 2 inherently composed of multiple harmonics of Eγ = 4γe hω¯ L, linear backscatter is preferred to produce quasi-monochromatic γ-rays.

14 Chapter 3

Thomson Backscatter Experiments with the TPW

3.1 LPA Experimental Setup

The production and characterization of multi-MeV Thomson backscatter γ- ray beams was investigated in experiments carried out at the Texas Petawatt (TPW) Laser facility [30, 29]– referred to as LWFA 5.5 (January 2016), LWFA 6.0 (January 2017), and LWFA 7.0 (May 2017). The uniquely powerful TPW laser enabled a series of experiments that explored Thomson backscatter (TBS) in a regime largely inaccessible to the LPA community, currently.

Figure 3.1: A top-down schematic of the LWFA 5.5 experimental setup used for generating and characterizing the GeV-scale laser wakefield accelerator and PM-based Thomson γ-ray source at the Texas Petawatt.

15 Figure 3.1 depicts a layout of the LWFA 5.5 experimental setup. The TPW laser provided LPA drive pulses with 1057 nm center-wavelength, <195> fs duration, and energy between 75 and 110 J. An upgrade was performed af- ter LWFA 5.5, improving the Strehl ratio, increasing the laser energy stability (<100> J), and shortening the average pulse duration (<150> fs). The am- plified pulses were focused in vacuum by a f/40 spherical mirror into the entrance aperture of a 7-cm-long gas cell. The gas cell was uniformly filled with 6 Torr helium gas prior to each shot. Upon reaching LWFA conditions the pulses fully ionize the gas, generating plasmas with typical electron den- 17 −3 sities of ne ≈ 5 × 10 cm , and generate self-injecting plasma bubbles that accelerated electrons to GeV energies [84].

3.1.1 Plasma Mirror Performance

For every shot, a glass coverslip or plastic film was placed in-line with the laser, after the gas cell, to act as a plasma mirror (PM). The front edge of the LPA-driving pulse that transmitted through the gas cell generated the PM that then retro-reflected a majority of the remaining light towards the accelerated electrons. The PM was offset 8◦ from normal incidence with the nominal laser axis to avoid reflecting the still-energetic pump pulse backward into the amplifier chain. The reflection efficiency of the PM was investigated during LWFA 5.5 using a probe pulse generated by frequency-doubling a split-off portion of the main pulse. The probe, which was simultaneously reflected from the PM surface as it was activated, was imaged to a charge-coupled device (CCD) camera through spectral filters that rejected scattered light from the main pulse and the plasma. ◦ The probe beam was incident to the PM surface at θi ∼ 53 , nearly the Brewster’s angle for fused silica (nref ≈ 1.46) – the PM material used for LWFA 5.5 – in vacuum at 529 nm. Fresnel’s equations can be used to calculate

16 Figure 3.2: Probe beam reflectivity calibration: (a) The (null) probe beam profile imaged from the coverslip surface after scaling the gray values, account- ing for reflection and transmission losses of the imaging system, to the initial incident intensity (I0). (b),(c) A localized region of the coverslip surface is activated by the transmitted LPA-driving pulse, enabling a greater propor- tion of probe light to be reflected from the surface. The gray values are then normalized to I0 to approximate the percent reflected. the expected reflectivity from the glass surface.

tan(θi − θt) rk = , (3.1) tan(θi + θt) where Snell’s law provides the angle of the transmitted beam,

sin θi θt = arcsin( ). (3.2) nref

The p-polarized probe will therefore reflect only ∼ 0.06% of its energy from the glass coverslip surface without the PM activated. The probe imaging system required an OD 5.0 and FGS900 bandpass filter to reject the strong

17 scattered light from the main beam. To maintain the imaging plane, only an OD 1.0 filter was removed for null (no PM) shots that were used for calibration of the reflectivity. The intensity within the FWHM of the null probe beams was averaged, and, by accounting for the Fresnel reflectivity and additional

OD 1.0, the average gray value was scaled to an average intensity (I0) incident on the coverslip surface. I0 is represented by an average since the probe and main beams are generally not spatially uniform and experience pointing jitter, meaning the exact overlap of the probe where the PM was formed, shot-to- shot, is not known. For this reason, the PM reflectivity is only conservatively estimated to be > 50%.

3.1.2 Radiation Diagnostics

Figure 3.3: (a) Electron spectrum (left) with peak at 2.2 GeV and correspond- ing betatron x-ray profile (upper right) recorded on IP. Secondary particles from γ-ray conversion produced a bright spot near center of metal disk (lower right) on a separate shot. (b) Scintillator signals with PM in place (top), showing Thomson γ-ray profile, and with no PM (bottom).

To measure and calibrate the electron energy, the accelerated electrons were horizontally deflected by a 1.1 Tesla magnet before interacting with two sets of tungsten wire fiducials, separated along the z-axis, that imprinted ver- tical shadows into the profiles of the electron beam and betatron x-rays (seen

18 in Fig. 3.3a, left). An imaging plate (IP) located at z = 2.7 m recorded the magnetically-dispersed accelerated electrons, and keV betatron x-rays [66], af- ter they passed through a 50 µm thick aluminum foil (not shown) that deflected any remaining drive pulse into a beam dump. Energy-dependent electron num- ber dNe/dEe and total q were determined from measured photo-stimulated luminescence (PSL) levels scanned from exposed IPs, and quantified using a calibration procedure described in Ref. [84]. Thomson γ-rays passed through the PM, laser deflector, IP, and a 3.3-mm-thick Al back plate of the vacuum chamber (which blocked collinear betatron x-rays) before a pixelated CsI(Tl+) scintillator detected them at z = 5.5 m. Calculations of γ-ray attenuation [75], according to the Beer-Lambert law, show that secondary particles that the γ- rays generate in these materials account for < 3% of the scintillator signal. The γ-rays alone left no discernible trace on the IP. However to characterize the spectrum of betatron x-rays [27], we covered ∼ 6 cm2 of the IP with a planar array of forty 4-mm-diameter, 20-200 µm-thick K-edge filters of vari- ous metals (Fig. 3.3a, upper right). On some shots, when a γ-ray pulse passed through one disk, a small fraction of its energy converted to secondary elec- trons (e−) and positrons (e+) that did expose the IP (Fig.3.3a, lower right), allowing us to determine the number Nγ of photons in the pulse.

Figure 3.4: Shot-to-shot pointing fluctuations. (a) Electron spectra (left), γ-ray profiles (right) for two shots showing equal but opposite vertical dis- placements and differing horizontal γ-ray displacements, with respect to the alignment axis. (b) Plot of vertical γ-ray vs. electron displacements.

19 Shot-to-shot fluctuations in the pointing and angular divergence of the Thomson γ-ray beam closely tracked corresponding fluctuations of the GeV electron beam, and thus provided valuable e-beam diagnostics. As an ex- ample, Fig. 3.4a shows matching ±1 mrad vertical angular displacements of horizontally-dispersed electrons (left) (±2.7 mm at z = 2.7 m) and centroid of γ-ray profiles (right) (±5.4 mm at z = 5.5m) for two shots with respect to a common horizontal alignment plane (solid horizontal white line). Figure 3.4b displays good agreement in the γ-ray and electron beam vertical displacements, 2 which fit to a linear function dγ = 0.92de + 0.46 mrad (R = 0.92). The simul- taneous observation of γ-ray horizontal and vertical deflections differing by ∼ 1 mrad between the two shots (see Fig. 3.4a (right)) demonstrates different horizontal e− deflections, a fact not easily discerned from the horizontally- dispersed electron spectra themselves. Thus the γ-centroid diagnoses electron launch angle from the LPA, an essential parameter in calibrating the magnetic spectrometer, more accurately and directly than 2-screen electron detection methods [15, 84].

3.2 Linear Thomson Backscatter

The focus for LWFA 5.5 and half of LWFA 6.0 was the generation of γ-ray beams spectrally-peaked (i.e. quasi-monoenergetic) in the tens-of-MeV regime by linear Thomson backscatter (LTBS).

3.2.1 Laser Intensity Approximation

The PM was positioned 3.3 cm after the nominal gas cell exit plane for most LTBS shots. The laser intensity was approximated by assuming the exiting laser expands as a gaussian pulse such that the intensity can be described as,

2P −2r2 I(r, z) = exp( ), (3.3) πw2(1 + z 2) w2(1 + z 2) 0 zR 0 zR

20 where P is the laser power, w0 is the laser’s minimum waist, z is the position along the propagation axis, and zR is the Rayleigh length of the expanding beam. The minimum waist of the beam occurs when the laser is in the self- guided condition, which is a necessary requirement for LWFA. Side-scatter imaging reveals that the laser maintains a self-guided channel up to or very near the gas cell exit.

Figure 3.5: Side-scatter emission of the laser-induced plasma channel seen through a glass window in the helium gas cell. The laser propagates from left to right. A logarithmic function was applied to the image to dampen the strong scattering near the beginning of the gas cell and enhance the visibility of the channel near the end. The bright edge on the right is the exit aperture of the gas cell.

It is therefore assumed that the beam expansion begins at the gas cell exit plane (i.e. z = 0 cm). Experimental observations [11] and simulations [84] suggest w0 ranges from 20−30µm for the TPW laser under LWFA conditions. While the Rayleigh length in free-space can be calculated using a simple expression, the tapering plasma density at the exit of the gas cell changes the expansion rate of the beam before reaching the PM. Therefore, an effective Rayleigh length is inferred by using the spatially calibrated PM reflectivity measurement. The laser intensity required for PM activation for glass is well- known to be ∼ 1014 W/cm2 [21], and the boundary of the high reflectivity region is at ≈1 mm from the beam center. Assuming an axially symmetric beam, the above intensity equation for z = 3.3 cm and r = 0.5 mm can be used to solve for an effective Rayleigh length. It is clear from the above side-scatter image that the LPA-driving laser

21 loses a substantial portion of its energy while traversing the gas cell; we esti- mate only ∼50% of the laser energy will exit the cell. Therefore an initially

750 TW pulse, with w0 = 30µm at the exit yields a zeff ≈ 4 mm, whereas the

Rayleigh length in free-space zR ≈ 2.7 mm. This example demonstrates upper extremes in the laser power, bubble radius, and zeff ; however, propagating the gaussian pulse to the PM plane will regardless yield a peak intensity that roughly ranges from 2 − 4 × 1017 W/cm2 — i.e. the laser strength dropped from a0 ∼ 3 at the LPA exit to ∼0.5 at the PM, where it yielded consistently high (> 50%) PM reflectivity and reliable LTBS.

3.2.2 Bremsstrahlung Contributions

Observed γ-ray signals that depend on the PM could be generated from GeV electrons either by forward bremsstrahlung radiation within the PM or by LTBS in front of the PM. Multiple methods were used to investigate the relative contribution of bremsstrahlung radiation compared with the total ob- served signals. To distinguish these possibilities, we observed how the scintil- lator signal depended on PM thickness (L), PM material, and intensity IR(z) reflected from the PM. Bremsstrahlung is proportional to L and quadratically dependent on the PM material’s effective atomic anumber (Z), but does not depend on IR(z). LTBS, on the other hand, does not depend on PM thickness or material, but is proportional to IR(z), which we varied by adjusting the distance z over which the spent drive pulse diverged from accelerator to PM. This intensity in turn determined the PM reflectivity [81]. As an example, Fig. 3.6 compares scintillator signals from two shots driven by nearly identical laser pulses that yielded electron bunches spectrally peaked at Ee = 920 ± 20 MeV with total charge q = 50 (a) or 125 pC (b). The signals near the centers of Fig. 3.6a and 3.6b were generated with glass PMs of L = 100 (a) or 180 µm (b), and located at z = 3.3 (a) or 5.5 cm (b), as illustrated at the top of Fig. 3.6. While the peak amplitudes of the two signals were nearly the same, the integrated intensities averaged over their

22 respective FWHM have a ratio of Sb/Sa = 1.3. In contrast, the more divergent bremsstrahlung signal at the left-hand edge of panel (b) is 2.4× stronger than its counterpart in panel (a), a consequence of the 2.5× higher q.

Figure 3.6: Scaling of scintillator signal with position z and thickness L of PM: (a) z = 3.3 cm, L = 100µm; (b) z = 5.5 cm, L = 180 µm. Nearly identical laser pulses drove both shots; both yielded electrons with energy peaked at 0.92 GeV and corresponding charge (a) 50 or (b) 125 pC.

A more direct comparison between the two ∼1 mrad signals can be made by normalizing Sa and Sb to their respective charge, with which both bremsstrahlung and LTBS scale linearly. Therefore the normalized ratio [Sb/Sa]n =

Sb/Sa × qa/qb = 1.3 × 0.4 = 0.52. Signals dominated by bremsstrahlung would have yielded [Sb/Sa]n ≈ 1.8, in view of the 1.8× thicker PM in case (b). On the other hand, signals originating mostly from LTBS should yield [Sb/Sa]n ≈ 2 −2 IR(zb)/IR(za). The diverging laser’s squared field strength a0(z) ∝ z inci- 2 2 dent on each PM was estimated to be a0(za) ≈ 0.25 and a0(zb) ≈ 0.09, which yield slightly different PM reflectivities Ra ≈ 0.7 and Rb ≈ 0.9 [81]. Thus we 2 2 expect IR(zb)/IR(za) = (0.9/5.5 )/(0.7/3.3 ) ≈ 0.46, in good agreement with the observed [Sb/Sa]n = 0.52. As a second example, the calculated bremsstrahlung energy loss of the FWHM 50 pC of electrons within the Ee ≈ 2.2 GeV (∆Ee = 0.25 GeV) peak in Fig. 3.3a traveling through L = 100 µm fused silica (density ρSiO2 = 2.5

23 g/cm3) is 14 Ebrem ≈ αBρSiO2 qL ≈ 6.2 × 10 eV (3.4)

2 where αB ≈ 80 MeV-cm /g is the radiative stopping power [74] of 2.2 GeV electrons in silica. The simulation toolkit GEANT4 [4] yielded similar Ebrem ≈ 7.4 × 1014 eV. These values will be compared with the calculated LTBS beam energy in the next section. During LWFA 6.0, a greater number of shots were dedicated toward distinguishing bremsstrahlung from linear TBS signals. The PM remained at z = 3.3 cm for these shots, and bremsstrahlung signals were manipulated by: changing the PM material, changing its thickness, and adding layers of ma- terial behind the PM. All of these things change the “bremsstrahlung factor”

(fbrem), which would be proportional to observed scintillator signals propor- tional if bremsstrahlung does dominate.

02 fbrem = ΣiZi Li (3.5)

0 Zi is the effective atomic number (weighted by mass-fraction if a com- pound) and Li is the thickness of each material. Layers of 100µm glass or copper were placed behind the 100µm glass or plastic PMs, which varied from 12.5 − 125µ m. The imaged fluorescence from a pixelated, 1 cm-thick CsI(Tl) scintilla- tor placed ∼2.86 m downstream of the plasma mirror provided shot-to-shot fluence profiles of the Thomson backscatter/ bremsstrahlung source. The am- plitude of each point was calculated by first integrating the fluorescence of the beam profile observed on the scintillator within the x & y FWHM. The 2 amplitude of the integrated fluence for each shot was divided by Qtot < γ > to suppress variations from non-fbrem contributions. The data suggest that bremsstrahlung cannot be the major contributor of signal since we observe only, at best, a five-fold increase in signal with a nearly 100-fold increase in fbrem. Furthermore, assuming LTBS is the primary contributor, the shot-to-shot variations in amplitude are much more easily

24 Figure 3.7: Scaling of the integrated fluence with fbrem at zPM = 3.3 cm. The blue, dashed curve has a slope of unity and illustrates the expected scaling if bremsstrahlung radiation were the only contributor of signal. The grey, dotted curve represents the best-fit for a linear relationship. explained by shot-to-shot fluctuations in LTBS efficiency.

3.2.3 Linear Thomson Spectra

A relatively simple method to calculate the spectral density of LTBS within the observed solid emission angle ∆Ω = 0.92 µsr (Fig. 3.3b, top) is [70]

2 " # dNγ γea0 dNe ≈ αf ∆Ω , (3.6) dEγ 8¯hωL dEe

where αf is the fine structure constant, and (for data in Fig. 3.3a(left))

γe = 4400, a0 ≈ 0.3 retro-reflected from the PM. Fig. 3.8 (gold curve) shows (FWHM) the resulting dNγ/dEγ peaked at Eγ = 85 MeV with ∆Eγ = 18 MeV. 7 P The FWHM contains Nγ = 7.6 × 10 photons of total energy (Nγ × Eγ) = 6.8 × 1015 eV, about 11× the estimated bremsstrahlung yield in the PM — calculated in the previous section. This supports the conclusion that most observed γ-rays originate from LTBS. The entire dNe/dEe in Fig. 3.3 generated

25 Figure 3.8: Quasi-monochromatic Thomson γ-ray spectra generated as Ee tuned from 0.5 to 2.2 GeV. Spectra are labeled with multipliers that normalize true peak heights to the height of the two lowest energy curves.

8 a total Nγ ≈ 2 × 10 photons from 20 < Eγ < 100 MeV. Fig. 3.8 displays ten quasi-monochromatic Thomson γ-ray spectra peak- ing from 5 to 85 MeV, determined from measured dNe/dEe using Eq. 3.6.

We verified the accuracy of Eq. 3.6 for estimating dNγ/dEγ by analyzing the secondary e− e+ yield of a 40 MeV Thomson γ-ray pulse that produced the IP exposure in Fig. 3.3a (lower right) upon passing through a Ag (75µm)/Cu

(34µm) film pair. We input the dNγ/dEγ from this shot (not shown), calcu- lated from the measured dNe/dEe via Eq. 3.6, into GEANT4, approximating (FWHM) it as a gaussian peaked at Eγ = 40 MeV with ∆Eγ = 20 MeV. Upon 7 passing through the converters, the simulated γ-ray pulse (total Nγ ∼ 10 ) generated e− and e+ energy distributions shown in Fig. 3.3 (lower right) with − + 5 total particle number (Ne + Ne ) ≈ 1.28 × 10 . We compared this with the total particle number NIP obtained directly from the measured PSL within the FWHM of the exposed spot, using published MS IP sensitivity ≈ 20 ± 5 5 mPSL/e [62]. The result — NIP ≈ 1.1 ± 0.2 × 10 — agreed well with the simulated value. One can use a more rigorous treatment to calculate the spectrum, like

26 Figure 3.9: A typical electron dN/dE for LWFA 6.0 and 7.0.

that of [26], such that it also includes the spectral spread from other harmonic contributions as the laser intensity increases. Figure 3.10 is the result of the aforementioned, rigorous treatment to calculate the expected photon energy- angle distribution for an example LWFA electron spectrum (Fig. 3.9) for two possible intensities. It should be noted that the spectrum along the 0 mrad axis in Fig. 3.10 is very nearly the same as the spectrum created using Eq. 3.6.

3.3 Nonlinear Thomson Backscatter

We further examined the behavior of the PM-mediated γ-ray source by ex- panding upon the methods described in Fig. 3.6. In order to validate the PM method as an alternative to other TBS schemes, the last half of LWFA 6.0 and LWFA 7.0 were dedicated to a PM z-scan to explore the technique’s effective- ness at higher intensities. As the PM is moved closer to the gas cell exit, the incident and backscatter intensities of the laser will increase. The data presented in Fig. 3.11 depict the scaling of γ-beam energy

27 Figure 3.10: (a) The first three harmonics of a TBS spectrum calculated from the above dN/dE, assuming a0 = 0.25. (b) The first three harmonics of a TBS spectrum calculated from the above dN/dE, assuming a0 = 0.5. within the FWHM as the PM z-position is moved closer to the LPA exit and, in the last case, within the gas cell. Unlike in Fig. 3.6, the incident intensity –hence Thomson backscatter intensity– is increased. The imaged fluorescence from a pixelated, 1 cm-thick CsI(Tl) scintilla- tor placed ∼2.86 m downstream of the plasma mirror provided shot-to-shot fluence profiles of the Thomson backscatter source. The 39 shots for the PM z-scan were accumulated throughout LWFA 6.0 and LWFA 7.0. The ampli-

28 Figure 3.11: Scaling of the integrated fluence with the PM’s z-position. The blue trendline is a second-order polynomial fit for a total of 39 shots, repre- sented by the light-orange boxes. The vertical red line represents the nominal exit plane of the gas cell. A statistical average and standard deviation is rep- resented by the singular data point with error bars at each respective PM position. tude of each orange box was calculated by first integrating the fluorescence of the beam profile observed on the scintillator within the x & y FWHM. To isolate the dependence of the measured signal from effects unrelated to the backscatter intensity, this spatially integrated fluence was then divided by the 2 factor Qtotal < γ > of the accelerated electron beam, which was calculated over the full measurable energy range (typically from 0.3 - 2.5 GeV). Finally, each amplitude was normalized relative to the largest measured amplitude. A statistical average and standard deviation is represented by the singular data point with error bars at each respective PM position.

The data indicate the expected scaling with a0, which validates the

PM’s usage from 0.1 < a0 <∼ 3 with the TPW laser and confirms the data

29 presented at z = 3.3 cm are generated from linear Thomson backscatter. This is corroborated by the little to no change in beam divergence between the 3.3 and 5.5 cm cases.

zPM Mean Divergence [cm] [mrad] -1 6.88 ± 1.41 1 5.80 ± 1.01 1.55 6.11 ± 0.91 2.3 3.95 ± 0.35 3.3 3.10 ± 0.66 5.5 2.44 ± 1.14

Table 3.1: Scaling of the γ-beam divergence (FWHM) along the laser polar- ization axis with PM z-position.

3.4 Future Work and Conclusions

3.4.1 γ-ray Spectrometer Measurements

There is great difficulty in accurately measuring the spectrum of MeV-scale γ- rays. One of the most direct methods to do so relies on measuring the energy of the secondary particles that are produced (either via forward Compton scatter or pair-production) inside of a converter. However, due to the non-zero thickness of the converter material, secondary particles will experience multiple scattering which blurs the true energy-angle distributions of the particles. This is true even for a mono-energetic photon source such as the one presented in Fig. 3.12. Unfortunately the data collected for LWFA 6.0 had multiple unexpected sources of background. Given the experimental time allotted, we were un- able to perform a rigorous characterization of the background sources, making the collected linear TBS signals extremely difficult to deconvolve without the help of supporting simulations. While the multiple background sources were

30 Figure 3.12: Simulation of e− / e+ energy-angle distributions produced by a monoenergetic, 10 MeV photon beam in 2 cm of carbon. Image and simulations courtesy of Luc Lisi.

Figure 3.13: (Left) A top-down view of the Compton & pair-production spec- trometer design. Higher energy electrons or positrons will deposit their signal further down the length of the spectrometer. (Right) The design and specifi- cations of the magnet housed within the spectrometer. Magnet drawing and specifications courtesy of Ganesh Tiwari. also present during nonlinear TBS shots, they were (as expected) orders-of- magnitude higher in photon number, vastly improving the signal-to-noise ra- tio. It is expected that true measured γ-ray spectra, collected during these experiments, will be produced once they are rigorously deconvolved.

31 3.4.2 Conclusions

Currently the energy spread of our LPA electrons’ high energy peak limits (FWHM) ∆Eγ. However, LPAs have produced ∆Ee < 3 MeV at Ee = 180 MeV

[64] and < 0.2 MeV at Ee < 1 MeV [31], using specialized injection methods. Simulations show such widths can be preserved to GeV energy [31]. Moreover, 2 a0 of the backscatter pulse (and thus Nγ) can be increased considerably — and easily (see Fig. 3.11) — without significant LTBS spectral broadening, especially if a collimator is used to filter out the off-axis second harmonic component. These combined improvements could decrease Eγ (FWHM) to ∼ 0.1 MeV, opening up nuclear spectroscopy applications.

Although we did not measure Eγ directly, we measured the energy dis- tribution of accelerated electrons that produced them with ±5% accuracy on every shot using the calibrated magnetic spectrometer [84]. We inferred peak

Eγ spanning the entire spectral range currently available from large-scale GeV- linac-based LTBS sources [85, 5]. Over the tuning range, θγ (half-cone) av- (FWHM) eraged 1 ± 0.3 mrad and ∆Eγ of the spectral peaks averaged 15 ± 11 MeV, where variances denote standard deviation.

Drive pulse energy was the primary control variable in tuning Ee and Eγ, although shot-to-shot fluctuations in pulse duration, focal profile, and wave- front also played a role. For all but two of the peaks, Nγ within the FWHM (0.1% bandwidth) fell in the range 0.3 to 14×107 (0.2 to 8.8×105). For the two 7 5 exceptions, Nγ was greater: 45 and 173 ×10 (36.5 and 38.6 ×10 ) within the FWHM (0.1% bandwidth). Combining these numbers with estimated γ-ray 17 −3 pulse duration τγ ≈ 80 fs (i.e. half a plasma period for ne ≈ 5 × 10 cm ) and estimated source-size radius of 20 µm at z = 3.3 cm, we estimate peak- brilliance ranging from (0.1 − 4.6) × 1021 photons/s/mm2/mrad2 within 0.1% bandwidth. The highest number originates from the most energetic spectral peak in Fig. 3.8. In summary, we provide proof of principle results in which we con- verted a compact 0.5–2.2 GeV laser-plasma electron accelerator into a bright fs-pulsed, quasi-monochromatic Thomson γ-ray source with peak photon en-

32 ergies tunable from 5 to 85 MeV by inserting a low-Z plasma mirror near the accelerator exit. By taking advantage of improved acceleration and injec- tion schemes for LPAs, we foresee such γ-ray sources eventually complementing large linac-based LTBS sources in nuclear photonic research and applications.

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