One of the most prominent applications of modern particle accelerators is the generation of radiation. In a synchrotron or an x-ray free electron laser (XFEL), high energy electrons oscillating in periodic magnetic structures emit bright x rays. In spite of their scientific appeal that will remain evident for many decades, one limitation of synchrotrons and XFELs is their typical mile-long size and their cost, which often limits access to the broader scientific community. This tutorial reviews the principles and prospects of using plasmas produced by intense lasers as particle accelerators and x-ray light sources, as well as some of the applications they enable. A plasma is an ionized medium that can sustain electrical fields many orders of magnitude higher than that in conventional radio frequency accelerator structures and can be used to accelerate electrons. When short, intense laser pulses are focused into a gas, it produces electron plasma waves in which electrons can be trapped and accelerated to GeV energies. This process, laser-wakefield acceleration (LWFA), is analogous to a surfer being propelled by an ocean wave. Many radiation sources, from THz to gamma-rays, can be produced by these relativistic electrons. This tutorial reviews several LWFA-driven sources in the keV-MeV photon energy range: betatron radiation, inverse Compton scattering, bremsstrahlung radiation, and undulator/XFEL radiation. X rays from laser plasma accelerators have many emerging applications. They can be used in innovative and flexible x-ray imaging and x-ray absorption spectroscopy configurations, for use in biology, industry, and high-energy density science.
I. INTRODUCTION
Since they were proposed in 1979 by Tajima and Dawson,1 laser plasma electron accelerators have been extensively studied through theory, simulations, and experiments and have expanded their reach to applications that can span many disciplines, such as medicine, industry, defense, material, and high-energy density sciences.2 One such application is the production of compact light sources with unique properties,3 offering alternatives to large synchrotrons and free electron lasers.4,5
This tutorial paper reprises many recent results and findings on the subject of x-ray sources driven by laser wakefield acceleration (LWFA) and gives the tools to understand and design such sources for a particular application. The paper is organized as follows: In Sec. II, we review the principles and current status of laser wakefield acceleration, sufficient to provide a good understanding of the electron beam properties that govern the production of light sources; in Sec. III, we present four sources produced by laser wakefield accelerated electrons: betatron radiation, inverse Compton scattering (ICS), bremsstrahlung radiation, and undulator/XFEL radiation. While they can be described using similar formalism, each has a different level of maturity and application space, which we discuss as well. Finally, before concluding and providing open questions, we give an overview of three application techniques in Sec. III, with potential applications in medicine, defense/industry, and high-energy density sciences.
There are many existing reviews of x-ray sources driven by LWFA. Reference 3 presents betatron radiation, ICS, and undulator radiation within a unified formalism, and Refs. 4 and 5 connect these sources to potential applications. Since these reviews have been written, much progress has happened in the field. First, the creation of high power laser networks, such as LaserNetUS,6 has reinvigorated the field, and the 2020 roadmap on laser-plasma accelerators2 cites LWFA-driven light sources as an important application. Second, a LWFA-driven XFEL was demonstrated recently by two groups in the unseeded7 and seeded8 regimes. These results are very promising for new applications. Finally, high repetition rate laser technology, coupled with automation, is progressing rapidly,9 which will help to make LWFA-driven light sources practical and reliable for applications requiring stable beams.10 An exhaustive description of applications and their connections to the various light sources were given in Ref. 5, and in this new manuscript, Sec. IV focuses on three applications where new results have been published since.
II. ACCELERATION OF ELECTRONS IN LASER-PRODUCED PLASMAS
LWFA theory and current status have been discussed in many review articles,2,11 and this section gives an overview of the mechanisms at play to understand electron beam parameters governing light emission. We start with a brief description of the propagation of ultrashort laser pulses in an underdense plasma, nonlinear effects (relativistic self-focusing and the ponderomotive force), the formation of electron plasma waves (the accelerating structure), trapping and acceleration of electrons in electron plasma waves, and finally, light source-relevant regimes of laser plasma acceleration.
A. Propagation of ultrashort laser pulses in a plasma
Throughout this tutorial, we will always assume that intense laser beams have sufficient intensity to form fully ionized plasmas.14 LWFA can be realized with different gases, such as hydrogen (full ionization threshold of W/cm2), or helium (full ionization threshold of W/cm2.) In this case, the laser, with frequency ω0 and wavenumber k, will propagate in the plasma if its electron density ne is less than the critical density nc (underdense regime) such that . Then, the pulse propagates and obeys the dispersion relation , where is the electron plasma frequency, the natural oscillation of electrons in the plasma. The corresponding plasma period is , and the ion plasma frequency . For cm−3, s−1, μm, and ωp. When discussing the formation of a laser plasma accelerator, especially at ultrashort (10's of fs) laser pulse duration, we will generally consider the ions to be immobile.
B. Nonlinear effects
1. Relativistic self-focusing
2. Ponderomotive force
Illustration of the ponderomotive force creating a longitudinal density perturbation and electrical field Ez. The field, represented in 1D, has an amplitude Emax and accelerating/decelerating phases.
Illustration of the ponderomotive force creating a longitudinal density perturbation and electrical field Ez. The field, represented in 1D, has an amplitude Emax and accelerating/decelerating phases.
C. Electron plasma waves
D. Trapping of electrons in electron plasma waves
E. Limitations to electron energy gain
Three main characteristic lengths can limit the electron energy gain in laser wakefield acceleration: diffraction, dephasing, and depletion lengths. When designing a light source, it is important to keep them in mind. The diffraction length is simply the length over which the laser stays focused to maintain sufficient intensity. It is usually no more than a few Rayleigh lengths, which is why a soft focus is better.
The dephasing length is the length over which the electrons catch up with the wave so that they are no longer in an accelerating field and start to decelerate (see Fig. 1). As electrons are accelerated, their velocity increases to approach the speed of light. The plasma wave travels with a phase velocity vp, which is close to the laser group velocity and . Eventually, the electrons outrun the plasma wave and dephase. If we define the dephasing length Ld as the length the electron must travel to slip by 1/2 period with respect to the plasma wave, then . With the electron velocity close to the speed of light, then the cold, 1D limit for the dephasing length is . For cm−3 ( μm), and , then Ld = 3.3 mm. An ideal laser wakefield accelerator is when the acceleration length is equal to the dephasing length, and, thus, energy gain will be . In 3D, the dephasing length expression takes into account the transverse dimensions of the plasma wave (dictated by the laser focusing geometry).24 A current active area of research, which is very promising for optimizing LWFA-driven light sources even at the potential cost of laser energy, is the design of dephasingless laser wakefield accelerators,25 enabled by the use of a flying focus.26
As electrons are accelerated, the laser transmits energy to the plasma wave until it is depleted. The pump depletion length Lpd is calculated by equating the laser pulse energy to the energy left in the wakefield , where Ez and EL and the electrical fields for the wakefield and laser, respectively. We consider that the resonance condition in the 1D limit is satisfied. For the laser field, we consider , and using the definition of the laser normalized potential, we get the expression . For a Gaussian laser pulse, and, thus, , we get, in the linear regime, . For cm−3 ( μm) and , then Lpd = 2.8 cm.
F. Light source-relevant regimes of laser wakefield acceleration
Since the work of Tajima and Dawson,1 many laser wakefield acceleration schemes have been studied, mainly due to the rapid progress in laser technology and large scale computer simulations. A regime is dictated by the interplay between laser intensity, pulse length, spatial dimensions, and electron density. A description of each of them can be found in the literature,11 and the main regimes in which light sources have been developed are described here.
1. Blowout regime
2. Self-modulated regime
In self-modulated laser wakefield acceleration (SMLWFA), the laser pulse is several plasma periods in length. This regime has been widely studied in the 1990s33 for laser pulse lengths on the order of a picosecond, before high intensity femtosecond lasers became available. Betatron radiation in this regime was first reported in 200834 for intensities above 1020 W/cm2 and then in 201735 for lower intensities.
In SMLWFA, the electron plasma wave is excited by the self-modulation and Raman forward instabilities.36 The Raman forward instability occurs when an electromagnetic wave with frequency ω0 (the laser) is decomposed into a plasma wave with frequency ωp and scattered wave with frequency ωs such that . While this process can be detrimental in inertial confinement fusion (ICF) experiments (it reduces the coupling between the laser and the target and can send laser light back into the system), it can excite very large amplitude electron plasma waves. It is initiated when the laser ponderomotive force creates a density perturbation at the plasma frequency ωp. The backscattered wave with frequency ωs propagates in the opposite direction to that of the incident laser pulse, which creates a beatwave pattern of the laser envelope at ωp. This modulated envelope then resonantly interacts with the plasma wave, which in turn increases its amplitude. When it reaches the wavebreaking limit, electrons can be trapped and accelerated into the plasma wave. Because electrons are trapped into multiple plasma wave periods, unlike the blowout regime, the spectrum is characterized by a Maxwellian distribution. As the laser pulse is typically longer than in the blowout regime, the plasma can get hotter, which reduces the theoretical wavebreaking limit and, thus, the maximum electron energy. Due to the growth rate of the Raman instability, SMLWFA is also better suited for picosecond-scale pulses.
III. X-RAY LIGHT SOURCES
In this section, we review the four main mechanisms producing x rays in the keV–MeV energy range with LWFA electrons, and the properties of the photons they emit. For Betatron, undulator, and inverse Compton scattering radiation, the process is very similar and can be parametrized3 because the spectrum is that of a relativistic electron undergoing oscillations. These oscillations are, respectively, induced by space-charge separation in the wakefield, an externally applied magnetic field, and by a laser field. A schematic representation of the four light sources is shown in Fig. 2.
Schematic representation of x-ray sources driven by laser wakefield acceleration discussed in this tutorial.
Schematic representation of x-ray sources driven by laser wakefield acceleration discussed in this tutorial.
A. Betatron
Illustration of Eq. (27), for θ = 0, which corresponds to on-axis radiation, and for several critical energies.
Illustration of Eq. (27), for θ = 0, which corresponds to on-axis radiation, and for several critical energies.
There are several methods to simulate betatron radiation spectra and beam profiles. The first one is to use single electron models, which is very useful when trying to design a betatron x-ray experiment. Equation (14) can be solved by using a fourth-order Runge–Kutta algorithm to obtain the single electron trajectories for given initial conditions and fields.42,43 The electron trajectory is then used to calculate the intensity radiated by the particle per unit frequency ω and solid angle Ω with Eq. (21). Similarly, the betatron x-ray beam profile is calculated by integrating Eq. (21) over frequencies. Figure 4 shows an example of electron trajectory, with its corresponding betatron x-ray spectrum and beam profile. For this particular case, the parameters are cm−3, γ = 200, x0 = 1 μm, , and α = 0. The trajectory was calculated using 3000 time steps (with each unit step ). At each point of calculation of the trajectory, the spectrum and beam profile were calculated using frequency steps of 100 eV. For the chosen parameters, ωc = 4.2 keV and . The beam has a divergence of and along the direction parallel and perpendicular to the plane of the oscillations, and the on-axis spectrum peaks at keV. Although more computationally intensive, the other method uses electrons trajectories obtained from PIC simulations and post-processes them using Eq. (21) to calculate the spectrum and profile with a much better resolution.44 This is usually better for the self-modulated regime, where trajectories are more complex.35
From left to right: example of an electron trajectory in the plasma calculated with a fourth order Runge–Kutta algorithm, with the corresponding betatron x-ray beam profile and spectrum observed on-axis. Shown on the right plot is the full spectrum (solid line), calculated using Eq. (21) and containing the harmonic structure of the radiation. The asymptotic limit, calculated using Eq. (27), corresponds to the envelope of this curve. For this example, the parameters are cm−3, γ = 200, x0 = 1 μm, , and α = 0. Here, the critical frequency Ec (keV) = (cm−3)r (μm) = 4.2 keV and . The beam has a divergence of and along the direction parallel and perpendicular to the plane of the oscillations.
From left to right: example of an electron trajectory in the plasma calculated with a fourth order Runge–Kutta algorithm, with the corresponding betatron x-ray beam profile and spectrum observed on-axis. Shown on the right plot is the full spectrum (solid line), calculated using Eq. (21) and containing the harmonic structure of the radiation. The asymptotic limit, calculated using Eq. (27), corresponds to the envelope of this curve. For this example, the parameters are cm−3, γ = 200, x0 = 1 μm, , and α = 0. Here, the critical frequency Ec (keV) = (cm−3)r (μm) = 4.2 keV and . The beam has a divergence of and along the direction parallel and perpendicular to the plane of the oscillations.
B. Inverse Compton scattering
X-ray spectra in the case of Compton scattering (black) and Thomson scattering (red) limits. Left parameters: scattering laser = 20 ps FWHM pulse duration, 532 nm wavelength, 34 μm rms spot size, 150 mJ; electron beam = 116 MeV, 40 μm rms spot size, 20 ps FWHM bunch length, 0.5 nC beam charge, 6 mm mrad normalized emittance. Right parameters: laser = 10 ps FWHM pulse duration, 532 nm wavelength, 12 μm rms spot size, 150 mJ; electron beam = 250 MeV, 15 μm rms spot size, 10 ps FWHM bunch length, 0.25 nC beam charge, 1 mm mrad normalized emittance. Reproduced with permission from Albert et al., Phys. Rev. Spec. Top. Accel. Beams 14, 050703 (2011); Copyright 2011 licensed under a Creative Commons Attribution (CC BY) license.51
X-ray spectra in the case of Compton scattering (black) and Thomson scattering (red) limits. Left parameters: scattering laser = 20 ps FWHM pulse duration, 532 nm wavelength, 34 μm rms spot size, 150 mJ; electron beam = 116 MeV, 40 μm rms spot size, 20 ps FWHM bunch length, 0.5 nC beam charge, 6 mm mrad normalized emittance. Right parameters: laser = 10 ps FWHM pulse duration, 532 nm wavelength, 12 μm rms spot size, 150 mJ; electron beam = 250 MeV, 15 μm rms spot size, 10 ps FWHM bunch length, 0.25 nC beam charge, 1 mm mrad normalized emittance. Reproduced with permission from Albert et al., Phys. Rev. Spec. Top. Accel. Beams 14, 050703 (2011); Copyright 2011 licensed under a Creative Commons Attribution (CC BY) license.51
The theory of Compton scattering from the interaction of relativistic electrons with high intensity laser pulses has been well studied and includes cases such as nonlinear Thomson scattering theory for linearly or circularly polarized incident laser fields of arbitrary intensities and for electrons of arbitrary energies,52,53 scattering pulses with very few cycles,54 nonlinear effects producing broad spectral distributions of scattered photons with patterns of subpeaks,55 or weakly nonlinear effects.56 The idea of using LWFA for Compton scattering for high x-ray energies was originally proposed,57 before being demonstrated with the scattering beam provided by a reflection of the drive beam off a plasma mirror58 or by a secondary laser pulse.59
C. Undulator and free electron laser
Because current LWFA electron beam properties hardly satisfy the requirements for an XFEL, several undulator schemes have been numerically investigated to overcome the large energy spread of LWFA beams. A detailed discussion on this subject is presented in another Ref. 3. A transverse field variation into the FEL undulator reduces the effect of beam energy spread and jitter, and this method shows that it can produce soft x rays from 1 GeV electron beams with a 1% rms energy spread, for a 5 m long undulator with a periodicity of 1 cm.66 Another concept has shown that FEL gain can be obtained for EUV rays with an electron beam energy spread of 1% rms and a bunch charge of 5 pC by using a large undulator strength > 1 and bunch decompression.67 The electron energy considered was 300 MeV, and the FEL wavelength was calculated to λ = 134 nm. A chicane can also be used as a bunch stretcher,68 which reduces the gain length for an XFEL operating with an energy spread on the order of the Pierce parameter. Space-charge effects due to the high peak beam currents (10–100 kA) of LWFAs are a problem as well. Solutions include the generation of electron beams with a negative energy chirp (the energy in the front of the beam is lower than at the tail) or the use of a tapered (variable period) undulator.69 Thomson scattering was proposed as a method for conditioning FEL electron beams.70 In this case, Thomson scattering of an intense focused laser pulse produces a correlation between the energy loss by an electron and its transverse location in the laser field.
For a long time, only undulator radiation had been produced, with 55–75 MeV, 1% energy spread electron beams in the visible wavelengths,71 and with 200 MeV electron beams in the soft x-ray range, down to a few nm.72 However, teams recently demonstrated lasing of a LWFA-driven XFELs at 27 and 270 nm (seeded) (Refs. 7 and 8). Transport quadrupoles and magnetic chicanes were necessary to properly shape the electron beam as it enters the undulator. A comparison between the results of this experiment and the performance of LCLS is shown in Fig. 6. Institutions worldwide continue to actively pursue the design of LFWA-driven XFELs.
Left: experimental setup used to produce a LWFA-driven XFEL and comparison between the experimental results and the LCLS parameters. Left figure reproduced with permission from Wang et al., Nature 595, 516–520 (2021) Copyright 2021 Springer.7
Left: experimental setup used to produce a LWFA-driven XFEL and comparison between the experimental results and the LCLS parameters. Left figure reproduced with permission from Wang et al., Nature 595, 516–520 (2021) Copyright 2021 Springer.7
D. Bremsstrahlung
In a bremsstrahlung radiation source, high-energy electrons are converted into gamma-ray beams as they pass through a dense target. This process has been well investigated with conventional particle accelerators and is employed for flash-radiography systems. Bremsstrahlung sources from laser–plasma interaction experiments at relativistic intensities have been well studied, and in this case, the MeV electrons can be produced by various processes, including ponderomotive acceleration, direct laser acceleration, inverse bremsstrahlung, resonance absorption, or heating mechanisms. By comparing with these, LWFA produces electron beams with higher energies and lower emittances, which is attractive for applications requiring MeV-class photons, high flux, and small source sizes.
LWFA-driven bremsstrahlung sources have been first studied in the self-modulated regime.74–76 Similar experiments were reproduced with a femtosecond laser system.77 Electron beams (20–200 MeV), with Maxwellian temperatures around 40 MeV, interacting with a Tantalum converter, were used to produce gamma-rays with a small source size (320 μm) and low divergence (a few degrees). The source duration is expected to be on the order of the laser pulse duration (30 fs), and the photon dose is on the order of 1 Gy a few centimeters from the source. As a comparison, tumors are typically treated with photon doses on the order of 10's or Gy.
The source size can be as small as 30 μm with proper optimization of the electron beam parameters and using fs-class laser systems.78 Approximately 108 photons were generated in the 8–17 MeV gamma-ray region by 10–45 MeV LWFA electron beams produced with a 10 TW laser system and crossing a 2 mm Tantalum slab.79 The yield of gamma-rays produced by LWFA electrons from a similar laser system exceeds the yield of gamma-rays from direct irradiation of solid targets by two orders of magnitude.80 Progress made on LWFA electron beams now permits the production of tunable gamma-ray sources based on bremsstrahlung. A ∼15 pC, 220 MeV, quasi-monoenergetic electron beam can produce 109 photons around 10 MeV.81 A 300 pC, 1 GeV, electron beam traversing a 1 mm Tungsten target would produce photons/shot, with 0.1% of these having an energy greater than 15 MeV.
E. Summary of x-ray sources properties
One of the principal advantages of x-ray sources driven by LWFA is their ability to cover a broad spectral range, which is particularly useful for applications. The exact performance of the sources is dictated by the laser and plasma parameters, and for a modest 50 TW laser system, betatron radiation, ICS, and Undulator radiation will produce photons with an average energy of 5 keV, 25 eV, and 650 keV, respectively,3 with a number of photons/beam around . Most of these sources are now routinely produced on laser systems with powers up to a few 100 TW, and Table I gives an overview of the most current properties, as observed experimentally. Figure 7 shows the ideal spectral range operation of each source, which current laser technology. A comparison of Betatron, ICS, and Bremsstrahlung radiation performed with the same electron beam parameters (a Maxwellian electron distribution extending up to about 300 MeV) can be found in Ref. 76. Therefore, betatron dominates for 1–20 keV, ICS for 20–200 keV, and Bremsstrahlung beyond 200 keV. With the establishment of specialized high power laser networks, such as LaserNetUS,6 and the construction of new multi-PW laser systems, one can expect the photon energy and flux to be extended. High repetition rate laser technology, coupled with automation, will also improve the source repetition rate and stability.
. | Betatron . | Compton . | Bremsstrahlung . | Undulator . | XFEL . |
---|---|---|---|---|---|
Energy range (eV) | 170 | 46 | |||
Bandwidth (%) | 100 | 50 | 100 | 22 | 2–7 |
Number of photons | 109 | 108 | 1010 | ||
Source size (μm) | 1.8 | 1.5 | 320 | 270 | 2000 |
Duration (fs) | < 30 | < 30 | < 30 | < 30 | < 30 |
Collimation (mrad, fwhm) | 2.5 | 10 | 50 | 0.18 | |
Repetition rate (Hz) | 10 | 10 | Limited by solid target | 10 | 1–5 |
. | Betatron . | Compton . | Bremsstrahlung . | Undulator . | XFEL . |
---|---|---|---|---|---|
Energy range (eV) | 170 | 46 | |||
Bandwidth (%) | 100 | 50 | 100 | 22 | 2–7 |
Number of photons | 109 | 108 | 1010 | ||
Source size (μm) | 1.8 | 1.5 | 320 | 270 | 2000 |
Duration (fs) | < 30 | < 30 | < 30 | < 30 | < 30 |
Collimation (mrad, fwhm) | 2.5 | 10 | 50 | 0.18 | |
Repetition rate (Hz) | 10 | 10 | Limited by solid target | 10 | 1–5 |
IV. OVERVIEW OF CURRENT APPLICATION TECHNIQUES
Comprehensive reviews of potential applications in biology, medicine, industry, defense, material, and high energy density science have been done elsewhere,2,4,5 and here, we focus on three application techniques with which LWFA-driven sources have seen significant progress in the past 5 years and are poised to have an impact. We also present some requirements necessary to take them to the next level.
A. X-ray phase contrast imaging
Conventional x-ray radiography of objects relies on absorption contrast, which comes from density differences and variations in material composition and thickness. In materials where there is little absorption, such as soft biological tissue or carbon-based compounds, the radiography image contrast is very poor. In phase contrast imaging, contrast is obtained by phase variations in the transmitted beam, which arise from changes of the index of refraction. Phase contrast imaging is approximately a thousand times more sensitive than absorption contrast, but the advantage over absorption contrast will be more prominent in the hard x-ray region.82
XPCI has been used in LWFA experiments for imaging biological samples, such as small animals86–88 or bone samples.89 Studies have demonstrated soft tissue phase contrast imaging and extraction of quantitative information by phase retrieval has also been performed,90 and recent simulations show that it is possible to extend the resolution to the sub-micron regime.91 Although betatron radiation is mostly employed, the inverse Compton source could also be used, and ICS with a conventional accelerator has been used for biological imaging.92 Monoenergetic high energy x-ray sources are promising for this type of application because they can be tuned to maximize contrast at an absorption edge.93 Applications are now expanding beyond biological and medical imaging and include imaging of surface defects in alloys,94 inertial confinement fusion (ICF) capsules,95,96 parts from additive manufacturing,97 industrial imaging,98 or the propagation of laser-driven shocks in high energy density matter.99 Some examples are shown in Fig. 8.
Examples of imaging experiments done with LWFA-driven sources. (A) Tungsten image quality indicator (IQI) radiography with a bremsstrahlung source. Reproduced with permission from Ben-Ismail et al., Nucl. Instrum. Methods Phys. Res. Sect. A 629, 382–386 (2011). Copyright 2011 Elsevier.78,109 (B) Phase contrast imaging of vacuum grease bubbling into vacuum with a betatron source of critical energy in the 2–5 keV range and size of 5 μm. Reproduced with permission from Vargas et al., Plasma Phys. Controlled Fusion 61, 054009 (2019). Copyright 2019 IOP Publishing.97 (C) Phase contrast imaging of a 2 mm diameter capsule used in inertial confinement fusion experiments taken with a betatron source of critical energy around 15 keV and a source size < 4 μm. Reproduced with permission from Fourmaux et al. Opt. Express 28, 13978–13990 (2020). Copyright 2020 Optica Publishing.95 (D) Image of copper pins embedded in aluminum radiographed with an inverse Compton scattering source peaking at 100 keV and with a source size < 14 μm. Reproduced with permission from Ma et al., Matter Radiat. Extremes 5, 064401 (2020). Copyright 2020 AIP.112
Examples of imaging experiments done with LWFA-driven sources. (A) Tungsten image quality indicator (IQI) radiography with a bremsstrahlung source. Reproduced with permission from Ben-Ismail et al., Nucl. Instrum. Methods Phys. Res. Sect. A 629, 382–386 (2011). Copyright 2011 Elsevier.78,109 (B) Phase contrast imaging of vacuum grease bubbling into vacuum with a betatron source of critical energy in the 2–5 keV range and size of 5 μm. Reproduced with permission from Vargas et al., Plasma Phys. Controlled Fusion 61, 054009 (2019). Copyright 2019 IOP Publishing.97 (C) Phase contrast imaging of a 2 mm diameter capsule used in inertial confinement fusion experiments taken with a betatron source of critical energy around 15 keV and a source size < 4 μm. Reproduced with permission from Fourmaux et al. Opt. Express 28, 13978–13990 (2020). Copyright 2020 Optica Publishing.95 (D) Image of copper pins embedded in aluminum radiographed with an inverse Compton scattering source peaking at 100 keV and with a source size < 14 μm. Reproduced with permission from Ma et al., Matter Radiat. Extremes 5, 064401 (2020). Copyright 2020 AIP.112
These recent experiments are promising; however, some improvements are still necessary to make LWFA-based sources competitive for this application. To obtain quality images from XPCI, a sufficient number of photons Nph is necessary. Since x-ray CCDs used for these experiments are typically 1 Megapixels and the fluctuations from Poisson statistics scale with , where nij is the number of photons detected per pixel; then, we should have (assuming photons uniformly fill the detector). More photons are better, since the source is generally not uniform and the detection efficiency can be on order of a few %. In order to improve the quality of XPCI experiments with betatron radiation, future directions include repetition rate increase and a better field of view, currently limited to tens of mrad. Data acquisition rates of XPCI beam lines at synchrotrons are > 10 Hz and allow real-time visualization of internal physiological mechanisms. Current medical systems, as well as synchrotrons, have a field of view of ∼10 cm, whereas current betatron x-ray imaging experiments have a field of view of limited to about a cm, depending on magnification.
B. High-energy, high-resolution radiography
Gamma-ray radiography is widely used for nondestructive evaluation100,101 in a number of applications such as the inspection of cargo containers or welded structures (pipes, vessels, tanks) produced by large industries. Compton scattering and bremsstrahlung from LWFAs present several advantages that are desired for this application: high energy photons (MeV) to penetrate dense objects, a low dose for safety, and a small source size (a few μm) for good spatial resolution.
Short pulse laser/solid interactions can directly produce gamma-rays suitable for radiography. High intensity laser pulses ( W/cm2) are absorbed into hot electrons with a temperature on the order of the ponderomotive potential.102 These hot electrons, observed in early experiments,103,104 can produce copious amounts of gamma-rays with solid, high-Z targets, such as Gold or Tungsten.105,106 At intensities of 1019 W/cm2, 104 photons/eV/Sr have been reported and were used to radiograph a high area density object (up to 85 g/cm3).106 The drawback is the rather large source size, about 400 μm, which limits the spatial resolution. Recent techniques, using shaped targets, such as compound parabolic concentrators,107,108 have demonstrated yield improvement.
A better resolution can be achieved with bremsstrahlung produced by the interaction of LWFA electrons with a solid target in the self-modulated74 and blowout77 regime. The resolution in the first blowout regime experiment was 320 μm,77 which was well improved to 30 μm with optimization of the electron beam parameters.78,109
Compton scattering is a promising source for this application, because of its potential tunability, narrow bandwidth, and small source size, when compared to bremsstrahlung. Gamma ray photons with energies up to 10 MeV and a spectral bandwidth of 10% have been measured for potential radiography applications.110 In this experiment, using a driver for the electron beam and a scattering beam, the x-ray source size was measured to be 5 μm using a cross correlation technique in which the scattering pulse is scanned. In addition, the narrow divergence of the beam is well suited for long standoff imaging. A USB flash drive was radiographed with a 1.5 μm, 100 keV Compton scattering x-ray source,58 with observation of very small features. For security applications, experiments have demonstrated that a 6–9 MeV Compton source can be used to detect concealed threats.111 Figure 8 shows an example of imaging with a 100 keV inverse Compton source.
C. Time-resolved x-ray absorption spectroscopy
Using a sub-ps duration source for x-ray absorption spectroscopy is of potential great interest to study electron-ion equilibration processes in warm dense matter because the absorption spectrum allows retrieving the evolution of the ionization state , the electron temperature Te, and the ion temperature Ti. Figure 9 illustrates this and shows x-ray absorption spectra for an aluminum sample at different temperature conditions. The evolution of the electron temperature has been measured with XANES in optically heated warm dense copper,116 aluminum,117 and iron.118 Another class of experiments includes the study of various materials at Mbar pressures obtained from laser-driven shocks. In this case, x-ray diagnostic techniques can be either XANES,119–122 or EXAFS.123 Models used in these experiments can be improved with better temporal resolution, and, thus, several experiments have been performed using shorter duration synchrotron x rays to look at the electronic structure of warm dense copper and silicon dioxide. XANES experiments and XFEL probe have looked at shocked compressed matter, near the Molybdenum LIII edge (2.520 keV),124 and the iron K-edge.122 However, the stochastic nature of the SASE FEL spectrum makes this type of measurement extremely challenging.
XANES and EXAFS simulations (courtesy Y. Ping at LLNL) done with the FEFF code, an ab initio multiple-scattering code for calculating excitation spectra and electronic structure.113,127 The simulations show the variation of the x-ray absorption spectrum for an aluminum sample near its K-edge, for different electron temperatures.
XANES and EXAFS simulations (courtesy Y. Ping at LLNL) done with the FEFF code, an ab initio multiple-scattering code for calculating excitation spectra and electronic structure.113,127 The simulations show the variation of the x-ray absorption spectrum for an aluminum sample near its K-edge, for different electron temperatures.
Using betatron radiation for x-ray absorption spectroscopy in warm dense matter has been successfully attempted in several proof-of-principle experiments. A 200 TW laser was used to produce 106 photons/eV betatron x rays in the 5 keV region, sufficient for XANES at the K-edge of a Titanium sample.125 Another experiment used the source for XANES at the Copper L-edge, with about 105 photons/eV at 1 keV, and >50 shot accumulations were necessary for the measurement.126 For practical use as a user-facility-type source, the betatron source stability and flux still need to be improved. A successful XANES or EXAFS experiment needs to have a spectral resolution better than 2 eV. In general, the oscillation amplitude of the EXAFS signal is on the order of a few % of the total absorption signal (the edge step). Ideally, the random statistical noise, , where NPh is the number of x-ray photons in the energy band of interest, should be 1/1000 of the EXAFS signal. This means that the condition /eV must be fulfilled to realize an EXAFS experiment with good statistics. The recent experiments125,126 are around this threshold. The LWFA-driven betatron x-ray source should, in the near future, benefit from increased repetition rate laser systems and the emergence of PW-class laser user facilities. In addition to the quality of the x-ray source, instrumentation techniques (focusing, spectroscopy) can be specifically adapted for betatron x-ray radiation in order to achieve good spectral resolution.
V. CONCLUSION AND OPEN QUESTIONS
X-ray sources driven by laser plasma acceleration are now well understood and enable unique new opportunities for applications. If one considers the four processes presented in this tutorial (betatron radiation, inverse Compton scattering, bremsstrahlung radiation, and undulator/XFEL radiation), these sources can produce tunable photons in the keV-MeV energy range, collimated beams (mrad), small source sizes (μm), and ultrashort pulse durations (fs-ps). Additionally, they are compact and can be synchronized with drive laser systems. Figure 10 shows a comparison of these sources with conventional light sources, adapted from a recent Ref. 5. Due to their properties, LWFA-driven light sources enable applications in medical, biological, and industrial imaging, radiography of dense objects, pump-probe experiments to understand transient phenomena and matter in extreme conditions by using absorption spectroscopy. With the emergence of modern high intensity laser facilities, such as the Extreme Light Infrastructure in Europe and open access high intensity laser networks such a LaserNetUS, we can expect to see many new developments in the coming years. Several open questions remain, among which, two important ones: First, will we ever have a portable, mini XFEL? Second, what will it take to make these sources practical for applications for users who want to use them without any background and expertise in laser-plasma physics?
Peak brightness of betatron, inverse Compton and bremsstrahlung radiation from LWFA compared with conventional light sources in the same energy range. Sources included in this plot are: The APS synchrotron U30 undulator (Argonne National Laboratory, USA), the ALS synchrotron (Lawrence Berkeley National Laboratory, USA), the Spring8 synchrotron (RIKEN, Japan), x-ray tubes (Copper and Molybdenum Kα), the LCLS free electron laser (SLAC, USA), and high harmonics generation from laser-produced plasmas. The images show a conventional radiograph from the author taken in the 1980s with an x-ray tube (bottom) and a phase contrast image of a laser-driven shock taken with the LCLS XFEL (top).128 Reproduced with permission from Albert and Thomas, Plasma Phys. Controlled Fusion 58, 103001 (2016). Copyright 2016 IOP Publishing.
Peak brightness of betatron, inverse Compton and bremsstrahlung radiation from LWFA compared with conventional light sources in the same energy range. Sources included in this plot are: The APS synchrotron U30 undulator (Argonne National Laboratory, USA), the ALS synchrotron (Lawrence Berkeley National Laboratory, USA), the Spring8 synchrotron (RIKEN, Japan), x-ray tubes (Copper and Molybdenum Kα), the LCLS free electron laser (SLAC, USA), and high harmonics generation from laser-produced plasmas. The images show a conventional radiograph from the author taken in the 1980s with an x-ray tube (bottom) and a phase contrast image of a laser-driven shock taken with the LCLS XFEL (top).128 Reproduced with permission from Albert and Thomas, Plasma Phys. Controlled Fusion 58, 103001 (2016). Copyright 2016 IOP Publishing.
A portable, mini-XFEL is likely, but not in the near future. Many improvements are still needed on the LWFA beam properties. First, higher electron energy is necessary to produce harder x rays than the recent demonstration at 27 nm.7 The current highest energies produced by LWFA are reported at 8 GeV (5 pC),62 5 GeV,63 and possibly 10 GeV.129 Then, shot-to-shot electron beam energy stability will need to be improved by a factor of 10–100 for viable operation. Finally, the recent experiments, while a major breakthrough, demonstrated gain, but not full saturation.
In order to make these sources practical for applications, especially for communities not familiar with laser-plasma interaction experiments, several improvements are required, primarily source stability, and source flux. This will be made by the use of repetition rate technology, not only for the laser but also for the targets and diagnostics, and use of automation and machine learning to optimize source performance and data analysis, and accelerate the rate of discovery.130,131 Steps in this direction are already taken for LWFA.10 Ultimately, it will be the intersection of different communities with laser and plasma physicists that will drive innovation for applications of x-ray sources driven by laser wakefield acceleration.
ACKNOWLEDGMENTS
This work was performed under the auspices of the U.S. Department of Energy under Contract No. DE-AC52-07NA27344 with support from the DOE Office of Science Early Career Research Program under No. SCW1575-1.
AUTHOR DECLARATIONS
Conflict of Interest
The author has no conflicts to disclose.
Author Contributions
Felicie Albert: Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal).
DATA AVAILABILITY
Data sharing is not applicable to this article as no new data were created or analyzed in this study.