Highly efficient laser-driven Compton gamma-ray source
The recent advancement of high-intensity lasers has made all-optical Compton scattering become a promising way to produce ultra-short brilliant -rays in an ultra-compact system. However, so far achieved Compton -ray sources are severely limited by low conversion efficiency (lower than ) and spectral intensity ( ). Here we present a highly efficient gamma photon emitter obtained by irradiating a high-intensity laser pulse on a miniature plasma device consisting of a plasma lens and a plasma mirror. This concept exploits strong spatiotemporal laser-shaping process and high-charge electron acceleration process in the plasma lens, as well as an efficient nonlinear Compton scattering process enabled by the plasma mirror. Our particle-in-cell simulations demonstrate that in this novel scheme, brilliant -rays with very high conversion efficiency (higher than ) and spectral intensity ( ) can be achieved by employing currently available petawatt-class lasers with intensity of . Such efficient and intense -ray sources would find applications in wide-ranging areas.
The pursuit of compact -ray sources is motivated by many applications in fundamental science, industry, and medicine [1, 2]. High-energy -ray radiation has become an immensely useful tool for probing hot dense matter , photonuclear spectroscopy , inspection of nuclear waste , material synthesis , and cancer therapy . With the rapid development of laser technology, the production of -rays based on laser-plasma interactions has attracted considerable attention in the past decade. In contrast to conventional -ray sources based on large-scale and costly particle accelerators [8, 9], the -ray source based on an all-optical approach is much more compact. In addition, it possesses unique properties, such as ultrashort duration, ultrahigh brilliance, and small source size [1, 2], which potentially makes it possible to realize a tabletop -ray source with much higher spatiotemporal resolution than the conventional ones.
Several schemes have been proposed to produce compact -rays based on laser-plasma interactions, including laser-driven bremsstrahlung radiation [10, 11, 12, 13, 14, 15] and Compton (or Thomson) scattering [16, 22, 17, 18, 19, 20, 23, 24, 21, 25]. For a laser-driven bremsstrahlung source, where a laser-wakefield accelerated electron beam impinges on a high- target, very high-energy (up to 100 ) gamma photons can be generated [13, 14, 15]. So far the peak brilliance of the -ray source ( ) achieved in this scheme, however, is limited by wide divergence angle and large source size, and the conversion efficiency (less than ) is limited by a small cross section. The Compton (or Thomson) scattering, based on the collision between a laser-wakefield accelerated electron beam and another counter-propagating laser pulse [16, 17, 18, 19, 20, 21] or a reflected laser pulse by a plasma mirror [22, 23, 24, 25], has been considered a promising scheme for the production of high-energy high-brilliance -rays, since it exploits the double-Doppler upshift of the laser photon energy by relativistic electrons. In this scheme, multi- -rays with high peak brilliance ( ) have already been produced experimentally . However, due to the limitations on the number of high-energy electrons and the laser photons participating the scattering process, the presently achieved energy conversion efficiency (less than of total laser energy) and the spectral intensity (less than ) of the -rays are rather low in this scheme [16, 22, 17, 18, 19, 20, 23, 24, 25, 21], which severely limits their usefulness in aforementioned applications. Recently synchrotron photon emission in a relativistic transparency regime [26, 27, 28, 29, 30, 31], where an ultra-intense laser pulse is incident onto a relativistically underdense target, was proposed as a relatively efficient scheme for the production of brilliant -rays. However, this scheme becomes effective for lasers at intensity exceeding or even , which has good prospects for the next-generation lasers  but holds little promise for the presently available lasers . So far the production of brilliant -rays, especially with high conversion efficiency and spectral intensity that are essential for many demanding applications, however, remains out of reach.
Based on the very recent technological advances in high-power short-pulse laser with a very high contrast [34, 35, 36], in this article, we propose a highly efficient approach to produce copious gamma photons by irradiating a high-intensity laser pulse on a microsized bilayer plasma device, which consists of a near-critical-density (NCD) plasma lens [37, 38, 39] and a solid-density plasma mirror . The plasma lens acts to strongly compress the laser pulse and simultaneously provides the source for high-charge (tens of ) and high-energy (hundreds of ) electrons, which are directly accelerated by the strong laser field within tens of micrometers. The plasma mirror acts to effectively reflect the laser pulse, and the reflected laser pulse collides with the counter-propagating electron beam. In this case, nonlinear Compton scattering  of the strongly focused laser pulse by the high-charge high-energy electrons occurs, emitting copious gamma photons. As will be demonstrated, this novel approach makes it feasible to produce brilliant -rays with very high conversion efficiency and spectral intensity using currently available lasers at intensities .
Schematic of the gamma photon emitter
The schematic of the efficient gamma photon emitter is shown in Fig.1. In this approach, a laser pulse is incident onto a microsized bilayer plasma device, as shown in Fig.1a, which consists of a plasma lens target with near-critical density ()  and a plasma mirror target with solid density (), where is the plasma density, is the critical density, is the average Lorentz factor, and is the dimensionless vector potential of the laser pulse. In this setup, the plasma lens is relativistically transparent for the laser pulse, but the plasma mirror is opaque. At an early stage, the laser pulse will penetrate into the plasma lens, as shown in Fig.1b. The plasma lens here has dual functions. On one hand, the laser pulse undergoes rapid self-shaping process in the plasma lens due to the combined nonlinear effects of relativistic self-focusing and relativistic self-phase modulation [37, 38, 39]. As a result, the peak laser intensity can be significantly enhanced during the shaping process. On the other hand, the ponderomotive force of the shaped laser pulse expels electrons from the central region to form a plasma density channel, as shown in Fig.1b. In the plasma channel, still a significant number of electrons are confined by the self-generated electromagnetic fields, and they are directly accelerated by the strong laser electric field in the direct-laser acceleration (DLA) regime . Due to the relatively high plasma density and high-gradient accelerating electric field, a high-charge high-energy electron beam can be produced in the plasma lens, and it moves together with the laser pulse, as shown in Fig.1b. At a later stage, when the laser pulse reaches the solid-density target, its rising edge ionizes the target, forming a plasma mirror  that effectively reflects the main part of the laser pulse, as shown in Fig.1c. In such case, the reflected laser pulse collides with the forward-propagating electron beam. The nonlinear Compton scattering process between the high-charge high-energy electron beam and the strongly focused laser pulse occurs efficiently, and copious gamma photons are emitted, as shown in Fig.1c. The current setup provides a simple and efficient approach for gamma photon emissions by harnessing direct-laser acceleration and nonlinear Compton scattering, whereby copious relativistic electrons and laser photons are involved and high-order multiphoton scattering  is dominant. Note that, this scheme is completely different from the well-established schemes based on laser-wakefield acceleration and linear Compton scattering, which provide inefficient gamma-ray sources.
Laser-shaping and electron acceleration in plasma lens
To demonstrate the efficiency of the novel gamma photon emitter, fully three-dimensional particle-in-cell (PIC) simulations were carried out (see the Methods section for details). The corresponding simulation results are shown in Figs.2-5. Due to the relativistic transparency, the laser pulse propagates into the plasma lens and experiences spatiotemporal self-shaping process, as shown in Fig.2a and Fig.2b. The corresponding self-focusing length can be estimated as [38, 39] , where is the beam radius. When the length of the plasma lens is comparable to this characteristic length (about ), the laser-shaping process can occur effectively and the laser intensity can be remarkably enhanced. During the laser-shaping process, the laser beam gradually shrinks into a radius about , which corresponds to the balance between the laser ponderomotive force and the radial electrostatic force . Here refers to the dimensionless vector potential of the self-shaped laser pulse, is the plasma frequency, and is the speed of light in vacuum. Accordingly, the amplification factor of the laser intensity can be expressed as , where is the peak laser intensity of the self-shaped laser pulse, is the initial laser intensity, and is the laser wavelength. Figure 2a shows that, after the shaping process, the laser pulse duration (initially ) is reduced into about (full-width at half-maximum, FWHM). The peak laser intensity is enhanced by a factor of and reaches about , as indicated from Fig.2b, which is in good agreement with the theoretical amplification factor of . This clearly demonstrates that the relativistic plasma lens can induce strong shaping for the laser pulse, leading to the generation of a much shorter and stronger laser pulse. The laser focusing induced by the plasma lens is more effective than the optical focusing by the reflection of a plasma mirror , which shall be discussed later. The necessary level of the input laser intensity for efficient gamma photon emissions could be relaxed significantly in this manner.
On the other hand, when the laser pulse propagates into the plasma lens, a plasma density channel is formed by the laser ponderomotive force, as shown in Fig.3a. Figure 3b shows that a dense ( ) electron beam, which is micro-bunched with the laser wavelength, is confined by the strong magnetic field ( ) self-generated in the plasma channel, as shown in Fig.3e. The particle tracing demonstrates that after an initial injection process, electrons are confined by the magnetic field and execute betatron oscillations, as shown in Fig.3e. In the present scheme, these electrons are directly accelerated by the strong laser field (see Fig.S1 and the corresponding Supplemental Note 1 in Supplemental Materials). The longitudinal charge separation electric field () is negligible compared with the ultra-intense laser electric field ( ), as indicated in Fig.3d. The laser electric field can accelerate the electrons to about within tens of micrometers, as shown in Fig.3f. As a result, an electron beam with ultra-high energy density ( ) is generated, as shown in Fig.3c. These high-energy electrons co-propagate with the laser pulse and they are phase-locked to the laser electric field, as indicated in Fig.3d. Figure 3f shows that the accelerated electron beam has a broad energy spectrum. The total charge of the electron beam reaches up to (the charge of electrons with energy above is about ), which is about three orders of magnitude larger than that in previous Compton scattering scheme based on laser-wakefield electron accelerators using rather low-density plasmas [22, 17, 18, 19, 20, 23, 24, 25, 21]. It clearly shows that the plasma lens, on the other hand, acts as an effective medium for high-charge (tens of ) and high-energy (hundreds of ) electron acceleration.
Nonlinear Compton scattering and efficient gamma photon emissions
The laser-electron beam collision process enabled by the plasma mirror leads to efficient emission of gamma photons through nonlinear Compton scattering, as shown in Fig.4. The plasma mirror effectively reflects the enhanced laser pulse, and the reflected laser pulse collides with the forward-moving electron beam, as indicated in Fig.4a and Fig.4b. It is noted that the self-shaped laser pulse in plasma lens is further focused after the reflection by the plasma mirror due to the relativistically curved surface , as can be seen from Fig.2b and Fig.4a, which induces an increase on the laser intensity from to . Despite this, in our scheme the relativistic self-focusing in plasma lens is still the dominant laser focusing scheme, which is more effective than the optical focusing induced by plasma mirror. In the colliding process, the photons of the ultra-intense laser pulse () are frequency-upshifted to -ray range through nonlinear Compton scattering by the high-charge high-energy electrons. In this process, the quantum photon emission parameter [46, 47] is also calculated, as shown in Fig.4c, where is the Schwinger field, is the mass of electron, is the elementary charge, is the reduced Planck constant, and refer to the electric field and magnetic field acting on the electron, is the electron velocity, and is the Lorentz factor. This parameter determines the photon emission rate and the radiation power by a single electron. In particular, when , the quantum effects in the emission process become non-negligible . Figure 4c shows that the electron beam has a large average in the localized region where the reflected laser pulse is present. Before the laser reflection, the maximum value of is only about in the copropagating configuration, where the Lorentz force from the magnetic field of the laser pulse counteracts the force from the electric field of the laser pulse. After the laser reflection, the maximum value of reaches about , which is comparable with that achieved in previous experiment at SLAC . In the head-on colliding configuration, can be simplified as , which compares the radiated gamma photon energy to the electron energy . Here refers to the electric field perpendicular to the electron velocity, is the laser photon energy, is the radiated photon energy, and is the electron energy. In our case with , the quantum recoil effect is not negligible, thus the interaction process here is described as Compton scattering rather than Thomson scattering. For electrons with and , the energy of the radiated gamma photons can reach about .
The properties of the gamma photons emitted in the nonlinear Compton scattering process is shown in Fig.5. It is shown from Fig.5a and Fig.5b that the gamma photons are bunched with the laser wavelength, which is in accordance with the electron beam shown in Fig.3b. The duration (FWHM) of the whole gamma photon beam is about (corresponding to ), as shown in Fig.5b. Figure 5c shows that the gamma photons are collimated within a solid angle of steradian (), and the maximum number of high-energy gamma photons ( ) emitted per square degree (or ) reaches about . Figure 5d shows that both the gamma photon number and energy are greatly enhanced after the laser reflection. Accordingly, the average power of gamma photon emission is also greatly enhanced and the maximum power is as high as , as shown in the inset of Fig.5d. The gamma photon beam has a broad energy spectrum in this strongly nonlinear regime, as shown in Fig.5d. The gamma photon energy reaches up to , which agrees well with the above theoretical estimation. The spectral intensity at reaches about , which gives a peak brilliance of at (see the Methods section for brilliance calculation). In addition, about of the laser energy (or of the electron energy) is converted into the forward-going gamma photon beams, whereby about is converted into photons with energy above and about is converted into photons with energy above , as shown in Fig.5e. As a comparison, the single target case without the plasma mirror is also considered, as shown in Fig.5e and Fig.5f. In this case, the nonlinear Compton scattering cannot occur and the betatron radiation (or synchrotron radiation) by electrons oscillating in the plasma channel becomes dominant . It is shown that in the present scheme using a bilayer plasma device, both the conversion efficiency and high-energy gamma photon number (with energy above ) are about one order of magnitude larger than those in the single target case. In particular, approximately two orders of magnitude enhancement can be achieved for the high-energy photons above , as indicated from the inset figures of Fig.5e and Fig.5f.
Parametric dependence of efficient gamma photon emission
To demonstrate the robustness of the present scheme on efficient gamma photon emissions, a series of two-dimensional PIC simulations were carried out by considering different laser and plasma parameters (see the Methods section for details). The corresponding results are shown in Fig.6. As a comparison, the single target cases either with the plasma lens alone or with the plasma mirror alone are also considered. Figure 6 shows that the present scheme works effectively for a wide range of laser intensities and plasma densities. In particular, for the lasers delivering intensities of , exploiting the present scheme can achieve more than one order of magnitude enhancement on the conversion efficiency and gamma photon flux when compared with the plasma lens target case (or the betatron radiation scheme). The conversion efficiency roughly scales as for in the present scheme. For the lasers at intensities above , the conversion efficiency can exceed . In this case, the radiation reaction effects significantly impact the radiation process  and the scaling of the conversion efficiency is reduced as . In the present scheme, the required laser intensity for efficient gamma photon emissions can be much lowered, for example, the required laser intensity for conversion efficiency is about , which can be easily achieved with the existing petawatt-class lasers . In contrast, to achieve conversion efficiency in the single target cases, the required laser intensity is above for the NCD plasma lens and is above for the solid-density plasma mirror. In addition, the length of the plasma lens is also an important parameter to optimize the gamma photon emission (see Fig.S2 and the corresponding Supplemental Note 2 in Supplemental Materials). Especially, in order to enable the Compton scattering process, the length of the plasma lens should be less than the laser depletion length in NCD plasmas, which can be approximated as  , with being laser pulse duration.
The present scheme using a microsized bilayer plasma device provides a compact and efficient way for producing high quality -rays. For the available lasers at intensities , brilliant ( ) -rays with very high conversion efficiency (-) and spectral intensity ( ) can be realized in the present scheme. Such -ray source is about times more brilliant than a laser-driven bremsstrahlung source [10, 11, 12, 13, 14, 15] and a conventional Compton ray source based on large-scale accelerators . When compared with the recently reported Compton ray sources based on laser-wakefield electron accelerators [16, 22, 17, 18, 19, 20, 23, 24, 25, 21], the present -ray source is about ten times more brilliant, and especially its spectral intensity is about times higher. In particular, in contrast to the previous Compton -ray sources with a conversion efficiency less than , the present scheme can deliver an unprecedentedly high conversion efficiency. In addition, in comparison with other existing schemes (e.g., the betatron radiation or synchrotron radiation) using a single plasma target, exploiting the current scheme also makes it feasible to produce -rays with much superior properties in terms of conversion efficiency, spectral intensity, peak brilliance, and photon flux.
The efficient and intense gamma-ray source generated in our scheme could be useful for a wide range of applications. In particular, many of applications for photonuclear spectroscopy, inspection of nuclear waste, material synthesis, cancer therapy, etc., require sufficient integrated dose in as a short time or a small number of shots as possible. The gamma-ray emitter proposed here promises a superiority in spectral intensity and a micrometer-sized monolithic structure to the existing high-energy accelerator-based laser Compton sources, which have four to five orders magnitude lower spectral intensity and a - size footprint. Such high-flux gamma-ray source here operated at the repetition rate of is comparable with a conventional low-flux source operated at the repetition rate of . The recent advance of petawatt laser technology already makes it possible to be operated at . As an example, the high-flux gamma-ray source presented here could be useful for nuclear spectroscopy such as nuclear resonance fluorescence, by observing the fluorescence at a large angle from the initial photon beam direction  or by narrowing the bandwidth with a spatial filter .
The present scheme can operate for a wide range of laser and plasma parameters. To realize this scheme in experiments, the key is to employ the NCD plasma lens that is relativistically transparent for a high-intensity laser pulse. Recently several techniques such as highly compressed gas jet , ultra-low density plastic foams , and carbon nanotube foams , have been proposed to produce NCD plasmas, which makes it feasible to achieve the present scheme within current technical capabilities. In addition, in order to avoid destroying the plasma lens by the pre-pulse that deteriorates the temporal quality of the laser pulse, a high contrast for the high power laser of intensity is necessary in experiments because in such case the pre-pulse cannot create pre-plasmas, which was demonstrated in recent pre-plasma experiment using the ultrafast optical parametric amplifier petawatt laser . It is noted that in previous Compton scattering experiments using a plasma mirror, the pre-pluses lead to significant reflectivity reduction of the plasma mirror , which will reduce the efficiency on the Compton scattering process and thus the gamma-ray production. In our proposed scheme, such an issue can be also suppressed due to the fact that during the laser-shaping process in plasma lens, the pre-pulses can be effectively absorbed and the pulse contrast can be significantly improved prior to the plasma mirror [38, 39], which makes the effects of pre-pulse become negligible in our scheme. Experimentally, an ultra-intense laser pulse of the order of with the contrast level better than and even at prior to the peak has been achieved by using a double plasma mirror system , which can greatly reduce the level of pre-plasma creation. On the other hand, in our proposed scheme, the pair production effects and the bremsstrahlung radiation generated inside the plasma mirror can also be neglected (see the Methods section). Accordingly, the experimental feasibility of our proposed scheme is quite convincing for the state-of-art petawatt laser system.
The robustness of the present scheme makes excellent prospects for next-generation lasers. For example, the required laser intensity for reaching the quantum-radiation-reaction dominated interaction process (corresponding to ) can be much lowered in the present scheme (see Fig.S3 and the corresponding Supplemental Note 3 in Supplemental Materials). This makes it possible to explore the quantum-radiation-reaction effect, which is an intriguing unsolved problem of quantum electrodynamics, in laboratories by employing a laser with intensity of . In addition, for future lasers at intensities above , exploiting this scheme could open up the possibility of creating high-flux photons  and dense electron-positron pairs , which are especially attractive for laboratory astrophysics .
In summary, we have proposed a highly efficient and compact laser-driven gamma photon emitter, which can convert an appreciable fraction of laser energy into high-energy gamma photons for a laser with intensity of . This novel gamma photon emitter consists of a plasma lens and a plasma mirror irradiated by a single laser pulse. The present scheme harnesses the nonlinear Compton scattering process through the combination of relativistic plasma optics and the DLA electron accelerator that produces extremely high-charge, high-energy electron beam. This scheme opens up the possibility for developing ultra-brilliant -ray sources with unprecedentedly high conversion efficiency and spectral intensity, which holds great promise for many applications in a broad range of fields, including medicine, industry, military science, material science, and high energy density science.
Three-dimensional particle-in-cell simulations were conducted using the EPOCH code  that incorporates the quantum photon emission process via a Monte Carlo algorithm [46, 47]. The radiation reaction effect on the electron dynamics is calculated self-consistently. In our simulations, the laser pulse is linearly polarized and the peak intensity is , which corresponds to for the laser pulse with a central wavelength of . Here refers to the dimensionless vector potential of the laser pulse. The laser pulse is characterized by a spatially Gaussian profile with and a temporally Gaussian profile with duration of (full width at half maximum). Such laser pulse can be achieved by the femtosecond petawatt lasers at CoReLS . In the simulations, the plasma target is composed of the near-critical density (NCD) plasma layer and a thin solid-density aluminum plasma layer. For the NCD layer, the electron density is and the thickness is . For the solid-density layer, aluminum is initialized as with the electron density of and the thickness is . The simulation box is in space with a cell size of along direction and along and directions, respectively. Here -axis corresponds to the laser propagation direction and -axis corresponds to the laser polarization direction. The simulation box is filled in with about macroparticles. The initial electron temperature is assumed to be . To demonstrate the robustness and effectiveness of the present scheme for different laser and plasma parameters, a series of two-dimensional particle-in-cell simulations were also conducted. In these simulations, the laser intensity, the electron density, and the thickness of the first layer target are adjusted but the other laser and target parameters are fixed, which are the same as above. In the simulations, the simulation box is resolved with the cell size of along the laser propagation axis and along the transverse axis. In these simulations, current smoothing technique and high-order weighting functions are employed to suppress the numerical heating.
In the simulations, we calculate the brilliance of the generated -rays by selecting the gamma photons within energy bandwidth (BW) at a specific energy , i.e., , where is the gamma photon energy. The duration, divergence angle, and source size are calculated by reconstructing the spatiotemporal distribution of these selected gamma photons. For in our three-dimensional simulations, the spectral intensity of the gamma photon beam is about , the reconstructed duration is about , the divergence angle is about , and the source size is about , which gives a peak brilliance of at the source point.
Pair production effects
In strong laser fields, electron-positron pairs can be produced when gamma photons interact with the laser photons via the multi-photon Breit-Wheeler process. In the head-on colliding configuration presented here, the quantum parameter that determines the probability of pair production can be expressed as [46, 47], where is the gamma photon energy, is the electric field perpendicular to the photon momentum, and is the Schwinger field. In this case, one has . When , the Breit-Wheeler process becomes dominant and pair production plays a significant role. In our case with , , thus the pair production can be neglected. It is anticipated that pair production plays a significant role ( or ) when the input laser intensity exceeds (See Fig.S3 in the Supplemental Materials) in the present scheme.
Bremsstrahlung radiation can be produced when the electron beam accelerated in the plasma lens interacts with the plasma mirror target. However, the bremsstrahlung radiation only becomes effective for electrons interacting with a thick target composed of high-Z materials. In our scheme, the number of photons with the energy from to via bremsstrahlung radiation generated by electrons with energy and charge interacting with a 2 thick aluminum plasma mirror target can be estimated as (the detailed derivation can be seen in Supplemental Note 4 in Supplemental Materials). To confirm the above estimation, a simulation of bremsstrahlung radiation using the GEANT4 code  is also conducted, which gives a total number of gamma photons about , on the same order of our theoretical estimation. Hence, the number of bremsstrahlung photons generated in aluminum plasma mirror is negligibly small, compared to the number of photons of the order of (see Fig.5f) generated via nonlinear Compton scattering. Thus the contribution of bremsstrahlung radiation can be neglected in our scheme.
The data that support the findings of this study are available from the corresponding authors upon request.
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We acknowledge the fruitful discussions with Prashant Kumar Singh, Vishwa Bandhu Pathak, Naser Ahmadiniaz, and Ki Hong Pae and we also acknowledge Jong Ho Jeon for the help provided in GEANT4 simulations. This work was supported by IBS(Institute for Basic Science) under IBS-R012-D1, and also by GIST through the grant “Research on Advanced Optical Science and Technology”. The EPOCH code was developed as part of the UK EPSRC grants EP/G056803/1 and EP/G055165/1.
Author contributions statement
T.W.H. developed the concept and conducted the particle-in-cell simulations. T.W.H., C.M.K., and C.T.Z. analysed the simulation data. The manuscript was written by T.W.H., C.M.K., and C.T.Z. This work is supervised by C.M.K. and C.H.N. All authors (T.W.H., C.M.K., C.T.Z., M.H.C., K.N., C.M.R., S.C.R., and C.H.N.) were involved in discussions and manuscript preparation.
Competing interests: The authors declare no competing interests.