Introduction
The Shanghai High Repetition Rate X-ray Free Electron Laser and Extreme Light Facility (SHINE) will offer a photon beam with energy spanning from 0.4 to 25 keV, leveraging its MHz-level high repetition rate and fs-level ultra-short pulse, to achieve exceptionally high average brightness and peak brightness [1-3]. As a fourth-generation X-ray source, SHINE will provide cutting-edge experimental platforms for scientists across diverse fields worldwide. The ultra-intense laser induces high-energy particle accelerators, taking advantage of compactness, tunability, and high brightness of laser systems [4, 5] to open new opportunities for multidisciplinary research, including superheavy nuclei synthesis [6-8], quantum-mechanical processes [9], fundamental particles [10], nuclear structure, and photonuclear physics [11-13]. With its 100 PW laser at the Station of Extreme Light (SEL) [14, 15], which is upgraded and constructed based on the existing Shanghai Superintense Ultrafast Laser Facility (SULF) with 10 PW and 1 PW, and the 8 GeV electron beam of the Superconducting Linear Accelerator (SLA) [16, 17], various particle beams can be generated by laser target shooting of the ultra-intense ultra-short laser (UIUSL) system, such as the high-energy γ-rays, positron sources, and even heavy-ion beams. γ-rays offer vast promising applications in different energy regions, for example, low-energy γ-rays (1-30 MeV) could be used to investigate the laboratory astrophysics [18-20], and the enhanced low-energy γ-rays also provide a strong platform for medical isotope production [21, 22], photo-transmutation [23-25], and activation experiments [26, 27] through photonuclear reactions [18, 28, 29]; medium-energy γ-rays (≥ 100 MeV) could be used to study photonuclear spallation reactions, improving the photonuclear reaction database [13, 30, 31]; high-energy γ-rays (
For collisions between the UIUSL and high-energy electron beam [40, 41], γ-rays are generated through nonlinear inverse Compton scattering (NICS), and electron-positron pairs are yielded through the multiphoton Breit-Wheeler process (MBWP) of the quantum electrodynamics (QED) effects when the optical laser field is sufficiently intense [42-44]. Several experiments have successfully obtained γ-ray beams through NICS: (1) an electron beam accelerated by a laser of intensity 4 × 1019 W/cm2 undergoes NICS with a laser of intensity 8 × 1018 W/cm2 at the Rutherford Appleton Laboratory (RAL), generating a γ-ray beam with a maximum energy of 18 MeV and peak brilliance of 1.8 × 1020 photons/(
Considering all the favorable factors mentioned above, high-quality γ-ray and positron beams can be generated by an SEL 100 PW laser and an SLA 8 GeV electron beam through the NICS and MBWP processes in SHINE. In comparison with the GeV-level γ-rays produced by bremsstrahlung [50], the NICS makes it possible to produce a first-class high-quality γ-ray source above the GeV level in SHINE and significantly improve the energy of γ-ray source at the nearby Shanghai Laser Electron Gamma Source (SLEGS) [51]. The upcoming γ-ray, positron, and electron beams may have practical multidisciplinary applications. One unique and complementary application is photonuclear reactions and related applications of γ-rays: the different cross-sections of photonuclear reactions induced by high-energy γ-rays allow for the differentiation between stable and unstable isotopes in samples using γ-ray spectroscopy [52, 53], radioactive isotope production for medical applications [21, 54], and reaction mechanisms of nuclear spallation reactions [13]. These studies have the potential to be performed within γ-ray energies ranging from hundreds of MeV to 8 GeV. The strong penetrating power of γ-rays can be applied to the non-destructive testing of large engineering samples, and the high-brilliance γ-ray beam can also serve as a microscope for the study of material lattice dynamics [55]. Another application is nonlinear strong-field QED verification: experiments for precision measurements of high-energy heavy element reaction events can be conducted to verify the predictions of nonlinear QED effects using these three types of particles [56-58]. Motivated by these promising opportunities, the particle-in-cell (PIC) program SMILEI was employed to simulate the entire processes between the UIUSL and high-energy electron beam, and the feasibility of this scheme was elucidated, which also fulfilled the gap between the γ-ray and positron beam research. This article is organized as follows. In Sect. 2, the key physical mechanisms and parameter settings of the simulations are highlighted. The simulation results, including the spatial distribution, energy spectrum, and spatial electric field distribution of the particles, are presented in Sect. 3. The beam parameters and specific applications of the particles are discussed in Sect. 4. The main findings are summarized in Sect. 5.
Models and simulations
The SMILEI toolkit, which is a collaborative, open-source, and user-friendly PIC code, has been applied to a wide range of physics studies, from relativistic laser-plasma interactions to astrophysical plasmas [59]. Within all the simulated grids, the motion of particles in the electromagnetic field satisfies Vlasov’s equation and gradually forms a self-consistent dynamical system [60-62]. The mechanism of high-energy γ-ray production in collisions between the UIUSL and high-energy electron beam is an incoherent process known as NICS. The dynamics of a single electron with charge -e and mass m could be determined by the Lorentz equation in an arbitrary external field, which is described by the covariant form of the Lorentz equation with the electromagnetic field tensor 
The parameters adopted in the SMILEI simulation are based on SHINE, where the monoenergetic electron beam density is 3.2 × 1024/m3, the beam charge is 200 pC, the full-width-at-half-maximum (FWHM) is approximately 66 fs, and the beam spot size is 10 μm × 10 μm, derived from the appropriate rectangular reduction of the highly intensive electron beam distribution. The laser is set to be a Gaussian laser with a wavelength λ = 1 μm, a focal spot size of 5 μm, a FWHM of 15 fs, and a peak intensity 
Results
When the electrons interact with the laser and the number of positrons no longer increases, the results for particle production are shown under both the CPL and LPL patterns, including the spatial distributions of the produced particles, the energies of the produced particles, and the space electric field.
Particle spatial distribution
The spatial distributions of the particles are plotted in Fig. 2. For the CPL pattern, as shown in Fig. 2(a), (c), and (e), the spatial distributions of γ-rays, compared with those of electrons and positrons, are more dispersed in the Y direction. The spatial distributions of the electrons and positrons almost overlap. The central sizes of the three generated particle beams are almost equal to the initial electron beam size. The central density of γ-rays is greater than that of electrons, and positrons have the lowest central density. For the LPL pattern, as shown in Fig. 2(b), (d) and (f), the spatial distribution of particles resembles a “crown” adorned with a “gem”, which is the beam center (black dashed box), and it is quite different from the “meteor” pattern in the “rotating forward” CPL pattern. The γ-rays are also more dispersed in the Y direction than the electrons and positrons. γ-rays have the highest central density, followed by electrons, and then positrons, the latter being similar to the electrons. Compared with the CPL pattern, the particles in the LPL pattern are markedly spread on the sides of the beam center in the vertical direction and have a higher particle density. Under both patterns, the same diffusion phenomena of particles occur in the Y direction close to the beam center, and the particles in the horizontal direction are distributed mostly to the left of the beam center, with a cluster of electrons at the “tail end”, which refers to the left end of the X axis and the center of the Y axis.
Particle energy
The energy spectra of the produced particles are plotted in Fig. 3. The energy spectrum of γ-rays decreases rapidly in the range of
Space electric field
The electric field strength reflects the spatial and momentum evolution of charged particles at their positions. Figure 4 shows the electric field, which offers a more detailed reference for interpreting particle beams. Charged particles exhibit greater stability in regions where the electric field remains stable. As shown in Fig. 4(a)–(f), the electric field reaches its maximum at the “tail end” of the particles, decreasing towards both sides of the Y axis and the right side of the X axis. For electrons and positrons, the electric field at the beam center is relatively low, enabling most particles to move forward collectively. Conversely, the electric field is higher at the“tail end”, causing particles at the rear to diverge outward. The electric field is weaker in the CPL pattern than in the LPL pattern.
As seen from Fig. 4(g), the electrons and positrons of the CPL pattern are subjected to an electric field force in the Z direction, whereas those of the LPL pattern are not subjected to any electric field force in the Z direction. It was revealed that the electrons and positrons at the “tail end” diverge in three dimensions in the CPL pattern, whereas they only diverge in the X and Y directions in the LPL pattern.
Discussion
To specifically discuss the characteristics of particle beams produced in the simulations, an area of
Angular spectrum
For convenience,
Particle beams parameters
The main parameters for the particle beams in the simulated results, namely, beam brilliance, beam emittance, and beam flux, are further discussed. The particle beam brilliance is given by Eq. (6),
The particle beam emittance in 2D space is described by
For comparison, the 10 PW and 1 PW lasers at the SULF facility were also simulated, which collided with the same electron beam to yield particle beams. The SULF 10 PW and 1 PW laser intensities were 1021 W/cm2 and 1020 W/cm2, respectively, with focal spot sizes of 5.5 μm and 40 μm, respectively, and FWHMs of 30 fs [72, 73]. In Fig. 6, the simulated particle beam brilliance spectra for the 1 PW and 10 PW lasers in SULF, as well as the 100 PW laser in SHINE on the high-energy electron beam and experimental cross-sections of particles [74-76] are plotted. The remarkable differences between the simulated results are that fewer positrons can be produced in the SULF 10 PW laser and that positrons cannot be produced in the SULF 1 PW laser. It should be noted that the trends of the energy-brilliance for beam particles are similar to the trends of the energy spectra for all particles in the SEL 100 PW laser. Although in different laser polarization states and the number of particles in the beam region, the peak energy of electrons and positrons in the CPL pattern is still higher than that in the LPL pattern. The maximum value of beam brilliance in the CPL pattern is slightly lower than that in the LPL pattern. In accordance with the beam brilliance of the SEL 100 PW, SULF 10 PW, and 1 PW lasers, the phenomena clearly demonstrate that a more intense ultrashort laser produces more γ-rays when colliding with an electron beam and that more positrons are also produced.
Table 1 presents the parameters of particle beams simulated by SMILEI for collisions between the SEL 100 PW and SLA 8 GeV electron beam according to Fig. 6. The γ-ray beam brilliance in the CPL pattern (up to 1.09 × 1027 photons/(s·mm-2·mrad2)) is higher than that in the LPL pattern, and the positron beam brilliance in the LPL pattern (up to 4.93 × 1024 positrons/(s·mm-2·mrad2)) is higher than that in the CPL pattern. Interestingly, the beam emittance is approximately 0.1 mm·mrad in the CPL pattern, which is considerably smaller than 0.2 mm·mrad in the LPL pattern. Moreover, the peak flux of γ reaches 1025 photons/s, which is considerably higher than existing γ-ray sources [52], for example, 106-9 photons/s in HIγS and 105-10 photons/s in SLEGS, and the high γ-ray flux results not only from the ultrashort pulse duration but also from the fact that the γ-ray flux of existing γ-ray sources is usually the average γ-ray flux.
| P | T | ||||||
|---|---|---|---|---|---|---|---|
| CPL | 1.09 × 1027 | 0.232 | 7.950 | 0.109 | 1.82 × 1025 | 4.47 | |
| Electron | 1.52 × 1025 | 0.676 | 7.726 | 0.099 | 2.48 × 1023 | 0.18 | |
| Positron | 3.97 × 1024 | 0.633 | 6.598 | 0.101 | 6.57 × 1022 | 0.05 | |
| LPL | 8.89 × 1026 | 0.158 | 7.975 | 0.165 | 4.26 × 1025 | 5.96 | |
| Electron | 1.05 × 1025 | 0.418 | 7.727 | 0.156 | 4.49 × 1023 | 0.19 | |
| Positron | 4.93 × 1024 | 0.421 | 6.860 | 0.152 | 2.11 × 1023 | 0.09 |
In the CPL pattern, γ-rays are the most abundant in the beam region, followed by electrons, and positrons are the least numerous. The electron beam brilliance is 1.52 × 1025 electrons/(s·mm-2·mrad2), and the positron beam brilliance is 3.97 × 1024 positrons/(s·mm-2·mrad2). Similarly, the γ-ray energy conversion efficiency of 4.47% is the maximum, and the energy conversion efficiencies of electrons and positrons are 0.18% and 0.05%, respectively. The γ-rays and electrons have the highest energy in the beam region (up to 8 GeV), whereas the maximum particle energy of the positron beams is approximately 7 GeV. The average particle energy of the electron and positron beams, which is approximately 0.6 GeV, is higher than that of the γ-ray beam (≈ 0.2 GeV).
In the LPL pattern, the beam brilliance, energy conversion efficiency, maximum particle energy, and average particle energy of the particles have the same numerical order in terms of the three types of particles: γ-rays, electrons, and positrons. The γ-ray and electron beam brilliances are 8.89 × 1026 photons/(s·mm-2·mrad2) and 1.05 × 1025 electrons/(s·mm-2·mrad2), respectively. The energy conversion efficiency of γ-rays is 5.96%, which is marginally higher than the 2% given by the all-optical scheme for laser energy into γ-rays in 2012 [77]. The energy conversion efficiencies of electrons and positrons are 0.19% and 0.09%, respectively. The maximum particle energies are similar to those in the CPL pattern. The average particle energy of the electron and positron beams is approximately 0.4 GeV, and the average particle energy of the γ-ray beam is approximately 0.2 GeV. Although the maximum energy of γ-rays approaches the initial electron energy during the collision process, most of the γ-rays still have lower energy. Meanwhile, most of the positrons have higher energies.
In general, the energy conversion efficiency of particles in the CPL pattern is lower than that in the LPL pattern, and the maximum particle energy in the CPL pattern is nearly equal to that in the LPL pattern, and the average particle energy in the CPL pattern is higher than that in the LPL pattern. These conflicting results could be attributed to the fact that more positrons are generated with lower energy and greater spatial emittance in the beam region in the LPL pattern. The CPL pattern demonstrates superior beam quality for generating γ-rays and electrons, whereas the LPL pattern may achieve higher beam quality for generating positrons in SHINE.
Facility layout and specific applications
The simulations in this work provide an alternative way to produce high-quality γ-ray and positron beams, which is distinct from the all-optical scheme [78-80], where the UIUSL first generates a high-energy electron beam and then collides with another UIUSL. The simulated results are aimed at assessing the feasibility and advantages of electron-laser colliding γ-ray sources and positron beam facilities, which provide new opportunities for high-energy photonuclear reactions and positron-related physics within the aforementioned energy ranges. Examples of different (
A concept design for a possible colliding station based on the SEL 100 PW laser and SLA 8 GeV electron beam in SHINE is shown in Fig. 7(e). First, the spatial distributions of the three types of particles overlap, as demonstrated by the simulated results. In addition, beam separation can be achieved by placing deflecting magnets around the beam region [44, 82, 83]. Finally, neutral γ-rays propagate in the positive direction along the X axis, whereas electrons and positrons propagate in opposite directions along the Y axis [43, 79, 84]. Particle energies follow a continuous spectrum defined by the surrounding temperature in the high-temperature, high-density plasma of extreme astrophysical environments, including γ-ray bursts in active galactic nuclei, pulsars, stellar interiors, supernovae, neutron star mergers, and so on. Utilizing a beam with a continuous energy spectrum could more effectively simulate the overall effects of particles in real astrophysical environments, such as the integrated reaction rates under a continuous γ-ray spectrum, which are crucial for experimentally verifying model parameters in the evolution of nuclear celestial bodies and may reveal new phenomena in astrophysics. The potential high-quality γ-ray beams in SHINE would significantly promote nuclear reaction research and strange phenomena in nuclear physics and nuclear astrophysics. Ultra-intense γ-rays are ideal for studying the photonuclear reactions of short-lived unstable nuclides with high cross-sections and minimal rare nuclide target material [85], and γ-ray-assisted multiphoton fusion processes [86].
However, several questions remain regarding both the technique and theory. One is how to achieve collisions by synchronizing the electron beam and laser within a few microns and femtoseconds [87-89], which requires extremely high initial beam quality and technical precision [50, 90, 91]. This might be solved by using a spherical mirror to control the collision angle and by triggering the SLA electron beam with a laser pulse that shares the seed of the SEL 100 PW laser for precise time control. Another question is whether the maximum energy of the three types of particles may exceed the maximum energy of the initial electron beam, which requires increasing the electron beam energy of the accelerator to obtain higher γ-ray and positron beam energies. The third is that the aforementioned applications, such as those involving photonuclear reactions, necessitate the development of detectors with higher sensitivity and the exploration of theoretical models under extreme conditions.
Conclusion
A comprehensive simulation was performed on particle production in collisions between the SEL 100 PW laser and SLA 8 GeV electron beam based on SHINE using the PIC program SMILEI. Most of the γ-rays and electron-positron pairs generated by the NICS and MBWP were localized at the beam center, where the beam center size matched that of the initial electron pulse. The majority of γ-rays are distributed in the lower energy range (Ek < 0.9 GeV), and the generated electrons and positrons are concentrated at Ek = 0.2 GeV for CPL and Ek = 0.1 GeV for LPL. Electrons and positrons moved forward in the beam center, whereas those in the “tail end" spread out in three-dimensional space for the CPL pattern and in the X and Y directions for the LPL pattern. Within the selected beam region, the angles of the particle momentum were clustered around 0°, and the beam brilliance increased with increasing laser intensity. The beam brilliance of the γ-rays, with a maximum energy of up to 8 GeV, reached 1027 photons/(s·mm2·mrad2). The beam emittance was approximately 0.1 mm·mrad in the CPL pattern, and its energy conversion efficiency was up to 5.96% in the LPL pattern. The maximum energy of positrons reached 7 GeV, with a beam brilliance of up to 4 × 1024 positrons/(s·mm2·mrad2), a beam emittance of approximately 0.1 mm·mrad in the CPL pattern, and an energy conversion efficiency of 0.09% in the LPL pattern. High brilliance, high energy, and low emittance are the advantages of the γ-ray, positron, and electron beams, which are generated in simulated collisions. The γ-ray beam brilliance was higher, and the beam emittance was lower in the CPL pattern than those in the LPL pattern. The positron beam brilliance was higher, and the particle energy conversion efficiency was larger in the LPL pattern than in the CPL pattern. The insights gained from these results may inspire us to choose distinct laser polarization patterns, various energy ranges achieved through moderating materials, and diverse particle beams guided by magnets to achieve specific goals of experimental research, such as studying photonuclear reactions and verifying strong-field QED theory.
In addition to quantitatively and comprehensively assessing top-quality γ-ray and positron beams with the most intense laser, this work explores the feasibility of the facility design scheme. Multiple frontier applications have been presented with these γ-ray and positron beams, including γ-ray microscopy in material science and engineering, γ-ray spectrum diagnostics of radionuclides, positron emission tomography (PET) for advanced nuclear analysis technology, and others. Moreover, if the particle beams, including the electrons of the SLA and the SEL 100 PW laser [92], can be polarized [93, 94] and vortexed [95], they will have significant potential to enhance research in plasma physics and advance studies in nuclear physics and astrophysics [96, 97].
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