Preamble

GeV-level -ray and positron beams produced by collisions of multi-PW laser on high-energy electron beam Wan-Qing Su, 1, 2, 3 Chun-Wang Ma, 1, 4, Xi-Guang Cao, 2, 3, 5, Guo-Qiang Zhang, 2, 3, 5 and Yu-Ting Wang 1 School of Physics, Henan Normal University, Xinxiang 453007, China Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Institute of Nuclear Science and Technology, Henan Academy of Sciences, Zhengzhou 450015, China University of Chinese Academy of Sciences, Beijing 100049, China Based on collisions between the 100 PW laser and 8 GeV superconducting linear accelerator constructing in Shanghai High Repetition Rate X-ray Free Electron Laser and Extreme Light Facility, the building of GeV- level -ray as well as positron beams are proposed according to particle-in-cell simulations. Key processes are considered involving the nonlinear inverse Compton scattering for -ray generation and the multiphoton Breit- Wheeler process for electron-positron pair production. Regardless of laser polarization, the simulations indicate -ray beams achieve energy up to 8 GeV, brilliance around 10 photons/( ), and emittance as low as 0.1 , while positron beams attain energy up to 7 GeV, brilliance around 4 positrons/( ), and emittance as low as 0.1 . Various applications could benefit from the possible high-energy -ray and positron beams, which may potentially be built in SHINE, including fundamental physics of strong-field quantum electrodynamics theory validation, nuclear physics, nuclear astrophysics, imaging and so on.

Keywords

-ray source, positron beam, nonlinear inverse Compton scattering, multiphoton Breit-Wheeler process, ultra- intense ultra-short laser, particle-in-cell

INTRODUCTION

The Shanghai High Repetition Rate X-ray Free Electron Laser and Extreme Light Facility (SHINE) will offer a pho-

ton beam with energy spanning from 0.4 to 25 keV, leverag- 4

ing its MHz-level high repetition rate and fs-level ultra-short pulse, to achieve exceptionally high average brightness and peak brightness [ ]. As a fourth-generation X-ray source, the SHINE will provide cutting-edge experimental platforms for scientists across diverse fields worldwide.

The ultra- intense laser induces high-energy particle accelerators, tak- ing advantages of compactness, tunability and high bright-

ness of laser system [ 4 , 5 ] to open new opportunities to multi- 12

disciplinary researches including superheavy nuclei synthesis

[ 6 – 8 ], quantum-mechanical processes [ 9 ], fundamental par- 14

ticles [ ], nuclear structure and photonuclear physics [ With its 100 PW laser of Station of Extreme Light (SEL) [ ], which is upgraded and constructed based on the existing Shanghai Superintense Ultrafast Laser Facility (SULF) of 10 PW and 1 PW, and the 8 GeV electron beam of Superconducting Linear Accelerator (SLA) [ ], vari-

This work is supported by the National Key Research and Development Program of China (No. 2022YFA1602404, No. 2022YFA1602402), the Strategic Priority Research Program of the CAS under Grant No.

XDB34030000, the National Natural Science Foundation of China (No. 12475134, No. 11975210, No. 12235003, No. U1832129), the Youth In- novation Promotion Association CAS (No. 2017309), and Natural Science Foundation of Henan Province (Grant No. 242300421048).

Chun-Wang Ma; College of Physics, Henan Normal University, Xinxiang 453007, China; 15836181225; machun- Xi-Guang Cao; Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China;

ous particle beams can be generated by laser target shooting of the ultra-intense ultra-short laser (UIUSL) system, such as the high-energy -rays, positron sources, and even heavy-ion beams.

For the collisions of the UIUSL and high-energy electron beam [ ], the -rays are generated through the non- linear inverse Compton scattering (NICS), and the electron- positron pairs are yielded through the multiphoton Breit- Wheeler process (MBWP) of the quantum electrodynamics (QED) effects when the optical laser field is strong enough ]. Several experiments have successfully obtained ray beams through NICS: (1) the electron beam accelerated by a laser of intensity 4 undergoes NICS with the laser of intensity 8 in the Rutherford Ap- pleton Laboratory (RAL), generating the -ray beam with the maximum energy 18 MeV and peak brilliance 1.8 photons/( ]; (2) the electron beam accelerated by a laser of intensity 7.7 also undergoes NICS with the laser of intensity 1.3 in the RAL, generating the -ray of critical energy

30 MeV [

]. Earlier theories and simulations demonstrated that: (1) the increase of electron Lorentz factor and laser in- tensity could increase the energy of -ray produced; (2) the enhanced stability of electron beam might reduce the emit- tance of the -ray beam [ ]; and (3) the increase of laser intensity might also enhance the laser energy conversion effi- ciency to -rays and positrons [

Combining all favorable factors above, the high-quality 48

-ray and positron beams could be generated by SEL 100 PW laser and SLA 8 GeV electron beam through NICS and MBWP process in SHINE. Compared to the GeV-level -rays produced by bremsstrahlung [ ], the NICS makes it possi- ble to produce the first class high-quality -ray source above

GeV-level in SHINE, and significantly improve the energy of 54

-ray source at the nearby Shanghai Laser Electron Gamma

Source (SLEGS) [ ]. Motivated by these promising op-

portunities, the particle-in-cell (PIC) program SMILEI is em- 57

ployed to simulate the whole processes between the UIUSL and high-energy electron beam now, and the feasibility of this scheme is elucidated, which also fulfills the gap between the

γ -ray and positron beam researches. This article is organized 61

as follows. In Section II , the key physical mechanisms and 62

parameter settings of simulations are highlighted. The simu- lation results, including the spatial distribution, energy spec- trum, and spatial electric field distribution of particles, are presented in Section . The beam parameters and applica- tions of particles are discussed in Section . The main find- ings are summarized in Section MODELS AND SIMULATIONS The SMILEI toolkit, which is a collaborative, open-source, user-friendly PIC code, has been applied into a wide range of physics studies from relativistic laser-plasma interaction to astrophysical plasmas [ ]. Within all simulated grids, the motion of particles in the electromagnetic field satisfy the Vlasov’s equation and gradually form a self-consistent dy-

namical system [ 32 – 34 ]. The mechanism of high-energy γ - 76

rays production in collisions between the UIUSL and high- energy electron beam is the incoherent process of NICS. The dynamics of a single electron with charge and mass 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 form of

d τ = − e mcF µν p ν . (1) 84

The Lorentz invariant quantum parameter for the electron is

χ = ���� F µν

���� = γ e E s

and the Lorentz invariant quantum parameter for the photon at the time of photon emission is denoted as

χ γ = γ γ E s

where γ e = ϵ e / � m e c 2 � and γ γ = ϵ γ / � m e c 2 � are the nor- 90

malized energies of the radiating particle and emitted photon, respectively; are their respective velocities, is the speed of light in vacuum. denote the electric field

and magnetic field, respectively; and E s = m 2 c 3 / ( ℏ e ) ≃ 94

V/m is the Schwinger field. The MBWP is the process of high-energy photons decay- ing into an electron-positron pair in the intense electromag- netic field [ ]. The strength of the QED effects for elec- tron and positron depends on the photon quantum parameter

χ BW γ = γ γ E s

where is the electric field orthogonal to the propagation direction of the photon.

The parameters adopted in the SMILEI simulation are based on the SHINE, where the mono-energetic electron beam density is 3.2 and the beam spot size is 10 , derived from the appropriate rectangular reduction of the highly intensive electron beam distribution. The laser is set to be a Gaussian laser of the wavelength m, with a focal spot size 5 m, a full-width-at-half-maximum (FWHM)

15 fs, and a peak intensity I = 10 23 W / cm 2 , which corre- 110

sponds to a normalized laser amplitude of 190 for cir- cularly polarized laser (denoted by CPL) and 269 for linearly polarized laser (denoted by LPL) [ ]. The spa- tial size of the two-dimensional and three-velocity (2D3V) particle-in-cell (PIC) simulation is set to be 300 with a spatial step size of 100 nm and a time step of 22 as.

Each grid initially contains 16 electrons in the electron beam 117

region. The electron beam moves straight from the center on the left towards the right, while the laser focusing on the elec- tron beam travels from the center on the right towards the left. -ray is immediately emitted by collision of electron and

photons through the NICS mechanism [ 40 , 41 ], specifically, 122

the Monte Carlo simulation [ ]. Almost simultaneously, the electron-positron pair is created by photons through the

MBWP mechanism. The collision processes, as well as the 125

colliding equations are illustrated in Fig. , which includes NICS : laser MBWP : laser laser ) and the high-energy electron beam ( The moving directions of particles are indicated by thick arrows.

RESULTS

At the time when the electrons interact with the laser and the number of positrons no longer increases, the results for particles productions are shown under both CPL and LPL pat- terns, including the spatial distributions of produced particles, the energies of produced particles, and space electric field.

Particle spatial distribution The spatial distributions for particles are plotted in Fig.

For the CPL pattern, as shown in Fig. (a), (c) and (e), the

spatial distributions of -rays, compared to electrons and positrons, are more dispersed in the direction. The spatial distributions of electrons and positrons almost overlap. The size of the beam center (black dashed box) almost equals to

the initial electron beam size. The central density of photons 142

is greater than that of electrons, and positrons have the lowest central density. For the LPL pattern, as shown in Fig. (d) and (f), the spatial distribution of particle resembles a “crown” adorned with a gem and the beam center is the “gem” on the crown, which is quite different from the “meteor” pat- tern in the “rotating forward” CPL pattern. The -rays are also more dispersed in the direction compared to electrons and positrons. -rays have the highest central density, fol- lowed by electrons, and then positrons similarly. Compared to the CPL pattern, the particles in the LPL pattern markedly spread on sides of the beam center in vertical direction and have a higher particle density. Under both patterns, the same diffusion phenomena of particles happen in the direction closed 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 axis and the center of the axis.

Particle energy The energy spectra of produced particles are plotted in -rays decreases quickly in

the range of Energy ∈ [0, 8] GeV. For the LPL pattern, more 163

photons are produced in the lower energy range ( Energy < 164

0.9 GeV), while for the CPL pattern, more photons are pro- duced in the higher energy range ( Energy

0.9 GeV), with

the maximum energies for both patterns approaching 8 GeV.

The electron energy broadens from the mono-energy to the low-energy region, and the energy spectra of electrons and positrons both gradually increase to form peaks and then de- crease with the increasing energy. The peaks of the electrons

and positrons distributions both are located at Energy = 172

0.2 GeV for the CPL pattern, and the peaks of the electrons

and positrons both are located at Energy =

0.1 GeV for the

174

LPL pattern, and more positrons and electrons are produced compared to the LPL pattern the peak positions. More elec- trons are produced in the LPL pattern than in the CPL when

Energy < 0.5 GeV, while opposite trends happens when 178

Energy 0.5 GeV. The number of positrons produced in the CPL pattern is similarly less than that produced in the

LPL pattern when Energy <

1.1 GeV, while the trend revers

181

Energy

1.1 GeV. Notably, the maximum energy of

electrons still approaches 8 GeV, and the maximum energy of positrons is close to 7 GeV.

Space electric field The electric field strength reflects the spatial and momen- tum evolution of charged particles at their positions. Figure shows the electric field, offering a more detailed reference for interpreting particle beams. Charged particles exhibit greater SMILEI simulated collisions between 100 PW laser and 8 GeV elec- tron beam based on the Station of Extreme Light (SEL) and Super- conducting Linear Accelerator (SLA) in the Shanghai High Repe- tition Rate X-ray Free Electron Laser and Extreme Light Facility (SHINE). (a) and (b) are for -rays production under circularly po- larized laser (CPL) and linearly polarized laser (LPL) patterns, re- spectively. (c) and (d) are for electrons production under CPL and LPL patterns, respectively. (e) and (f) are for positrons production under CPL and LPL patterns, respectively. Particle beam parameters are given in Section stability in regions where the electric field remains stable. As shown in Fig. (a)-(f), the electric field reaches its maximum at the “tail end” of the particles, decreasing towards both sides of the axis and the right side of the axis. For electrons and positrons, the electric field at the beam center is rela- tively low, enabling most particles to move forward collec- tively. Conversely, the electric field is higher at the“tail end”, causing particles at the rear to diverge outward. The electric field is apparently weaker in the CPL pattern compared to the LPL pattern.

Seen from Fig. (g), the electrons and positrons of the CPL pattern are subjected to an electric field force in the direc- tion, while these of the LPL pattern are not subjected to any electric field force in the direction. It is revealed that elec- trons and positrons at the “tail end” diverge in three dimen- sions in the CPL pattern, while they only diverge in the directions in the LPL pattern.

(Color online) Particle energy spectrum at 700 fs of the SMILEI simulated collisions between 100 PW laser and 8 GeV elec- tron beam based on the SEL and SLA in SHINE. The CPL and LPL denote the circularly polarized laser and linearly polarized laser, re- spectively.

DISCUSSION

To specifically discuss the characteristics of particle beams

produced in the simulations, an area of X ∈ [190, 230] µ m 209

and Y ∈ [45, 55] µ m is delimited for further estimation of 210

the angular spectrum, particle beams parameters, experimen- tal layout and potential applications in scientific researches.

Angular spectrum

For convenience, θ y = arctan( p y /p x ) and θ z = 214

arctan( are defined. The angular spectra of particles in the selected beam region are plotted in Fig. , which shows that the angular spectra for different particles in the CPL pattern are obviously narrower than those in the LPL pattern, with almost equal peak values ( 0). In terms of the three particles, the angular spectrum of -rays shows the widest distribution with the highest peak values (about CPL and for LPL). Electrons show an narrower an- gular spectrum with lower peak values around CPL and for LPL. Positrons display the narrowest angular spectrum with the lowest peak value (approximately for CPL and for LPL), closely resembling angular spectrum and peak value of electrons. The angular spectrum of different particles in the CPL pattern is similar to their corresponding angular spectrum in the CPL pattern, whereas the widths of the angular spectrum for particles in the CPL pattern are greater than that of the angular spectrum for corresponding particles in the CPL 8 GeV electron beam based on the SEL and SLA in SHINE. The panels (a), (c), and (e) denote the -rays, electrons and positrons in the CPL pattern, respectively. The panels (b), (d), and (f) denote rays, electrons and positrons in the LPL pattern, respectively. Panel (g) is for the electric field component distribution in the direction. pattern, with peaks of the angular spectrum approximately -ray beam, for electron beam, for positron beam. Notably, for all particles in the LPL pattern, they are focused on the 0, owing to the absence of electric field in the direction. Particles in the

CPL pattern display a significantly broader θ z angular spec- 238

trum compared to those in the LPL pattern. These discrep- ancies could be attributed to limitations in the 2D simulation,

which makes it difficulty to select the effective region in the director. = arctan( = arctan( ) in the beam re- gion at 700 fs simulated by SMILEI for collision between circularly polarized (CPL) or linearly polarized (LPL) SEL 100 PW laser and SLA 8 GeV electron beam.

Particle beams parameters The main parameters for the particle beams of simulated results, namely, beam brilliance, beam emittance and beam flux, are further discussed. The particle beam brilliance is given by Eq. (

L = N T × D 2 × θ 2 , (7) 248

where is the number of particles when the 2D area is

extended to the 3D space, T is approximately 30 fs, D = 250

, and (Lorentz factor is 12 mrad and 17 mrad for the CPL and LPL patterns, re- spectively [ ]. The particle beam emittance in 2D space is described by,

The peak flux of particle beam is defined as F = N/T . The 256

equation for energy conversion efficiency is η = E p /E le , 257

where is the total energy of the particle and is the

sum of the corresponding laser and initial electrons energies. 259

For comparison, the 10 PW and 1 PW lasers at the SULF facility are also simulated, which collide on the same electron beam to yield particle beams. The 10 PW and 1 PW laser in- tensities are 10 and 10 , correspondingly, with focal spot sizes of 5.5 m and 40 m, respectively, and FWHMs both of 30 fs [ ]. In Fig. , the simulated parti- cle beam brilliance spectrum for the 1 PW and 10 PW lasers in SULF, as well as the 100 PW laser in SHINE on high- energy electron beam and experimental cross-sections of par- ticles [ ] are plotted. The marvelous differences between the simulated results are that fewer positron can be produced in the SULF 10 PW laser, and then positron cannot be yielded in the SULF 1 PW laser. Note 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. Al- though in the different laser polarization states and the num- ber of particles in the beam region, the peak energy of elec- trons and positrons in the CPL pattern is still higher than those 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 SEL 100 PW, SULF 10 PW and 1 PW lasers, the phenomena clearly demonstrate that more intense ultra-short laser, more -rays are produced by colliding with electron beam, and more positrons are also lated by SMILEI for collisions between SEL 100 PW and tern, and the positron beam brilliance in the LPL pattern (up that in the CPL pattern. Interestingly, the beam emittance is around 0.1 in the CPL pattern, which is much smaller than 0.2 in the LPL pattern. Not least, the peak flux of -ray reach up to photons/s, which is much higher than existing -ray sources [ ], for example, photons/s in HI S and photons/s in SLEGS, and the ration, but also from the fact that the -ray flux of existing In the CPL pattern, the -rays are the most abundant in the beam region, followed by electrons, with positrons being the electrons/( ), and positron beam brilliance is positrons/( ). Similarly, the 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 -rays and electrons have the highest energy in beam region (up to 8 GeV), while the maximum particle energy of positron beams is approxi- mately 7 GeV. The average particle energy of electron and positron beams, which is around 0.6 GeV, is higher than that In the LPL pattern, the beam brilliance, energy conversion efficiency, maximum particle energy, and average particle en- ergy of particles have the same numerical order in terms of the three particles of -rays, electrons and positrons. The ray and electron beam brilliants are 8.89 photons/( ) and 1.05 electrons/( concretely. The energy conversion efficiencies of -rays is , which is marginally superior to 2 given by the all- optical scheme for laser energy into -rays in 2012 [ ]. The energy conversion efficiencies of electrons and positrons are and 0.09 , respectively. The maximum particle ener-

Particle beam parameters simulated by SMILEI for collision between circularly polarized (CPL) or linearly polarized (LPL) SEL 100 PW laser and SLA 8 GeV electron beam. The laser polarization (P), particle type (T), beam brilliance ( ), average particle energy ( maximum particle energy ( ), emittance ( ), peak flux ( ), and energy conversion efficiency ( ) are given. (particles/( (GeV) (GeV) (particles/s) Electron Positron Electron Positron gies are similar to those in the CPL pattern. The average par- ticle energy of electron and positron beams is about 0.4 GeV, and average particle energy of -ray beam is about 0.2 GeV.

Although the maximum energy of γ -rays approaches the ini- 328

tial electron energy during the collision process, the majority -rays still have lower energy. At the same time, most of the positrons have higher energy.

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 en- ergy in the CPL pattern is higher than that in the LPL pattern.

The conflicting results could be related to the fact that more positrons are generated, with lower energy and greater spa- tial emittance in the beam region in the LPL pattern. It is suggested that, to generate -rays and electrons, the CPL pat- tern demonstrate superior beam quality, whereas, to generate positrons, the LPL pattern may achieve higher beam quality in SHINE.

The simulations in this work provide an alternative way optical scheme designation [ ], which uses the UIUSL to generate a higher-energy electron beam that then collides with another UIUSL. The simulated results are aimed at as- sessing the feasibility and advantages of electron-laser collid- -ray source and positron beam facility, which provides

new opportunity to the high-energy photonuclear reactions 352

and positron related physics within the aforementioned en- ergy ranges. Examples of different ( , abs) and ( f) reactions within the high-energy scopes are also plotted in ing of nuclear structures such as a form factor, polarization, and resonances [ ], and the high-brilliance and high-flux of the particle beams may partly advance the nuclear reaction fined by the surrounding temperature in the high-temperature, high-density plasma of extreme astrophysical environments, including -ray bursts in active galactic nuclei, pulsars, stellar

interiors, supernovae, neutron star mergers, and so on. Utiliz- ing a beam with a continuous energy spectrum could more effectively simulate the overall effects of particles in real as- trophysical environments, such as the integrated reaction rates under a continuous -ray spectrum, which are crucial for ex- perimentally verifying model parameters in the evolution of nuclear celestial bodies and may reveal new phenomena in as- trophysics. The potential high-quality -ray beams in SHINE

would significantly promote the nuclear reaction researches, 372

as well as strange phenomena in nuclear physics and nuclear astrophysics.

Energy diagrams of rays in the beam region under CPL and LPL patterns, respectively, with the -ray energy of 100 MeV marked by the dashed line. (c) is a sketch drawing of a colliding station and its high-energy beamline and high-energy positron beamline based on the SEL 100 PW laser and SLA 8 GeV electron beam in SHINE [ ], and its specific applications.

The 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. . First, the spatial distributions of three types of particles overlaps as demonstrated by the sim- ulated results. Then, it is possible to achieve beam separation by placing deflecting magnets around the beam region suc- cessfully [ ]. Finally, neutral -rays would still prop- agate in the positive direction along the axis, while elec- trons and positrons would propagate in opposite directions along the axis [ ]. Further, the maximum energy -rays varies with momentum angle in the beam region at 700 fs, especially when the energy exceeds 100 MeV. rays near the 0 degree momentum angle, with energy below 100 MeV, have the highest proportion. The ultra-intense rays are ideal for studying the photonuclear reactions of short-

lived unstable nuclides with high cross-sections and minimal 390

rare nuclide target material [ ], and -ray-assisted mul- tiphoton fusion processes [ ]. Therefore, the potential appli- cations of -rays in different energy regions are as follows.

High-energy -rays could be used to research pion pho- toproduction on the nucleon [ ], and determine more accurate resonance coupling constants through more experimental measurements of the nucleon res- onance spectrum [

140 MeV

Medium-energy -rays could be used to study photonu- clear spallation reactions, improving the photonuclear reaction database [ 100 MeV).

Low-energy -rays could be used to investigate the lab- oratory astrophysics [ ], and the enhanced low- energy -rays also provide a strong platform for med- ical isotope production [ ], photo-transmutation ], and activation experiments [ ] through photonuclear reactions [ ] (1-30 MeV).

In concrete terms, the above high-quality particle beams may have practical multidisciplinary applications, for exam-

• unique and complementary photonuclear reactions and 411

related applications: the different cross-sections of photonuclear reactions induced by high-energy -rays allow for the differentiation between stable and un- stable isotopes in samples using -ray spectroscopy ], radioactive isotopes productions for med-

ical applications [ 73 , 85 ], and reaction mechanism of 417

nuclear spallation reactions [ ]. These researches are in potential be performed within -ray energy ranging from hundreds of MeV to 8 GeV. The strong penetrat- ing power of -rays can be applied for non-destructive testing of large engineering samples, and their high brilliance can also serve as a microscope for the study of material lattice dynamics [ positrons and related applications: as one type of anti- matter particles, the positrons have applications in the research of particle physics [ ], solid-state physics, such as diagnosing complex structures of Fermi sur- faces [ ], and Positron Emission Tomography (PET) for material sciences [ and nonlinear strong-field QED verification: exper- iments for precision measurements of high-energy heavy element reaction events can be conducted to ver- ify the predictions of nonlinear QED effects using these three types of particles [

However, several questions still remain in both techniques 436

and theory. One is how to achieve collisions by synchroniz- 437

ing the electron beam and laser within a few femtoseconds

and microns [ 94 – 96 ], which requires extremely high initial 439

beam quality and technical precision [ 28 , 97 , 98 ]. Another is 440

that the maximum energy of the three types of particles may

not exceed the maximum energy of the initial electron beam, 442

which requires to increase the electron beam energy of accel- erator to obtain higher -ray and positron beam energies. The

third is that the aforementioned applications, such as those in- volving photonuclear reactions, necessitate the development of detectors with higher sensitivity and the exploration of the- oretical models under extreme conditions.

CONCLUSION

The comprehensive simulation has been performed on the particle productions in collisions between the SEL 100 PW laser and SLA 8 GeV electron beam based on the SHINE by the PIC program SMILEI. Most of the -rays and electron- positron pairs generated by NICS and MBWP are found to be localized in the beam center, where the beam center size

matches that of the initial electron pulse. The majority of γ - 456

rays are distributed in the lower energy range ( Energy < 0.9 457

GeV), and the generated electrons and positrons are concen-

trated at Energy =

0.2 GeV for CPL and

Energy = 0.1 459

GeV for LPL. Electrons and positrons move forward in the beam center, whereas those in the “tail end" spread out in 3D space for the CPL pattern and spread out in the rections for the LPL pattern. Within the selected beam region, the angles of the particle momentum are clustered around 0 degrees, and the beam brilliance rises with increasing laser intensity. The beam brilliance of the -rays, with a maximum energy of up to 8 GeV, reaches 10 photons/( The beam emittance is approximately 0.1 d in the CPL pattern, and its energy conversion efficiency is up to in the LPL pattern. The maximum energy of positrons H. Chen, L. M. Zheng, B. Gao et al., Beam dynamics opti- mization of very-high-frequency gun photoinjector. Nucl. Sci.

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DECLARATIONS Conflict of interest Chun-Wang Ma and Xi-Guang Cao are the editorial board members for Nuclear Science and Tech-

niques and were not involved in the editorial review or the 903

decision to publish this article. All authors declare that there is no conflict of interest.