Fig. 1. Standard particle-in-cell (PIC) loop with four kernel parts.

Fig. 2. (a) and (b) Yee grid and position of each field component in 3D and 2D cases, respectively. In (b), the z direction is squeezed.

Fig. 3. Leapfrog algorithm for particle pushing and field advancing.

Fig. 4. q(χ) vs χ.

Fig. 5. Dynamics of an electron [p₀ = (4000, 0, 0)] scattering with an ultraintense linearly polarized laser pulse of Ey=100exp−ϕ−10010π2cosϕ, with ϕ ≡ t + x. Here, Lo., LL., and MLL. denote results calculated from the Lorentz, LL, and modified LL equations, respectively.

Fig. 6. Spin dynamics of an electron [p₀ = (4000, 0, 0), s₀ = (1, 0, 0)] scattering with an ultraintense linearly polarized laser pulse of Ey=100exp−ϕ−10010π2cosϕ, with ϕ ≡ t + x. Here, A, B, C, and D denote results calculated using the Lorentz + T-BMT, Lorentz + radiative T-BMT, LL + radiative T-BMT, and MLL + radiative T-BMT equations, respectively.

Fig. 7. Flowchart of spin- and polarization-resolved NCS.

Fig. 8. Dynamics of 1000 electrons via stochastic NCS, with the simulation parameters the same as those in Fig. 6. Blue lines are for ten sampled electrons, and black ones are the average value over 1000 sample particles.

Fig. 9. Dynamics of an electron beam (particle number N_e = 10⁴), with colors denoting the number density in arbitrary units and a logarithmic scale (a.u.); other parameters are the same as those in Fig. 6.

Fig. 10. (a) Energy spectra of scattered electrons (black curve) and generated photons (red curve). (b) Energy-dependent Stokes parameters ξ̄2 and ξ3̄, i.e., circular and linear polarization with respect to the y and z axes. The simulation parameters are the same as those in Fig. 6.

Fig. 11. Flowchart of the spin- and polarization-resolved nonlinear Breit–Wheeler (NBW) pair production process.

Fig. 12. (a) Normalized energy spectrum (black solid curve) and energy-resolved longitudinal spin polarization (red solid curve) of positrons. (b) Statistics of the longitudinal spin components of generated positrons. The laser and electron beam parameters are consistent with those in Fig. 9.

Fig. 13. Bremsstrahlung of 100 MeV electrons: (a) scattered electron spectra; (b) yield photon spectra. Solid curves represent PIC results and dashed curves Geant4 results. Reproduced with permission from F. Wan et al., Eur. Phys. J. D 71, 236 (2017). Copyright 2017, EDP Sciences, SIF, Springer-Verlag GmbH Germany.

Fig. 14. Bremsstrahlung of 1 GeV electrons: (a) scattered electron spectra; (b) yield photon spectra. Solid curves represent PIC results and dashed curves Geant4 results. Reproduced with permission from F. Wan et al., Eur. Phys. J. D 71, 236 (2017). Copyright 2017, EDP Sciences, SIF, Springer-Verlag GmbH Germany.

Fig. 15. (a) M(χ_γ) (red and blue solid curves) and the corresponding low-energy-limit constants, with red and blue dash-dotted lines equal to 4 and 7, respectively. (b) Relative error between M(χ_γ) and the low-energy-limit constant.

Fig. 16. VB effect of a γ-photon [ɛ_γ = 1 GeV, ξ = (1, 0, 0)] propagating through (a) static crossed fields with E_y = −B_z = 100 and (b) a laser field (the same as in Fig. 6).

Fig. 17. Data structure of SLIPs.

Fig. 18. Framework of SLIPs.

Fig. 19. Generation of polarized electrons: (a) number density log_{10}(d²N/dθ_xdθ_y) (a.u.); (b) spin polarization S_x.

Fig. 20. Generation of LP γ-photons: (a) number density log₁₀(d²N/dθ_xdθ_y) (a.u.); (b) linear polarization ξ₃.

Fig. 21. Generation of CP γ-photons with longitudinally polarized electrons: (a) number density log₁₀(d²N/dθ_xdθ_y) (a.u.); (b) circular polarization |ξ₂|.

Fig. 22. Laser–plasma interaction via 2D simulation: (a)–(c) spatial distributions of E_x, E_y, and B_z, respectively; (d)–(f) number densities (in logrithm) of target electrons, generated NBW positrons, and NCS γ-photons, respectively.

Fig. 23. Photons generated by laser–plasma interaction: (a) number density with respect to energy and angle, i.e., log₁₀(dN²/dγ_γdθ) (a.u.) with γγ≡Eγ/mec2 and θ ≡ p_y/p_x; (b) energy- and angle-resolved linear polarization degree ξ̄3; (c) energy-resolved number and polarization distributions; (d) angle-resolved number and polarization distributions.

Fig. 24. Positrons generated by laser–plasma interaction: (a) number density with respect to energy and angle, i.e., dN²/dγ₊dθ (a.u.), with γ₊ ≡ ɛ₊/m_ec² and θ ≡ arctan(p_y/p_x); (b) energy- and angle-resolved spin component S̄z; (c) normalized angular distribution n(θ) ≡ dN/dθ (a.u.); (d) angular distribution of S̄z (i.e., energy-averaged); (e) normalized energy distribution n(ɛ₊) ≡ dN/dɛ₊ (a.u.).

Table 1. VB effect in SLIPs.