Fig. 1. The diagrams on the left show the electric fields of two Laguerre–Gaussian (LG) laser pulses with distinct frequencies ω₁ and ω₂ and topological charges l₁ = −l₂ = 1. The middle diagram shows the electric field amplitude of the superposition of these two-color LG pulses. According to Eq. (1), the combination of these two LG pulses results in a twisted ponderomotive force potential, as shown by the diagram on the right.

Fig. 2. (a) Radial eigenfunctions of the composed mode, F_1,±1–F_0,±1 (solid blue curve), and the simple low-order mode, F_0,±1 (dashed red curve), as functions of the beam waist r/w_b for w_b,0 = 5 μm. (b) Corresponding axial magnetic fields normalized to (lπcj0̃/wb2)/(Δω2Δk) estimated by Eq. (6).

Fig. 3. (a) Amplitude |E_x| of the total electric field of two-color LG laser pulses and (b) isosurfaces of axial current density J_z = −3 × 10¹³ A/m² (blue) and 1.8 × 10¹³ A/m² (yellow) obtained from PIC simulation at 400 fs.

Fig. 4. (a) Isosurfaces of axial magnetic field B_z = −15.5 T (yellow) and 6.5 T (blue) obtained from PIC simulation at 400 fs and (b) the corresponding cross-sectional distributions in the x–y plane at z = 15 μm. (c) Isosurfaces of the axial magnetic field B_z = −15 T (red), −10 T (yellow), and 4.5 T (blue) obtained from PIC simulation at 800 fs and (d) the corresponding cross-sectional distributions in the x–y plane at z = 15 μm.

Fig. 5. Distributions in the x–y plane at z = 13.4 μm of (a)–(c) magnetic field lines, (d)–(f) radial current density J_r, and (g)–(i) angular current density J_θ obtained from PIC simulation at times t = 400 fs [(a), (d), and (g)], 600 fs [(b), (e), and (h)], and 800 fs [(c), (f), and (i)].

Fig. 6. Distributions on the axis of axial magnetic fields at t = 800 fs obtained from PIC simulation (blue) and estimated by the Biot–Savart law (red).

Fig. 7. Distributions in the x–y plane at z = 13.4 μm of (a)–(c) transverse current density J_xy (color contours) and transverse magnetic field B_xy (red arrows) and (d)–(f) axial current density J_z obtained from PIC simulation at different times t = 400 fs [(a) and (d)], 600 fs [(b) and (e)], and 800 fs [(c) and (f)].

Fig. 8. Distributions in the x–y plane at z = 13.4 μm of electron temperature obtained from PIC simulation at (a) t = 400 fs and (b) t = 800 fs. (c) Electron energy spectra obtained from PIC simulations at t = 400 and 800 fs. (d) Time evolution of electromagnetic field energy E_field, particle energy E_particle, and their sum E_sum within the simulation box.

Fig. 9. Distributions in the x–z plane at y = 0 of (a)–(c) axial magnetic field B_z and (d)–(f) axial current density J_z obtained from PIC simulation at t = 400 fs for three different beat frequency differences Δω = 0.05ω₀ [(a) and (d)], 0.1ω₀ [(b) and (e)], and Δω = 0.15ω₀ [(c) and (f)]. In each case, the plasma density is modified to satisfy the beating condition n₀ = m_eΔω²/4πe².

Fig. 10. Distributions in the x–y plane at z = 13.4 μm of the parameter lg[2πρB_z/(p₀B_θ)] obtained from PIC simulation at t = 800 fs for beat frequency differences Δω = 0.05ω₀ (a) and 0.15ω₀ (b). In each case, the plasma density is modified to satisfy the beating condition n₀ = m_eΔω²/4πe².