Fig. 1. Transverse distributions of the quasi-static axial self-generated magnetic fields (normalized by B₀ = m_eω₀/e) obtained from (a)–(d) the theoretical model and (e)–(h) 3D PIC simulations for lasers with different polarization states propagating in a plasma. The lasers have (a) and (e) l_y = 1, l_z = 1, Δφ = −π/2; (b) and (f) l_y = 1, l_z = −1, Δφ = −π/2; (c) and (g) l_y = 1, l_z = −1, Δφ = 0; (d) and (h) l_y = 2, l_z = −1, Δφ = 0. The electron number density n0,0=niniexp[−(r/rCH)6], where n_ini = 0.1n_c and r_CH = 4λ. For all the lasers, a_y = a_z = 0.2 and w_0y = w_0z = 4λ.

Fig. 2. Transverse distributions of different azimuthal currents (normalized by J₀ = n_cec): (a) Jnl,θt from the theoretical model; (b) Jdm,θt from the theoretical model; (c) Jnl,θs from the PIC simulation; (d) Jdm,θs from the PIC simulation. The laser parameters are l_y = 1, l_z = −1, Δφ = −π/2, a_y = a_z = 0.2, and w_0y = w_0z = 4λ. The electron number density n0,0=niniexp[−(r/rCH)6], where n_ini = 0.1n_c and r_CH = 4λ.

Fig. 3. Magnetic field (normalized by B₀ = m_eω₀/e) distributions (a) along y = 0 and (b) along θ at r = 3λ. The black line shows the results of the PIC simulations, the red line those of the theoretical model, and the green line those calculated from conservation of generalized vorticity. The laser parameters are l_y = 1, l_z = −1, Δφ = −π/2, a_y = a_z = 0.2, and w_0y = w_0z = 4λ. The electron number density n0,0=niniexp[−(r/rCH)6], where n_ini = 0.1n_c, and r_CH = 4λ.

Fig. 4. (a) Distribution of laser intensity with laser parameters l_y = 1, l_z = −1, Δφ = −π/2, a_y = a_z = 0.2, and w_0y = w_0z = 4λ. White and green ellipses represent laser polarization states that are left- and right-handed, respectively. (b)–(e) Trajectories of electrons in this laser for one laser period near (r, θ) = (2.8λ, 0), (2.8λ, π/4), (2.8λ, π/2), and (2.8λ, 3π/4), respectively, marked by the red points in (a). The color change from blue to red indicates the time evolution.

Fig. 5. Transverse distributions of the quasi-static axial self-generated magnetic fields (normalized by B₀ = m_eω₀/e) for different electron number density distributions: (a) and (c) n0,1=nini{1−exp[−(r/rCH)6]}; (b) and (d) n0,2=nini{0.5+exp[−(r/rCH)6]}. Here, n_ini = 0.1n_c and r_CH = 4λ. (a) and (b) show the results from the theoretical model, and (c) and (d) show the results from the 3D PIC simulations. The laser parameters are l_y = 1, l_z = −1, Δφ = −π/2, a_y = a_z = 0.2, and w_0y = w_0z = 4λ.

Fig. 6. Distributions of different azimuthal currents (normalized by J₀ = n_cec) along r at θ = π/2 (y = 0, z > 0) obtained from the theoretical model. The solid lines (case 0) show the results with the density profile n0,0=niniexp[−(r/rCH)6], the dotted lines (case I) the results with the profile n0,1=nini{1−exp[−(r/rCH)6]}, and the dashed lines the results with the profile n0,2=nini{0.5+exp[−(r/rCH)6]}. The red lines show the source current j_nl,θ, the green lines the diamagnetic current j_dm,θ, and the black lines the total azimuthal current j_θ = j_nl,θ + j_dm,θ. The plasma parameters are n_ini = 0.1n_c and r_CH = 4λ. The laser parameters are l_y = 1, l_z = −1, Δφ = −π/2, a_y = a_z = 0.2, and w_0y = w_0z = 4λ.

Fig. 7. Distribution of the axial magnetic field (normalized by B₀ = m_eω₀/e) obtained from the theoretical model for a laser with EzLG/E0=azhz(r)exp(−iθ) and EyLG/E0=ay,1hy,1(r)exp(iθ)+ay,2hy,2(r)exp(2iθ). The laser parameters are a_z = a_y,1 = a_y,2 = 0.2 and w_z = w_y,1 = w_y,2 = 4λ. The electron number density n0,0=nini⁡exp[−(r/rCH)6], where n_ini = 0.1n_c and r_CH = 4λ.

Fig. 8. Distributions of axial magnetic fields (normalized by B₀ = m_eω₀/e) along y = 0 generated by different polarized Gaussian beams. The red and blue lines show the results of PIC simulation for right- and left-hand (σ_x = ±1) circularly polarized lasers, respectively, the black line shows the result of the theoretical model for a right-hand (σ_x = 1) circularly polarized laser, and the green line shows the result of PIC simulation for a linearly (σ_x = 0) polarized laser. The laser parameters are a₀ = 0.3 and w₀ = 4λ. The plasma has n0,3=nini/[1+9exp(−r2/rCH2)], where n_ini = 0.1n_c and r_CH = 2λ.

Fig. 9. Distributions of axial magnetic fields (normalized by B₀ = m_eω₀/e) along y = 0 generated by different LG lasers in PIC simulations. The black, red, and green lines represent the cases of a left-hand CP (σ_x = −1) LG laser with l = 1, a left-hand CP (σ_x = −1) LG laser with l = −1, and a LP (σ_x = 0) LG laser with l = 1, respectively. The other laser parameters are a₀ = 0.2 and w₀ = 4λ. The electron number density n0,0=niniexp[−(r/rCH)6], where n_ini = 0.1n_c and r_CH = 4λ.