Fig. 1. (a) 3D schematic of the target and four regular laser beams with twisted pointing directions carrying AM collectively. The colored cylinders indicate the beams and the corresponding dashed lines show the way in which the twist is induced by the beams. (b) 2D projection of the beams onto the (y, z) plane, showing the beginning and the end in the emitter plane and the focal plane, respectively. Each arrow is the component of the wave vector (in a corresponding colored beam) transverse to the global direction (x axis) of propagation of the ensemble of beams. The parameters can be found in Table I. (c) Illustration of the axial magnetic field B_x after the lasers have left the simulation box (t = 20 fs). The blue, yellow, and red isosurfaces, from the outside to the inside, represent increasing magnetic field strength. The axial magnetic field profile is quantified in Fig. 2.

Fig. 2. Distribution of axial magnetic field at t = 20 fs. (a) Volumetric isocontours of axial magnetic field component for B_x = −0.2, −0.55, and −0.8 B₀ (purple, yellow, and red). (b) Distribution of the axial magnetic field in (x, r) plane. Azimuthal averaging is performed.

Fig. 3. Temporal evolution of axial magnetic field. (a) Distribution of axial magnetic field in (t, r) plane, with slices highlighted at radial distances r = 0 μm (black), 4 μm (red), and 8 μm (blue). Longitudinal and azimuthal averaging is performed. (b) Axial magnetic field for r = 0 μm, where max ⟨B_x⟩ = 1.78B₀. t = 0 fs is defined as the moment when the lasers leave the simulation space completely.

Fig. 4. Simulation results at three different times t = 20.0, 220.0, and 420.0 fs (from left to right). (a), (d), and (g) Longitudinal slices of electron density, where the density is normalized to the critical density and the black solid lines mark n_e = n_c. (b), (e), and (h) Longitudinal slices of the axial magnetic field, where the field is averaged over 20 fs and normalized to B₀ = 2πm_ec/|e|λ = 10.0 kT; the two black solid lines respectively represent the front (x = 0 μm) and rear (x = 3 μm) surfaces of the solid part of the target; the front surfaces (x = −5 μm) of the exponentially modulated preplasma are represented by the black dashed lines; the red and black dashed lines show the boundaries of the lineout region. (c), (f), and (i) Radial lineouts of the axial magnetic field, where the field is averaged azimuthally, temporally, and longitudinally (over the lineout region marked with red and black dashed lines in the middle row). Laser–plasma parameters are given in Table I.

Fig. 5. 2D longitudinal slices at t = 20 fs of all three components of the time-averaged (averaged over 20 fs output dumps) magnetic field from the 3D PIC simulation with the parameters listed in Table I. The fields are normalized to B₀ = 2πm_ec/|e|λ = 10.0 kT. B_x, B_y, and B_z are shown in the (x, y) plane (top row) and (x, z) plane (bottom row), respectively. Note that the color scale for B_x is different from that for B_y and B_z.

Fig. 6. 3D magnetic vector field and magnetic field line structure at t = 20 fs. (a) Vector arrows of magnetic field, where both the length and color of each vector represent the relative field strength. (b) Magnetic field lines reconstructed from the vector field. Areas with a higher density of magnetic field lines have a higher magnetic field strength, which can be visually observed from the color. The videos show the distribution from different viewpoints (see videos in the supplementary material).10.1063/5.0235188.110.1063/5.0235188.2

Fig. 7. (a) Temporal evolution of electron kinetic energy and axial magnetic field energy within a rectangular volume of length a = 17.9 μm (x ∈ [−19.9, −2.0] μm) and width and height b, c = 20 μm (y, z ∈ [−10.0, 10.0] μm). The time t = 0 fs is defined as the moment when the lasers completely exit the simulation domain. The red solid line represents the simulated kinetic energy of hot electrons within the region. The blue solid line depicts the simulated magnetic field energy, and the black dashed line with cross marks indicates the fit result of our model. (b) Temporal evolution of the peak axial magnetic field strength from simulation, alongside the results of Bxm derived from the fitting formula in Eq. (7). The results of the fitting model in (a) and (b) are both shown for t in the range from 0 to 1700 fs.

Fig. 8. Azimuthal current density j_ϕ (normalized to j₀ = −|e|cn_c = −4.8 × 10¹⁶ A m⁻²) at t = 20 fs. (a) Azimuthal current density j_ϕ averaged over ϕ as a function of x and r. (b) and (c) 2D transverse slices of j_ϕ at x = −10 and −5 μm, respectively.

Fig. 9. Density of axial OAM for electrons (top row) and ions (bottom row) normalized to L₀ ≡ n_cm_ecw₀ ≈ 1.65 kg m⁻¹ s⁻¹ at t = 20 fs in the simulation with the twist angle φ = 0.28π. (a) and (b) Azimuthally averaged densities of axial OAM L_xe and L_xi, respectively, as functions of x and r. (c) and (d) Transverse slices of L_xe and L_xi, respectively, at x = −10. (e) and (f) Transverse slices of L_xe and L_xi, respectively, at x = −5 μm.

Fig. 10. Simulation result for laser beams with a reversed twist (φ = −0.28π). 2D longitudinal slices at t = 20 fs of all three components of the time-averaged (averaged over 20 fs output dumps) magnetic field in the 3D PIC simulation with the parameters listed in Table I. The fields are normalized to B₀ = 2πm_ec/|e|λ = 10.0 kT. B_x, B_y, and B_z are shown in the (x, y) plane (top row) and (x, z) plane (bottom row). Note that the color scale for B_x is different from that for B_y and B_z.

Fig. 11. Simulation result for laser beams without a twist (φ = 0.0π). 2D longitudinal slices at t = 20 fs of all three components of the time-averaged (averaged over 20 fs output dumps) magnetic field in the 3D PIC simulation with the parameters listed in Table I. The fields are normalized to B₀ = 2πm_ec/|e|λ = 10.0 kT. B_x, B_y, and B_z are shown in the (x, y) plane (top row) and (x, z) plane (bottom row). Note that the color scale for B_x is different from that for B_y and B_z.

Fig. 12. 2D view of the spatial arrangement and polarization direction of the four laser beams in the (y, z) plane. (a) Locked LP₀ simulation: the linear polarization directions of all four laser beams are along the y axis. (b) Locked LP₁ simulation: a pair of laser beams (cyan and red) are polarized along the y axis, whereas the other pair (green and purple) are polarized along the z axis. (c) Random LP simulation: random phase shifts ξ ∈ (0, π) are added to the initial polarization directions of the four laser beams, disrupting the regular polarization arrangement of the lasers. (d) Average axial magnetic field within a rectangular volume of length a = 17.9 μm (x ∈ [−19.9, −2.0] μm) and width and height b, c = 16 μm (y, z ∈ [−8.0, 8.0] μm) as a function of time, where t = 0 fs is defined as the moment when the lasers leave the simulation space completely. The black, red, and blue solid lines represent the cases of Locked LP₀, Locked LP₁, and Random LP, respectively.

Fig. 13. (a) and (b) Two delay scenarios considered in the simulations: short delay and long delay. The individual pulse duration is τ_L = 600 fs and the considered delays are τ₁ = 250 fs and τ₂ = 1 ps. Note that the delays are random in the short-delay scenario, whereas they are fixed in the long-delay scenario. The delays are shown on different time scales. (c) Average axial magnetic field within a rectangular volume of length a = 17.9 μm (x ∈ [−19.9, −2.0] μm) and width and height b, c = 16 μm (y, z ∈ [−8.0, 8.0] μm) as a function of time, where t = 0 fs is defined as the moment when the lasers leave the simulation space completely. The black, red, and blue solid lines represent the cases with no delay, a short delay, and a long delay, respectively.

Fig. 14. Average axial magnetic field within a cuboid of length a = 17.9 μm (x ∈ [−19.9, −2.0] μm) and width and height b, c = 16 μm (y, z ∈ [−8.0, 8.0] μm) as a function of time, where t = 0 fs is defined as the moment when the lasers leave the simulation space completely. (a) The locked-phase case is depicted by the solid black line with round markers, while the random-phase case is shown as the solid red line with diamond markers. (b) Impact of the density profile at the laser-irradiated surface. The shelf density profile, the exponential density profile, and the nanowire target are represented by the blue, black, and red solid lines, respectively.

Fig. 15. Impact of laser pointing stability on generation of the axial magnetic field. The black curve is for the case without any fluctuations, using the setup shown in Fig. 2. The red curve is for the case with beam offset fluctuations and the blue curve for the case with angular fluctuations. In each simulation, the axial magnetic field is averaged over a rectangular volume with x ∈ [−19.9, −2.0] μm and y, z ∈ [−8.0, 8.0] μm. Note that the laser beams leave the simulation domain at t = 0 fs.

Fig. 16. Average axial magnetic field within a rectangular volume of length a = 17.9 μm (x ∈ [−19.9, −2.0] μm) and width and height b, c = 16 μm (y, z ∈ [−8.0, 8.0] μm) as a function of time, where t = 0 fs is defined as the moment when the lasers leave the simulation space completely. The black, red, and blue solid lines represent the cases of four LP Gaussian laser beams, a single LP LG mode laser, and a single CP Gaussian mode laser, respectively.