Fig. 3: Simulation revealing the Weibel instability features.

The plasma flows are injected into the simulation area from the left and right ends of the simulation box, and the number density and velocity of injection plasma are obtained via a radiation hydrodynamics simulation. Three distinct moments of interest are selected, 1.0 ns, 3.0 ns, and 6.0 ns, which correspond to linear and nonlinear stages of the evolution of WI, respectively. Panels (a–c) display the spatial distribution of the number density (n_e), x-directional current density (J_x), and z-directional magnetic field (B_z) at 1.0 ns. Correspondingly, panels (d–f) portray the corresponding data at 3.0 ns, and panels (g–h) are the corresponding data at 6.0 ns. The iso-contours in panel (f) and panel (i) represent the magnetic vector potential at 3.0 ns and 6.0 ns, and the black, red, and gold lines denote the iso-contours of the magnetic vector potential, indicating values of 2 × 10¹⁰, 3 × 10¹⁰, 4 × 10¹⁰Gs cm⁻¹ respectively. Panel (j) plots the magnetic field energy spectra ε_B(k, t) =  B(k)² obtained by a fast Fourier transform at different times, and the red and blue circles represent the energy spectrum extracted from the reconstructed path-integrated magnetic field in experiments. Panel (k) shows the peak wave number k_peak evolving with time.