Fig. 1. (a) Schematic of MFB model. (b) RECT spectrum broadband laser with a bandwidth Δω/ω₀ = 1.5%, which contains 200 beamlets. (c) Temporal envelopes of broadband laser intensity. The laser intensity I is normalized to the laser’s average intensity ⟨I⟩.

Fig. 2. (a1) and (a2) Intensity envelopes of a monochromatic laser and a broadband laser, respectively. (b1) and (b2) Reflectivities of the BSRS driven by the monochromatic and broadband lasers, respectively. (c1) and (c2) Spatiotemporal evolutions of EPWs driven by the monochromatic and broadband lasers, respectively.

Fig. 3. (a) Schematic of broadband driven-BSRS bursts. (b) Simulation schematic of a BSRS burst driven by a high-intensity broadband laser pulse. (c) Energy envelopes of the laser (black line) and the back-scattered light (red line) measured on the left boundary of the simulation box, which shows a reflectivity spike induced by the BSRS burst.

Fig. 4. Spatiotemporal evolution of (a) incident laser energy, (b) back-scattered light energy, and (c) EPW energy. The dashed line represents the path of the high-intensity pulse, and the dotted line represents the path of the back-scattered light. The numbers “1” and “2” indicate where the BSRS occurs, and v_laser and v_packet denote the group velocities of the pulse and EPW packets, respectively.

Fig. 5. (a) Time evolution of EPW k-spectrum. The white dashed line denotes the Langmuir wavenumber k_lw in the linear stage, and the two white dotted lines denote two TPI sidebands, marked as k_up and k_down. (b)–(d) k-spectra of EPWs in the linear, sideband, and turbulence-like stages, respectively. k_F represents a weak forward-stimulated Raman scattering (FSRS) component.

Fig. 6. Sideband growth rate after BSRS burst (red line), initial Landau damping γ_L0 (black solid line), decreased Landau damping 0.5γ_L0 (dashed line), and 0.1γ_L0 (dotted line).

Fig. 7. (a) Electron phase space in the linear stage (t = 600τ₀); the potential (black line) is periodic. (b) Electron phase space in the sideband stage (t = 800τ₀), where periodic disruption of the potential and initial vortex-merging are observed. (c) Electron phase space in the turbulence-like stage (t = 1050τ₀), where the burst triggers violent vortex merging. (d) Electron phase space at 1100τ₀, where a chaotic vortex structure is observed. The white dashed line represents the EPWs’ initial phase velocity v_epw = 0.29c.

Fig. 8. Partial enlargements of electron phase space at (a) t = 600τ₀, (b) t = 800τ₀, and (c) t = 1050τ₀. The dashed line represents the EPWs’ initial phase velocity v_epw = 0.29c, and the solid lines represents the upper and lower velocity limits of the electron vortices. (d) Comparison between the electron velocity distribution function and the initial distribution function at three times. The dashed line represents the initial phase velocity of the EPWs.

Fig. 9. (a) Electron velocity distribution function before (blue line) and after (red line) the burst, compared with the initial function (gray line). The black line represents the variation of the EPW phase velocity v_p with k_e calculated using the Bohm–Gross dispersion relation. (b) Electron energy distribution functions at 0, 600τ₀, 800τ₀, and 1050τ₀.

Fig. 10. Intensities of EPWs with different wavenumbers. The time at which the high-intensity pulse is incident on the left boundary is marked by the black dashed line.

Fig. 11. (a) and (d) Spatiotemporal evolution of EPWs and k-spectrum, respectively, driven by pulses with ⟨I_pulse⟩ = 1.0I_flat. (b) and (e) Spatiotemporal evolution of EPWs and k-spectrum, respectively, driven by pulses with ⟨I_pulse⟩ = 1.5I_flat. (c) and (f) Spatiotemporal evolution of EPWs and k-spectrum, respectively, driven by pulses with ⟨I_pulse⟩ = 2.0I_flat.

Fig. 12. (a) Time vs space of the plasma waves (E_x) for the high-plasma-density simulation (n_e = 0.18n_c and kλ_d = 0.22). (b) Time vs space of the plasma waves (E_x) for the low-plasma-density simulation (n_e = 0.13n_c and kλ_d = 0.30).

Fig. 13. (a1), (b1), and (c1) Dispersion relations of electromagnetic waves (EMWs), EPWs, and IAWs, respectively, for the case kλ_d = 0.22. (a2), (b2), and (c2) Dispersion relations of EMWs, EPWs, and IAWs, respectively, for the case kλ_d = 0.30. The white dotted lines represent ω2=ωpe2+c2k2, and the red dashed lines represent ω2=ωpe2+3vth2k2.

Fig. 14. Electron velocity distributions for the simulations with kλ_d = 0.22 (blue line) and kλ_d = 0.30 (red line). Here, v_epw1 and v_epw2 denote the phase velocities of the primary and secondary EPWs.