Fig. 1. Schematic of the resonant regions for absolute and convective modes of Re-BSRS instabilities in an inhomogeneous plasma.

Fig. 2. Evolution of the E_y field (contributed only by the laser’s electric field in 1D simulations) of simulation case (i) in x–t space.

Fig. 3. Time-resolved Ey2 spectrum of light collected at the left boundary for (a) case (i); (b) case (ii), and (c) case (iii). Different types of LPI signals can be identified, as indicated. The dashed lines are the boundaries of the primary BSRS modes.

Fig. 4. Snapshots of the in-flight Ey2 spectrum in the simulation of case (i) at (a) t = 6.0 ps, (b) t = 8.5 ps, and (c) t = 14.0 ps. Different types of LPI signals are indicated. The dashed lines in (c) are the turning points of the rescattered light with a range of frequencies.

Fig. 5. Time-integrated reflection fraction (a) due to backward-traveling light in different frequency ranges and (b) due to different types of LPI.

Fig. 6. [(a)–(d)] Comparison of the backward-propagating light spectra within the frequency range of [0.6, 0.95]ω₀ in cases (i) [(a) and (c)] and (ii) [(b) and (d)]. (e) Comparison of the convective amplification of a forward-propagating Re-BSRS light component with ω_s2 = 0.47ω₀ in cases (i) and (ii). The star symbols in (a)–(d) represent the most resonant light component that can serve as a pump for the Re-BSRS mode ω_s2 = 0.47ω₀ at the given moment. The circles and triangles in (e) represent the peak values vs the peak’s positions on the Ey2 envelope at different times in cases (i) and (ii). Snapshots of the Ey2 envelopes at three different times in case (i) are plotted as dashed curves.

Fig. 7. Correlation of hot electrons with Re-BSRS. (a) Temporal and spatial evolution of Re-BSRS light within the frequency range 0.35ω₀ < ω_s2 < 0.5ω₀. (b) Temporal and spatial evolution of the distribution of the backward-moving hot electrons with kinetic energies >50 keV. The presence of a bunch of hot electrons near the left boundary after t ≈ 18 ps is probably due to the boundary conditions in the long-time simulation and is expected to be artificial.

Fig. 8. 2D simulation results for case (vi). (a) Time evolution of Ey2 in k_x space in a spatial domain near n_e = n_cr/9. (b) Evolution of Ey2 of the mode ω_s2 = 0.4ω₀. The circles represent the peak value vs the peak’s position on the envelope at different times, while three snapshots of the envelopes at three different times are shown by dashed lines.

Fig. 9. Spectra in k_y–k_x space of (a) B_z representing incident and scattered light and (b) electron number density representing plasma waves in the region with a background density range of [0.06n_cr, 0.11n_cr] at t = 4.1 ps in case (vi).

Table 1. Simulation parameters.