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A Wave-Based Simulation Model for Cross-Beam Energy Transfer and Stimulated Brillouin Scattering in Laser-Plasma Systems

Y. Chen, Qing Wang, H. Wen, Y. Z. J. Xu, S. J. Peng, W. Q. Li, C. Y. Zheng, Z. J. Liu, L. H. Cao, C. Z. Xiao

TL;DR

The paper introduces WEBS, a wave-based simulation framework that uses a unified Schrödinger-type envelope and a Du Fort-Frankel solver to efficiently model CBET and SBS in laser-plasma systems. WEBS is validated against PIC benchmarks and fluid theory, and is used to reveal how CBET and SBS couple at high laser intensities, causing deviations from fluid predictions and producing asymmetric SBS reflectivity due to pump depletion. The work provides a practical tool for identifying parameter regimes where CBET-SBS interactions are strong and informs inertial confinement fusion scenario design, with planned extensions to SRS, TPD, and SBS side-scattering in inhomogeneous plasmas.

Abstract

We present WEBS (WavE-Based Simulations), an efficient wave-based simulation model designed to investigate the dynamic interplay between cross-beam energy transfer (CBET) and stimulated Brillouin scattering (SBS) in laser-plasma systems. By employing a unified Schrodinger-type envelope formulation for the laser and ion-acoustic waves, our model enables the use of a single, unconditionally stable Du Fort-Frankel numerical scheme, which maintains excellent long-term energy conservation even with coarse spatial grids. This approach not only achieves high computational efficiency validated against particle-in-cell simulations but also allows the selective activation or suppression of CBET and SBS processes, offering a clear diagnostic of their mutual coupling. Our simulations reveal that at high laser intensities, CBET and SBS reach a coupled steady state, leading to significant deviations from classical fluid theory predictions. Specifically, CBET gain is suppressed due to enhanced SBS reflectivity, while strong asymmetry in SBS reflectivity emerges between the interacting beams. These findings highlight regimes where the two instabilities strongly influence each other, providing critical insights for inertial confinement fusion research and offering a practical numerical tool for instability control and scenario design.

A Wave-Based Simulation Model for Cross-Beam Energy Transfer and Stimulated Brillouin Scattering in Laser-Plasma Systems

TL;DR

The paper introduces WEBS, a wave-based simulation framework that uses a unified Schrödinger-type envelope and a Du Fort-Frankel solver to efficiently model CBET and SBS in laser-plasma systems. WEBS is validated against PIC benchmarks and fluid theory, and is used to reveal how CBET and SBS couple at high laser intensities, causing deviations from fluid predictions and producing asymmetric SBS reflectivity due to pump depletion. The work provides a practical tool for identifying parameter regimes where CBET-SBS interactions are strong and informs inertial confinement fusion scenario design, with planned extensions to SRS, TPD, and SBS side-scattering in inhomogeneous plasmas.

Abstract

We present WEBS (WavE-Based Simulations), an efficient wave-based simulation model designed to investigate the dynamic interplay between cross-beam energy transfer (CBET) and stimulated Brillouin scattering (SBS) in laser-plasma systems. By employing a unified Schrodinger-type envelope formulation for the laser and ion-acoustic waves, our model enables the use of a single, unconditionally stable Du Fort-Frankel numerical scheme, which maintains excellent long-term energy conservation even with coarse spatial grids. This approach not only achieves high computational efficiency validated against particle-in-cell simulations but also allows the selective activation or suppression of CBET and SBS processes, offering a clear diagnostic of their mutual coupling. Our simulations reveal that at high laser intensities, CBET and SBS reach a coupled steady state, leading to significant deviations from classical fluid theory predictions. Specifically, CBET gain is suppressed due to enhanced SBS reflectivity, while strong asymmetry in SBS reflectivity emerges between the interacting beams. These findings highlight regimes where the two instabilities strongly influence each other, providing critical insights for inertial confinement fusion research and offering a practical numerical tool for instability control and scenario design.
Paper Structure (7 sections, 18 equations, 8 figures)

This paper contains 7 sections, 18 equations, 8 figures.

Table of Contents

  1. Introduction
  2. The fundamental equations and algorithms for WEBS code
  3. CBET simulations by WEBS in homogeneous plasmas
  4. SBS simulations by WEBS in homogeneous and inhomogeneous plasmas
  5. Steady-State Analysis of the Interaction between CBET and SBS
  6. Conclusion and discussion
  7. Acknowledgements

Figures (8)

  • Figure 1: The comparison between WEBS simulation results and PIC simulation results.(a) The amplitude of laser at $t = 6.6 \rm{ps}$ by WEBS simulation. (b) the normalized amplitude of two lasers after CBET, the results are obtained by the integral of $x$ in the red rectangle of (a). (c) The amplitude of laser at $t = 6.6 \rm{ps}$ by PIC simulation. (d) the normalized amplitude of two lasers after CBET, the results are obtained by the integral of $x$ in the red rectangle of (c).
  • Figure 2: The results of WEBS for different spatial mesh. The parameters of lasers and plasma are same to that in Fig \ref{['tw_pic']}. The black line is the amplitude of two laser at $t = 6.6\rm{ps}$ by spatial meshes $10~\mathrm{cells}/\lambda_0$. The blue dashed line is the amplitude of two laser at $t = 6.6\rm{ps}$ by spatial meshes $15~\mathrm{cells}/\lambda_0$. The red dot line is the amplitude of two laser at $t = 6.6\rm{ps}$ by spatial meshes $20~\mathrm{cells}/\lambda_0$.
  • Figure 3: The results of WEBS for different flowing velocities of plasmas. The parameters of lasers are same to that in Fig \ref{['tw_pic']}. The black curves represents the temporal evolution of the pump laser power, while the red curves corresponds to that of the seed laser power. Three different flow velocity cases are considered, CBET operates in the resonant regime when $V_{y} = C_{s}$.
  • Figure 4: The WEBS simulation results of SBS in homogeneous plasma. (a) Spatial distribution of the seed laser at $t=26.4$ ps.(b) Corresponding spatial distribution of the ion-acoustic waves. (c) Temporal evolution of the SBS reflectivity.
  • Figure 5: The WEBS simulation results in inhomogeneous plasmas. (a) and (b) are the Spatial distribution of seed laser and IAWs at $t = 13.2$$ps$, respectively when the peak intensity of pump is $4\times 10^{14}$$\rm{W/cm^2}$. (c) black line is the reflectivity of SBS at the center of pump laser, red dashed line is the reflectivity by Rosenbluth theory. (d) The gains of SBS for different pump intensities, black line is obtained by Eq. (\ref{['sbs_ros']}), red diamonds are the results from WEBS simulations.
  • ...and 3 more figures