Particle-in-cell simulations of laser crossbeam energy transfer via magnetized ion-acoustic wave

TL;DR

This study probes how external magnetic fields directly modify cross-beam energy transfer (CBET) between pump and seed lasers in magnetized plasmas, focusing on the ion-acoustic wave (IAW) quasimode as the mediator. Using 2D-3V PIC simulations with the EPOCH code, the seed fields are decomposed into two nondegenerate magnetized eigenmodes, and gains are quantified via $g_j(t)=\ln\frac{U_j(t)}{U_j(t_0)}$ with $U_j=\frac{\epsilon_0}{2}\int \tilde{E}_j^2 dx$. The results show that increasing magnetic field strength $B$ reduces CBET for initially parallel polarizations while enabling nonzero CBET for orthogonal polarizations, and that the two eigenmodes acquire different gains (X-mode typically larger than O-/R-/L-like modes) as the modes become nondegenerate; these trends align qualitatively with MagCBET theory and persist across a range of geometries and plasma conditions. Finite-size effects broaden the gain curves, and the observed behavior underscores the joint influence of the magnetized plasma wave and the EM eigenmodes on CBET, providing guidance for magnetized high-energy-density experiments and LPI interpretation. The work also delivers open data and analysis code to facilitate further investigation of magnetized CBET in PIC and related frameworks.

Abstract

Large magnetic fields, either imposed externally or produced spontaneously, are often present in laser-driven high-energy-density systems. In addition to changing plasma conditions, magnetic fields also directly modify laser-plasma interactions (LPI) by changing participating waves and their nonlonear interactions. In this paper, we use two-dimensional particle-in-cell (PIC) simulations to investigate how magnetic fields directly affect crossbeam energy transfer (CBET) from a pump to a seed laser beam, when the transfer is mediated by the ion-acoustic wave (IAW) quasimode. Our simulations are performed in the parameter space where CBET is the dominant process, and in a linear regime where pump depletion, distribution function evolution, and secondary instabilities are insignificant. We use a Fourier filter to separate out the seed signal, and project the seed fields to two electromagnetic eigenmodes, which become nondegenerate in magnetized plasmas. By comparing the seed energy before CBET occurs and after CBET reaches quasi-steady state, we extract CBET energy gains of both eigenmodes for lasers that are initially linearly polarized. Our simulations reveal that starting from a few MG fields, the two eigenmodes have different gains, and magnetization alters how the gains depend on laser detuning. The overall gain decreases with magnetization when the laser polarizations are initially parallel, while a nonzero gain becomes allowed when the laser polarizations are initially orthogonal. These findings qualitatively agree with theoretical expectations.

Figures (3)

• Figure 1: Setup of 2D-3V PIC simulations, where the simulation domain (dashed rectangle) is centered around the seed laser and magnetic field is at oblique angles. For $z$-$z$ polarization, the pump and seed lasers have initially parallel polarizations, while for $z$-$y$, their polarizations are initially orthogonal.
• Figure 2: Energy gain $g(\Delta\lambda)$ for MagCBET at $\theta_B=90^\circ$ and intermediate angle $\phi_B=30^\circ$. (a)-(c) For $z$-$z$ polarization, the gain reduces with $B$, and the IAW peak broadens and shifts. (d)-(f) For $z$-$y$ polarization, the gain increases with $B$. The total gain (a),(d) is within the X-mode gain (b), (e) and O-mode gain (c),(f). The gain at other $\theta_B$ and $\phi_B$ are qualitatively similar.
• Figure 3: Energy gain near the peak of the gain curves at $\theta_B=90^\circ$. (a) When the plasma wave $\Delta\mathbf{k}$ is near parallel to $\mathbf{B}$, the gains remain nearly constant until $B\sim$ 10 MG, where laser modes become magnetized. (b) When $\Delta\mathbf{k}$ is near perpendicular to $\mathbf{B}$, the plasma wave is magnetized. The gains are small at large $B$ and are insensitive to laser modes. (c) When $\Delta\mathbf{k}$ is at an intermediate angle to $\mathbf{B}$, both effects are at play, and the gains have features that resemble the two extreme cases.