Relativistic Magnetohydrodynamic Wave Excitation by Laser Pulse in a Magnetized Plasma

TL;DR

The paper investigates modulational instabilities induced by a strong laser pulse in a magnetized, relativistic plasma using a relativistic MHD framework with ions treated as a fixed background. It derives a nonlinear Schrödinger equation for the electromagnetic envelope and analyzes stability, obtaining the maximum growth rate $\Omega_i^{\max} = \frac{c^2 \omega_{P0}^2 Q}{\omega_0^3} |E_0|^2$, highlighting how plasma parameters and wave intensity govern the instability. The authors also identify electron-driven modes akin to Alfvén- and magnetoacoustic-like waves within the NLSE description and apply the Bogoliubov-Mitropolsky method to incorporate both nonlinear Landau damping and growth-damping effects via a complex perturbation $\Theta(A)$. This work provides a framework for understanding nonlinear wave evolution and soliton dynamics in relativistic magnetized plasmas, with implications for laser-plasma interactions and high-energy-density experiments.

Abstract

In the study of plasma, particularly in applications involving strong laser-plasma interactions, the propagation of a strong electromagnetic wave induces relativistic velocities in the electron flow. Given such conditions, the wave propagating through the plasma experiences modulational instability. In this paper, we investigate this instability using magnetohydrodynamic (MHD) equations. In the relativistic limit, the motion of ions can be neglected due to their significant inertia, allowing us to treat the ions as a background fluid. This simplification enables us to apply perturbation techniques to the electron fluid equations, leading to the derivation of the nonlinear wave equation in the form of the Nonlinear Schrödinger Equation (NLSE). We also explore the relationship between wave dispersion and the conditions for instability. We derive the maximum growth rate of the modulational instability and analyze its dependence on plasma parameters and wave intensity in the context of relativistic magnetized plasma, providing quantitative insights into the instability dynamics. Finally, we examine aspects of the perturbed NLSE using the Bogoliubov-Mitropolsky perturbation approach, treating real and imaginary coefficients separately, which explicitly incorporates both Nonlinear Landau Damping (NLLD) and growth-damping effects.