Modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas

TL;DR

This paper investigates the modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas, revealing how density influences stability and wave dynamics.

Contribution

It introduces a nonlocal 2D nonlinear Schrödinger-like model for UR degenerate plasmas and analyzes the density-dependent stability conditions and wave evolution.

Findings

Higher densities reduce MI growth rate

Stable and unstable regions shift with density

Wave packets disperse or blow up depending on initial conditions

Abstract

We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schr{\"o}dinger-like equations. The coupled set of equations are then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multi-dimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, $\beta\propto\lambda_C n_0^{1/3}$ (where $\lambda_C$ is the reduced Compton wavelength and $n_0$ is the particle number density), associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at $n_{0}\sim10^{30}$ cm$^{-3}$ to unstable (stable) ones at higher densities, i.e. $n_{0}\gtrsim7\times10^{33}$. It is also found that {the} higher the values of $n_{0}$, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multi-dimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs {and/or} pre-Supernova stars.