Stability and evolution of wave packets in strongly coupled degenerate plasmas

TL;DR

This paper investigates the nonlinear behavior and stability of wave packets in strongly coupled, relativistically degenerate plasmas, revealing conditions for stability, instability, and wave collapse with potential astrophysical applications.

Contribution

It derives a novel (3+1)-dimensional coupled nonlinear Schrödinger-like model for wave packets in such plasmas, analyzing their stability and collapse dynamics.

Findings

Wave packets are stable to parallel modulation but unstable to oblique modulation.

Short-wavelength wave packets are stable in weakly relativistic regimes.

Wave self-focusing and blow-up occur in (3+1) dimensions, but dispersion can arrest collapse.

Abstract

We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature associated with their strong coupling, whereas that of electrons is provided by the relativistic degeneracy pressure. Using a multiple scale technique, a (3+1)-dimensional coupled set of nonlinear Schr\"{o}dinger-like equations with nonlocal nonlinearity is derived from a generalized viscoelastic hydrodynamic model. These coupled equations, which govern the dynamics of wave packets, are used to study the oblique modulational instability of a Stoke's wave train to a small plane wave perturbation. We show that the wave packets, though stable to the parallel modulation, becomes unstable against oblique modulations. In contrast to the long-wavelength carrier modes, the wave packets with short-wavelengths are shown to be stable in the weakly relativistic case, whereas they can be stable or unstable in the ultra-relativistic limit. Numerical simulation of the coupled equations reveals that a steady state solution of the wave amplitude exists together with the formation of a localized structure in (2+1) dimensions. However, in the (3+1)-dimensional evolution, a Gaussian wave beam self-focuses after interaction and blows up in a finite time. The latter is, however, arrested when the dispersion predominates over the nonlinearities. This occurs when the Coulomb coupling strength is higher or a choice of obliqueness of modulation, or a wavelength of excitation is different. Possible application of our results to the interior as well as in an outer mantle of white dwarfs are discussed.