Vortex Solitons and Filamentation of Electromagnetic Beams in Relativistically Degenerate Plasmas

TL;DR

This work addresses the propagation and stability of electromagnetic vortex beams in relativistically degenerate plasmas using a self-consistent relativistic fluid–Maxwell framework. It derives a coupled set of dimensionless equations for the vector potential amplitude $A$ and scalar potential $\Psi$, analyzes stationary vortex solutions with topological charge $m$, and performs linear stability analysis of azimuthal perturbations alongside nonlinear simulations. The study reveals exponential azimuthal instabilities with growth rates depending on the beam power $P$, propagation constant $k$, and $m$, selecting a dominant mode that dictates filamentation; despite breakup, the vortex core remains topologically protected with $|A|^2=0$ at the center, and the vortex solitons act as nonlinear attractors with a finite basin of attraction. These findings persist across a broad range of degeneracy parameter values $d$, with dimensional threshold powers placing the regime in the hard X-ray band for multi-gigawatt beams, underscoring relevance to dense astrophysical plasmas near compact objects.

Abstract

We study the propagation and stability of electromagnetic vortex beams in relativistically de generate plasmas. We show that such plasmas support localized vortex solitons carrying orbital angular momentum and analyze their linear and nonlinear stability. Vortex solitons undergo az imuthal symmetry-breaking instabilities whose growth rates depend on beam power, propagation constant, and topological charge, with the dominant mode determining the number of filaments formed during breakup. We further demonstrate that vortex solitons act as nonlinear attractors with a finite basin of attraction, while the vortex core remains topologically protected, maintaining a strictly zero field intensity at the beam center throughout the evolution. The results persist across a broad range of degeneracy parameters and are relevant to hard X-ray radiation propagating in dense astrophysical plasmas.

Figures (7)

• Figure 1: Numerically found stationary potential profiles for $m=1$, $k=0.2$ (a) and $k=0.3$ (b)
• Figure 2: Stationary $m=1$ vortex amplitudes as functions of $k$
• Figure 3: Numerically found stationary potential profiles for $k=0.2$, $m=1$ and $m=2$
• Figure 4: Power carried by the stationary state as a function of its amplitude
• Figure 5: $\operatorname{Im}(K)$ as a function of $M$ for $k=0.02$, $0.10$, $0.20$ and $0.3$