Dynamical Instability of Charged Gaseous Cylinder

TL;DR

This paper investigates the dynamical stability of charged gaseous cylinders under radial oscillations, deriving criteria for instability based on physical parameters and comparing charged and uncharged cases in Newtonian and post-Newtonian regimes.

Contribution

It introduces a variational principle to determine oscillation frequencies and stability criteria for charged gaseous cylinders, considering both Newtonian and post-Newtonian limits.

Findings

Charged cylinders become unstable when contracting to a critical radius R_*.

The stability depends on the adiabatic index and charge presence.

Uncharged cylinders have different stability thresholds compared to charged ones.

Abstract

In this paper, we discuss dynamical instability of charged dissipative cylinder under radial oscillations. For this purpose, we follow the Eulerian and Lagrangian approaches to evaluate linearized perturbed equation of motion. We formulate perturbed pressure in terms of adiabatic index by applying the conservation of baryon numbers. A variational principle is established to determine characteristic frequencies of oscillation which define stability criteria for gaseous cylinder. We compute the ranges of radii as well as adiabatic index for both charged and uncharged cases in Newtonian and post-Newtonian limits. We conclude that dynamical instability occurs in the presence of charge if the gaseous cylinder contracts to the radius $R_{*}$.