Gravitational Instability of Rotating Viscoelastic Partially Ionized Plasma in the Presence of an Oblique Magnetic Field and Hall Current

M F El-Sayed,R A Mohamed

doi:10.5402/2011/597172

Abstract

The gravitational instability of a rotating Walters B′ viscoelastic partially ionized plasma permeated by an oblique magnetic field has been investigated in the presence of the effects of Hall currents, electrical resistivity, and ion viscosity. The dispersion relation and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitational unstable mode on the various physical effects. It is found that viscosity and collision frequency of plasma have stabilizing effects, while viscoelasticity and angular frequency of rotation have destabilizing effect; the electrical resistivity has a destabilizing effect only for small wavenumbers; the density of neutral particles and the magnetic field component in z-direction have stabilizing effects for wavenumbers ranges k<5 and k<10, respectively; the Hall current has a slightly destabilizing effect. Finally, the inclination angle to z-direction has a destabilizing effect to all physical parameters.

Highlights

The gravitational instability problem of an infinite homogenous medium was first considered by Jeans [1]
The combined effects of uniform rotation, Hall currents, finite conductivity, and finite Larmor radius on gravitational instability have been studied by Bhatia [3]
Bhatia [5] and Barbian and Rasmussen [6] studied the gravitational instability of a rotating anisotropic plasmas

Summary

Introduction

The gravitational instability problem of an infinite homogenous medium was first considered by Jeans [1]. According to Jeans’ criterion, an infinite homogenous self-gravitating atmosphere is unstable for all wavenumbers k less than Jeans’ wavenumber kj = Gρ/S, where ρ is the density, S is the velocity of sound in the gas, and G is the gravitational constant This problem has been studied by several authors under varying assumptions of hydrodynamics and hydromagnetics, and a comprehensive account of these investigations has been given by Chandrasekhar [2] in his monograph on problems of hydrodynamic and hydromagnetic stabilities. It would be of importance here to examine the effects of viscosity, viscoelasticity, Hall current, rotation, and finite conductivity for two components Walters B viscoelastic partially ionized plasma in a uniform oblique magnetic field. This problem, to the best of our knowledge, has not been investigated yet

Problem Formulation and Perturbation Equations

Dispersion Relation

Stability Analysis and Discussion

Conclusion