Rayleigh-Taylor Instability of Magnetized Plasma through Darcy Porous Medium

Gamal Abdallah Hoshoudy

doi:10.4236/jmp.2014.55029

Abstract

Effects of horizontal and vertical magnetic field components on the Rayleigh-Taylor instability of stratified incompressible plasmas layer of variable density through Darcy porous medium are studied. The basic magnetohydrodynamic (MHD) set of equations has been constructed and linearized. Then the linear normalized growth rate is obtained analytically as a function of the physical parameters of the system considered. Numerical calculations have been performed to see the effects of various parameters on the normalized growth rate of Rayleigh-Taylor instability.(For more information,please refer to the PDF.)

Highlights

The hydromagnetics stability of a magnetized plasma of varying density is of considerable importance in several astrophysical situations such as supernova explosions, in heating in solar corona, theories of sunspot magnetic fields, the formation and mixing of clouds and the stability of the stellar atmospheres in magnetic fields
Rayleigh-Taylor instability (RTI) occurs naturally in many phenomenons of astrophysics, geophysics, and laboratories. It derives its character from the adverse density distribution of the matter, where the investigation of Rayleigh-Taylor instabilities in a magnetized plasma is a problem of considerable interest in space, fusion and the astrophysical plasmas
The Rayleigh-Taylor instability problem of a finite layer of a fluid has been studied by several authors in hydrodynamics and in magnetohydrodynamics domain; the stabilizing effect of magnetic field on RTI problem for an incompressible plasma has been demonstrated by Kruskal and Schwarzschild [3] for a horizontal orientation of the magnetic field and by Hide [4] for a vertical orientation

Summary

Introduction

The hydromagnetics stability of a magnetized plasma of varying density is of considerable importance in several astrophysical situations such as supernova explosions, in heating in solar corona, theories of sunspot magnetic fields, the formation and mixing of clouds and the stability of the stellar atmospheres in magnetic fields. The Rayleigh-Taylor instability problem of a finite layer of a fluid has been studied by several authors in hydrodynamics and in magnetohydrodynamics domain; the stabilizing effect of magnetic field on RTI problem for an incompressible plasma has been demonstrated by Kruskal and Schwarzschild [3] for a horizontal orientation of the magnetic field and by Hide [4] for a vertical orientation. The RTI of a stratified plasma through porous medium in the presence or absence of magnetic field has been studied by a number of researchers (Chhajlani and Vaghela, Vyas and Chhajlani, Sharma and Bhardwaj, Sharma and Sharma, Sharma and Trilok, Sharma and Sunil, Shikha and Bhatia, Opara, Sharma and Sunil, Sunil and Sharma, Sharma and Thakur and Sharma and Rajput) In this case (Darcy’s model), the usual viscous term μ. We will discuss the role of resistive term (Darcy’s term) besides the components of magnetic field in both x − and z − direction on growth rates of RTI of plasma layer

Formulation of the Problem

A Continuously Stratified Plasma

LD υ2 fz