Rayleigh-Taylor Instability in Magnetized Plasma

G A Hoshoudy

doi:10.4236/wjm.2014.48027

Abstract

The Rayleigh-Taylor instability in stratified plasma has been investigated in the presence of combined effect of horizontal and vertical magnetic field. The linear growth rate has been derived for the case where plasma with exponential density distribution is confined between two rigid planes by solving the linear MHD equations into normal mode. Some special cases have been particularized to explain the roles the variables of the problem play; numerical solutions have been made and some stability diagrams are plotted and discussed. The results show that, the growth rate depends on the horizontal and vertical components of magnetic field and also depends on the parameter λ*=λLD (λ is constant and LD is the density-scale length). The maximum instability happens at λ*=-0.5 and to get more stability model we select λ* such that it is different than λ*=-0.5. The vertical magnetic field component have a greater effect than the horizontal magnetic field component in the case of large wavelength, while in the case of short wavelength, the horizontal magnetic field components have greater effect than the vertical magnetic field component.

Highlights

It is well-known that, plasma is a hot ionized gas consisting of approximately equal numbers of positively charged ions and negatively charged electrons
We have investigated the effect of magnetic field in both horizontal and vertical direction on the Rayleigh-Taylor instability of stratified incompressible plasmas layer
In the presence of both horizontal and vertical magnetic field, the square growth rate (Equation (32)) depends on the dimensionless thickness and depends on the parameter λ∗ = λ LD . (ii) The constant λ∗ = λ LD plays an important stabilizing role in the growth rate, where the maximum instability happens at λ∗ = −0.5 and to get more stability model, the values λ∗ must be different than λ∗ = −0.5 (i.e. −0.5 < λ∗ or λ∗ < −0.5 )

Summary

Introduction

It is well-known that, plasma is a hot ionized gas consisting of approximately equal numbers of positively charged ions and negatively charged electrons. The instability of stratified plasmas in the presence of horizontal magnetic field of incompressible plasmas with the effect of a transverse velocity shear was studied by Wu et al [16]. The effect horizontal magnetic field on RTI of a plasma layer in the presence of quantum mechanism was studied by Jintao et al [17]. The effects of vertical magnetic field in the presence of quantum mechanism on RTI inviscous and viscous plasma were studied by Hoshoudy [18] [19]. The analytically and numerically investigated stabilization of the linear growth of the RTI from density gradients, magnetic fields, and quantum effects, in an ideal incompressible magnetized plasma was studied by Wang et al [21].

Linearized Equations

A Continuously Stratified Plasma Layer

LD υ2 fz

Conclusions