Electrostatic Rayleigh-Taylor Mode in Electron-Positron-Ion Quantum Plasma

Sajad Ali,Mushtaq Ahmad

doi:10.4236/jmp.2017.84043

Abstract

Electrostatic Rayleigh-Taylor (ERT) mode/instability is studied in a non-uni-form quantum magnetoplasma, whose constituents are electrons and positrons with fraction of ions. The effects of quantum corrections (i.e. Bohm potential and temperature degeneracy) and magnetic field on ERT mode are investigated with astrophysical plasma application. A generalized dispersion relation is deduced under the drift wave approximation. The presence of positron makes the dispersion relation a cubic equation. Different roots of both real and imaginary parts of the RT mode are examined by applying the Cardano’s method of solving the cubic equation. The dispersion relation and the growth rates of RT instability are examined both analytically and numerically with effects of electron and positron density, and magnetic field variations. It is shown that the magnetic field and positron density have stabilizing effectuates on ERT mode while due to electron density the mode becomes unstable. The present work is antici-pated to be of physical relevance in the studies of laboratory laser-produced plasmas as well as in the study of compact magnetized astrophysical objects like white dwarfs.

Highlights

Classical plasma is usually considered to have low densities and high temperature plasmas
In simplified form the real and growth rate of RT mode was discussed with effect of positron concentration
The growth rate of RT instability is examined in detail with essence of pair plasma density and magnetic field variation

Summary

Introduction

Classical plasma is usually considered to have low densities and high temperature plasmas. The interFermion distance being smaller than the thermal de-Broglie wavelength in such cases, along with temperature degeneracy (a consequence of Pauli Exclusion Principle) and tunneling effects, give rise to new collective phenomena and the role of quantum corrections begins [15] This changes the dynamics by preventing two particles to be in the same state via exchange interaction. The Rayleigh-Taylor (RT) instability is an important hydrodynamic effect that occurs at the plane interface between two fluids of different densities when a heavy fluid is accelerated into a lighter one This type of instability for a fluid in a gravitational field was first investigated in his famous paper in 1882 by Rayleigh [26] and later Taylor in 1950 had applied it to all accelerated fluids [27]. The dispersion relation and growth rate of instability are studied by using the Cardano’s method of solving the cubic equation

Basic Formulation and Governing Equations

Dispersion Relation and ERT Instability

Instability Analysis by Cardano’s Method

Result and Discussion

Summary and Conclusion