Bhimsen K. Shivamoggi

Resistive instabilities in plasma

Instabilities produced by finite-resistivity effects in a plasma are of great interest in connection with research in fusion devices, solar flares, and geomagnetic substorms. We elucidate here the physical mechanism of this instability, and in particular, identify the tendencies in the system towards the instability and the tendencies opposing it, if any. As an illustration, we consider the example of the so-called gravitational interchange mode wherein a plasma with a statically stable vertical density gradient is situated in a vertical gravitational field and a sheared horizontal magnetic field. The physical picture developed here may be useful in sorting out phenomena that appear when more subtle properties of the resistive modes in a plasma are considered.

Electromagnetic circularly-polarised modes in plasmas with electron-streaming along the applied magnetic field

The effect of the electron-streaming along the applied magnetic field on the electromagnetic circularly-polarised modes in a Vlasov plasma propagating along the applied magnetic field is studied. It is found that the growth or decay of the circularly-polarised modes is affected by the electron-streaming in the presence of the thermal effects, unlike the case with the thermal effects absent.

Rayleigh–Taylor instability of a plasma in a magnetic field: nonlinear theory

Kaira & Kathuria used the method of multiple scales to develop nonlinear analysis of Rayleigh–Taylor instability of a plasma in a magnetic field. Their calculations remain valid only for wavenumbers k away from the linear cut-off value k c , and break down for wavenumbers near k c . The purpose of this paper is to treat the latter case. The solution uses the method of strained parameters. The results show the instability persists even at k = k c , despite the cut-off predicted by the linear theory.

Stationary surface waves in magnetohydrodynamics

A uniformly-streaming, semi-infinite, incompressible, infinitely-conducting plasma subjected to a gravitational field is confined by a vacuum magnetic field aligned with the stream. The system is disturbed by introducing a source of external steady pressure acting on the interface between the plasma and the magnetic field. The resulting wave motion at the interface is studied by using the Fourier-transform method to determine the solution for the displacement of the interface.

The instability of the electromagnetic ordinary modes in counterstreaming and counterrotating plasmas

The instability of a linearly-polarised electromagnetic ordinary mode in counterrotating plasmas and propagating perpendicular to a uniform magnetic field caused by a counterstreaming of electrons along the latter is studied using a cold-plasma model. It is found that: (i) In the presence of either a streaming or a rotation or both, the ordinary-wave propagation is possible even for frequencies less than the plasma frequency; (ii) the Coriolis forces like the applied magnetic field stabilise the ordinary modes.

Instability of the electromagnetic ordinary mode in counterstreaming plasmas

The instability of a linearly-polarised electromagnetic ordinary mode in a plasma and propagating perpendicular to a uniform magnetic field caused by a counterstreaming of electrons along the latter is studied using a Vlasov plasma model. The results show that (i) for weak magnetic fields, the thermal effects stabilise the ordinary mode; (ii) for strong magnetic fields, the thermal effects destabilise the ordinary mode.

Kelvin-Helmholtz Instability of a Plasma in a Magnetic Field: Finite-Resistivity Effects

This paper makes a study of the finite-resistivity effects on the Kelvin-Helmoholtz instability of a plasma in a uniform magnetic field acting parallel to the direction of streaming. It is found that the presence of a finite resistivity makes possible new modes in the plasma. In particular, an otherwise stable mode is found to become overstable and grow exponentially in the presence of a finite resistivity.

Rayleigh instability of compressible plasma in a vertical magnetic field

A study of the Rayleigh instability of a compressible plasma of density stratified in horizontal planes and subjected to a vertical magnetic field is made. The special case of a plane interface separating two superposed uniform plasmas of different densities and speeds of sound is treated as an example to illustrate the compressibility effects on the hydromagnetic Rayleigh instability. It is found that the hydromagneticcompressibility effects act toward reducing the growth rate in a hydrodynamically unstable situation.

Stationary waves at the interface between a plasma stream and magnetic field

A uniformly-streaming compressible and infinitely-conducting plasma is confined by a magnetic field aligned with the stream. The system is disturbed by introducing magnetic dipoles into the field. A Fourier-transform method is used to determine the displacement of the interface between the streaming plasma and the magnetic field within the framework of a ‘shallow-water’ approximation. For the case of a subsonic plasma stream, stationary waves appear on the interface upstream of the dipoles, and it is found that (i) these stationary waves are possible only if the gravity effects on the plasma are weak enough; (ii) the effect of surface tension at the interface is to reduce the amplitude and increase the wavelength of these waves. For the case of a supersonic plasma stream, however, stationary waves at the interface are not possible.

Magnetohydrostatic behaviour of a plasma column in a decreasing external axial magnetic field

A study is made of the magnetohydrostatic behaviour of a plasma column in a decreasing external axial magnetic field by exploiting its analogy with the behaviour of a vortex tube embedded in a decelerating irrotational flow. The theory that considers only the initial and the final static states, ignoring the dynamics of the transition, predicts that the increased expansion of the plasma column in a decreasing external axial magnetic field becomes catastrophic and the column would burst at a critical value of the latter.