A theoretical and experimental investigation of the forced radial magnetoacoustic oscillations of a magnetized plasma column is presented in this paper. Forced magneto-acoustic oscillations of a magnetized argon afterglow plasma are generated continuously by passing an RF current through a solenoid wrapped around the discharge tube. The radial variation of the amplitude of the magnetic field disturbance [bz(r)] associated with these oscillations is measured at various times during the decay of the afterglow plasma. A theoretical description of these oscillations is developed in which the collision frequencies between the various plasma constituents are treated as free parameters. The values of these free parameters at any given instant during the decay of the plasma are determined by fitting computed bz{r) radial profiles to the measured ones. The electron temperature Te, and the ion-neutral cross section for momentum transfer QD are deduced from these collision frequencies. The reliability of this plasma diagnostic technique is demonstrated by its ability to yield values for Te and QD which compare favourably with the results obtained by other workers.

Monochromatic electrostatic waves of large amplitude were excited by the interaction of an electron beam with a bounded plasma. These waves were identified as resonant beam modes, which are amplified by multiple reflexion in a cavity. Nonlinear effects, such as the generation of harmonies and sidebands, were observed.

A small-signal analysis is carried out for a geometry consisting of two parallel conducting planes, with a magnetized plasma resting on the one plane, and a vacuum gap between the plasma and the other. Each of the solutions found to fit the boundary conditions consists of a superposition of two ‘transverse’ wave-functions with one and the same longitudinal propagation constant. Numerical solution of the dispersion relations yields the following. (i) A set of slow waves, in good agreement with the well-known quasi-static approximation. (ii) Fast waves, which approximate TM waves (Hz ≐ 0) propagating only at relatively high frequencies. (iii) Fast waves propagating in the same frequency range as the TM waves, but with negligible longitudinal electric field component Ez, thus resembling TE waves. (iv) A set of waves with a dispersion which resembles that obtained from coupling between fast forward and slow backward modes of propagation. (v) A single wave, not obtainable from the slow-wave approximation which resembles the helicon wave of the one-dimensional case, with the frequency approaching the cyclotron frequency at small wavelengths, provided the magnetic field is relatively strong (ωc < ωp), the spacing between the conducting planes not too narrow and the fill-factor not too small. For relatively weak magnetic fields (ωc < ωp), this wave appears as a surface wave with frequency approaching the lower hybrid frequency at small wavelengths.

The standard model for fast magnetic-field reconnexion (Petschek 1964) is qualitatively valid, despite numerous criticisms of its quantitative details. It contains four slow magnetohydrodynamic shock waves, which radiate from a central diffusion region. On the basis of Petschek's rough analysis, it is generally stated that, for large values of the magnetic Reynolds number Rm, reconnexion can occur at a rate no faster than a fraction π/(4 log Rm) of the Alfvén speed. Alternative models of the region outside that of diffusion have been put forward by Yeh & Axford (1970), whose general solutions Vasyliusnas (1975) proved invalid, and by Sonnerup (1970), whose model is mathematically useful, but of limited practical applicability. But their results suggest that reconnexion can occur at any rate whatsoever, with the diffusion-region dimensions responding accordingly. The present paper analyses the external region for Petschek's mechanism in greater detail than hitherto, with the object of deciding whether or not there is a maximum rate. The inclinations of the shock waves are calculated as a function of the fluid speed ve at large distances, which is taken as a measure of the reconnexion rate. It is found that, in agreement with Petschek's rough analysis, there is indeed an upper limit on the allowable rate of magnetic-field reconnexion. Its variation with Rm is calculated, and it is shown, for log10 Rm ≫1, to be approximately 20% of Petschek's value. Typical values are 0·10vAe for Rm = 10·2 and 0·02vAe for Rm = 106. (vAe is the Alfvén speed at large distances from the diffusion region.)

In the presence of a sufficiently strong magnetic field, the shielding of a test particle in a two-dimensional Vlasov plasma disappears. An intermediate regime is investigated, for both a stationary and a moving test particle, in which the plasma frequency ωp and the cyclotron frequency ωc are of the same order of magnitude. In the case of a stationary test particle, this intermediate regime is approximately in the range ½ ≤ a ≤ 2, where a = ωp/ωc. For a < ½, only partial shielding occurs, the potential retaining its vacuum logarithmic dependence. For a < 2, the potential approximates to the field-free case, and falls off exponentially. For a test particle moving at electron thermal speed, the typical bow wave and wake phenomenon, associated with an unmagnetized plasma, is no longer present. We find, instead, that the potential possesses upstream—downstream symmetry.

This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly-conducting, inviscid and compressible fluid. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible discontinuities in their values across the jet surface. For large wavelength disturbances, the jet behaves as though it were incompressible. Numerical evaluation of the roots of the dispersion relation for a number of different magnetic-field strengths and jet velocities, but for disturbances of finite ranges of wavenumbers, indicates that the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic fields are sufficiently small. The magnetic field is found to have a stabilizinginfluence when compressibility is not very large; for high compressibility, it may have even a destabilizing effect. The paper explains physically the roles of compressibility and the magnetic field in bringing about the stability of the jet. When the wavelengths of disturbances are small, the dispersion relation reduces to that for a two-dimensional jet and a vortex sheet; and the results for these cases are known from earlier studies.

A solution of the Mhd equations is presented, which describes field-line reconnexion by stagnant diffusion in the middle of a piecewise-uniform convective hydromagnetic flow. This composite solution demonstrates that the diffusion region adjusts its shape and size in accommodation to the incident merging fluids.

Steady magnetohydrodynamic combustion waves for a perfectly conducting, electrically neutral perfect gas in an aligned field are examined in phase space, taking into account the effects of viscosity and the thermal conduction as transport processes. Steady defiagration does not exist. Conditions to be satisfied by the initial and final states of detonation waves are derived, which may include an extension of the evolutionarity condition and the Taniuti—Resler relation to shock waves with finite width and energy release. A constraint on the shock wave is given in a conservation form. The exact solution of the final state is also given in such a way that it depends linearly on the energy supply, and may be classified completely by means of the parameters of the solution itself.

The resonant interaction of three waves in a uniform hot magnetized plasma is examined. The coupling coefficients are obtained in a symmetric form from the Vlasov-Maxwell equations.

The properties of the field and flow near a two-dimensional X-type magnetic neutral line are considered for an incompressible, inviscid, conducting fluid in the steady state. In this region the magnetic field is not ‘frozen’ into the plasma, and finite conductivity effects must be considered. In the region surrounding the X line, it has hitherto been assumed that the field lines to lowest order form systems of hyperbolae (the field components increasing linearly with distance from the null), while the fluid flow lines form systems of rectangular hyperbolae with fluid flow perpendicular to the field on the axes of symmetry of the field lines. The assumption of such a configuration was based upon a somewhat cursary consideration of the governing equations, a detailed examination never having been carried out. We present the results of such an examination, which reveal that the above configuration is not a valid solution of the MHD equations, and that, for the case studied, the field to lowest order must form a neutral sheet. The properties of the field and flow parallel to the plane of symmetry are also considered. It is found that non-uniform fields and flows may exist within the diffusion region, in support of recent convection-region studies. This work shows clearly the need for more detailed and careful consideration of such systems.

A nonlinear fluctuation—dissipation theorem is derived for a turbulent plasma. The method of dressed test particles is generalized to a nonlinearly stable plasma; the turbulent state is described by the Dupree—Weinstock formalism. A comparison with the Cook—Taylor theory is discussed.

The exact theory of a wave of fixed profile travelling with speed c/n (0 < n < 1) through a uniform, cold, collisionless, unmagnetized plasma is investigated for the case in which the electric field has a non-zero transverse component, which lies in a fixed direction. The governing equations, referred to the frame of reference in which there is no space dependence, are studied analytically in each limit n→0, n→1. and by computation for other values of n. It is shown that, for each value of n, there is, in general, just one periodic solution of an arbitrarily given amplitude; and a quantitative description of these periodic solutions is provided in graphical form. A simple ‘dispersion relation’ is obtained for large- amplitude waves.

We derive dispersion formulae for the transverse and longitudinal waves propagating through a Vlassov plasma, valid for relativistic as well as non-relativistic temperatures, and compare them with those of earlier workers. We discuss wave propagation under various limiting conditions of temperature.

Using the Dupree—Weinstock perturbed-orbit model of plasma turbulence, we obtain the diffusion equation describing the evolution of the average one-particle distribution function for whistler mode turbulence. The numerical result for electron pitch-angle diffusion within this scheme leads us to conclude that the effect of the resonance broadening due to perturbed orbits on the pitch-angle diffusion coefficient is not large compared with that evaluated by the unperturbed orbit in the whistler mode spectrum with a finite width. Based on the explicitly evaluated resonance function, the effects of this broadening on the growth rate for the whistler wave are also discussed.

‘On effects of neutral gas friction and ion viscosity on the Rayleigh-Taylor instability of a stratified plasma in the presence of Hall currents’

By P. K. Bhatia,

J. Plasma Phys. vol. 11, 1974, pp. 1–10

Bhatia (1974) investigated the effects of neutral gas friction and ion viscosity on the dynamical stability of a composite plasma of variable density in the presence of the effects of Hall currents.

Index to Volume13, 1975

It is regretted that the following was omitted:

Landatj, R. W. New, almost electrostatic, anisotropy instability, 377