The effects of neutral gas friction, on the Rayleigh–Taylor instability of an infinitely conducting plasma of variable density, with ion viscosity and Hall currents, are investigated. For an ambient horizontal magnetic field, it is shown that the solution is characterized by a variational principle. Making use of the existence of this, proper solutions are obtained for a semi-infinite plasma, in which the density is stratified exponentially along the vertical, confined between two planes. In the simultaneous presence of the effects of ion viscosity and Hall currents, it is found that the potentially unstable stratification is unstable for all wavenumber perturbations, irrespective of whether or not the effects of neutral gas friction are included. Further, it is found that the growth rate increases with both Hall currents and neutral gas friction, and decreases with ion viscosity. The influence of the Hall currents and the neutral gas friction, therefore, is destabilizing, while that of ion viscosity is stabilizing. In the absence of Hall currents, it is found that the viscous plasma is stable, even for a potentially unstable stratification, for perturbations confined to a cone about the magnetic field vector. The angle of the cone of stable propagation of an inviscid plasma,. however, decreases with both Hall currents and effects of neutral gas friction.

A generalization of the Appleton–Hartree equation is made to include the effects of energy-dependent electron-neutron collisions, Coulomb encounters and spatial dispersion. The frequency of electromagnetic waves propagating in a magneto-plasma is sufficiently high that the ion motion may be neglected compared with the electron motion. The present analysis extends Dougherty (1963, 1964) to include the simultaneous effect on wave propagation of Coulomb forces, spatial dispersion and energy-dependent electron-neutral collisions, where one or more of these effects can have a significant influence on circularly polarized waves propagating at frequencies near electron cyclotron resonance. The electrical conductivity tensor is expressible in terms of appropriate velocity moments of the electron distribution function. The electron velocity distribution function is determined by expanding the inverse of the differential operator of the linearized kinetic equation in a small parameter ε2', where in one case ε2 is the ratio of Coulomb collision frequency to signal frequency, and in the second case ε2 is the ratio of electron-neutral collision frequency to signal frequency. For wave propagation along the magnetic field, the dispersion relations for right-hand and left-hand circularly polarized waves, and also the dispersion relation for longitudinal waves, are solved numerically, and graphs are presented to show the effects of collisionless damping, velocity dependent electron-neutral collisions and Coulomb collisions.

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

Within the range in which both electric field parameters are free, ionizing shock waves have a unique structure for each pair of chosen parameter values. In a relatively small shock speed range, however, conditions may exist for which at least one intermediate equilibrium region is imbedded within the overall transition. Non-unique structures consisting of different transitions between the same upstream and downstream equilibrium states may then occur. Steady trans-Alfvénic magnetohydrodynamic transitions (which are unacceptable in the pre-ionized case) may occur as part of an ionizing shock structure, because neigh bouring steady solutions always exist. This is due to the existence of skew ionizing shocks which are able to absorb rotational disturbances.

In this paper, a method developed by Whitham for obtaining equations governing the slow variation of finite-amplitude wave trains, is slightly modified. The relevant equations describing wave-wave interaction, and self-action are derived. The stability of a finite-amplitude wave train is treated in two different ways. The possibility of having a ‘solitary modulation’ on a finite-amplitude wave train is pointed out.

Previous calculations of β = 1 cusp losses are extended to the case where there exists a third ‘adiabatic’ invariant of the particle motion, related to the magnetic moment, and additional to the particle energy and angular momentum. Simple analytic results are obtained for the particle and energy loss rate from a Maxwellian plasma in both plane and axisymmetric geometry, electric fields being assumed zero everywhere. The results are valid for a plasma radius large relative to the ion gyro-radius, in which case the adiabaticity in the sense used reduces the loss rate by a factor ⅔λ⅔ to give an overall scaling as λ–⅔ with external mirror ratio λ. The absolute value is about a factor two less than the previously accepted result (for λ = 1 only) for an axisymmetric cusp. cusp. The enhanced scaling with A arises from the absence of a certain class of particles in the sheath, which must be everywhere adiabatic; its applicability to a simple theta pinch is queried, however. The end loss rate of angular momentum is also obtained, and is non-zero at a point cusp. This is shown to lead to rapid rotational instability in a collisionless theta pinch.

We present optical spectroscopic and magnetic probe observations of a laboratory discharge device, in which magnetic field line reconnexion occurs at an x−type neutral point. Time-resolved spectral-line profiles of the ionized argon line A II λ4348 are presented. These allow the determination of Doppler shifts and broadenings near the neutral point. Plasma heating occurs at the neutral point and downstream from it. Plasma is ejected from the downstream sides of the neutral point region at the local Alfvén speed at all times. This is equal to about one-tenth the upstream Alfvén speed at the one time it is known. The downstream magnetic Mach number or ‘local reconnexion rate’ is found to be nearly independent of the plasma conductivity and time. The rate of transfer of magnetic flux from the upstream to downstream regions is strongly dependent on conductivity and time.

A study is made of a parametric instability in a magnetized plasma in which an electromagnetic pump wave of either right- or left-hand circular polarization decays into a Langmuir wave and another circularly polarized wave, all with wave vectors colinear with the external magnetic field. The analysis is based on a multiple-time-scale perturbation expansion of the fluid equations, incorporating the effects of temperature, collisions, and the spatial variation of the pump wave. The threshold values of the pump field intensity required for instability and the growth rates above threshold are calculated.

The formalism for the calculation of the absorption of radiation by a hydrogen plasma at common laboratory conditions is summarized. The hydrogen plasma absorption coefficient for laser radiation has been computed for a wide range of electron densities (1015- 1018 cm-3) and temperatures (10 000–40 000 °K). The results of this computation are presented in a graphical form that permits a determination of the absorption coefficient for the following laser wavelengths: 0.176, 0.325, 0.337, 0.442, 0.488, 0.51, 0.633, 0.694, 1.06, 1.15, 2.36, 3.39, 5.40 and 10.6 Μm. The application of these results and laser radiation absorption measurements to plasma diagnostics is discussed briefly.

The reciprocity theorem for monopole antennas, a gridded parallel plate, parallel-plane grids and a plane plate, which radiate and receive an electron plasma wave in an unbounded plasma, is introduced theoretically, based on the electron fluid model. The theorem holds experimentally if the d.c. bias potential of antennas is lower than about the floating potential. The measured reception pattern of an antenna is equal to its radiation pattern. The wave amplitude and the impedance between the antenna and the plasma are measured experimentally.

A model for nonlinear Landau stabilization of a linear instability is treated analytically. The model may apply to any dissipative system described by: (i) a linear dissipation function γ(k), of one degree of freedom k, which presents a limited unstable domain δK and a damped region for lower values of k, and (ii) a transition probability for the nonlinear Landau damping (nonlinear wave–particle interaction) proportional to k – K'. For a sharply pointed γ(k), the model leads to a kinetic regime presenting periodic relaxation oscillations of large and constant amplitude. Starting from weak turbulence, the system organizes itself into a periodic regime, which may be of interest in connexion with research in morphogenesis. For a smoothed γ(k), the relaxation oscillations damp, slowing down towards a turbulent energy level.

Equilibrium and non-equilibrium properties of the three-dimensional guiding-centre plasma (in which the particles move with the guiding-centre drift across constant magnetic field lines, and according to Newton's laws along the field lines) are investigated. In equilibrium, the transverse spatial diffusion and conductivity coefficients are calculated, and are shown to be related via a generalized Einstein relation. The diffusion coefficient consists of a Bohm-like 1/B contribution which tends to zero as the plasma volume tends to infinity, as well as a classical 1/B2 contribution, which is independent of the size of the system. The Gibbs ensemble is constructed, and it is seen that thermal equilibrium results for the pair correlation, fluctuation spectra etc. are exactly the same as for the three-dimensional unmagnetized plasma. In the non-equilibrium case the appropriate Liouville equation and BBGKY hierarchy are considered. It is shown that to first order there is no tendency for the system (assumed spatially uniform) to relax towards thermal equilibrium.