The influence of the Hall effect on the spectrum of ideal magnetohydrodynamics (MHD) is investigated for axisymmetric perturbations of an infinitely extended circular cylindrical Z pinch with a diffuse current density. The pinch is bounded by an ideal conducting wall. The normal mode analysis exp i(kz—ωt) of the linearized perturbations gives a non-selfadjoint eigenvalue problem. The complex eigenvalues ω are considered which depend on the equilibrium function, the axial mode number k, and the dimensionless Hall effect parameter α which is inversely proportional to the square root of the mass density. A stabilizing influence of the Hall effect is shown by a sufficient stability criterion for equilibria without reversed magnetic fields which is more optimistic than the corresponding criterion of ideal MHD. If the Hall effect is retained in Ohm's law then there are, in contrast to ideal MHD, new simple points of accumulation of discrete eigenvalues when the radial mode number n of the eigenfunctions tends to infinity. The accumulation points are real, they are given by the extrema of the equilibrium function and they depend on the axial mode number k. The direction of accumulation is always along the real axis of the complex plane for equilibria without magnetic field reversal. From this it follows that accumulation points are no longer connected with stability criteria as is the case in ideal MHD. If the Hall effect parameter α tends to zero then the accumulation points coincide with the twofold k−independent accumulation point of ideal MHD. If the Hall effect is not neglected then the pure growth rates of ideal MHD are replaced by complex frequencies with smaller growth rates; and if α is greater than some critical value then the perturbation is stable. If the k0 mode is stable then all modes with k ≥ k0 are stable. For some continuous profiles of the current density the eigenvalue problem is solved numerically. The dependence of eigenvalues on the radial mode number and the dependence of the radial electron velocity on the Hall effect is shown. For equilibria with a reversal of the magnetic field, the unstable behaviour predicted by MHD theory cannot be excluded by consideration of the Hall effect.

The process of spontaneous excitation of electromagnetic (non-potential) and quasi-perpendicular (with respect to the external magnetic field) ion cyclotron waves by electron drift in a weakly ionized plasma is analysed. An infinite plasma placed in mutually parallel d.c. electric and magnetic fields is considered, and its dynamics is described by kinetic equations with BGK model collision integrals. The threshold electron drift necessary for the onset of the corresponding ion cyclotron instability is evaluated. It is shown that the instability sets in first for wavelengths much larger than the electron mean free path, so that the electron collisions, dominant in this range of wavelengths, play a facilitating rather than an impeding role in this process. The results are compared with those for the spontaneous excitation of electrostatic (potential) quasi-perpendicular ion cyclotron waves and, for the same set of plasma parameters, the threshold drift is found to be smaller for the electromagnetic waves.

We study the influence of static parallel electric fields on the characteristics of obliquely propagating electron Bernstein waves. Analysis of the equilibrium state defines the range of validity of the adopted model, viz. a collisionless, locally homogeneous medium described by the Vlasov and Poisson equations. An iterative method yields the modified dispersion relation whose numerical solution, for an idealized medium, suggests the relevance of the effects induced by static parallel electric fields in natural plasmas.

A formal method of multiple scales is used to study the effect of a harmonically varying applied uniform electric field, of magnitude much smaller than the Dreicer critical field Ec, on the runaway electrons in a Lorentz plasma.

Electrostatic plasma double layers are numerically simulated by means of a magnetized 2½-dimensional particle-in-cell method, periodic in one direction and bounded by reservoirs of Maxwellian plasma in the other. The investigation of planar double layers indicates that these one-dimensional potential structures are susceptible to periodic disruption by plasma instabilities. A slight increase in the double-layer thickness with an increase in its obliqueness to the magnetic field is observed. It is noted that weak magnetization results in the double-layer electric-field alignment of particles accelerated by these potential structures and that strong magnetization results in their magnetic-field alignment. Electron-beam-excited electrostatic electron cyclotron waves and ion-beam-driven electrostatic turbulence are present in the plasmas adjacent to the double layers. The numerical simulations of spatially periodic two-dimensional double layers also exhibit cyclical instability. A morphological invariance in two-dimensional double layers with respect to the degree of magnetization implies that the potential structures scale with Debye lengths rather than with gyroradii. Ion-beam-driven electrostatic turbulence and electron-beam-driven plasma waves are again detected. A simplified one-dimensional model of oblique plasma double layers, using water-bag velocity distribution functions, is presented in an appendix.

The linear stability of finite-β drift waves, near the plasmapause of the earth, is analysed for the case in which the magnetic field is non-uniform in two dimensions. The coupling of the drift wave to the oscillation of the magnetic field, due to non-zero β, is found to be destabilizing. The spatial structure of the unstable mode is found to be governed by the ‘curvature’ scale length of the equilibrium magnetic field.

The dynamic stabilization of electrostatic flute modes by an RF electric field is studied on the basis of the relatively simple model of a smooth cylinder with artificial gravity and an ambipolar field. It is found that the electrostatic flute modes can be effectively stabilized by the RF electric field together with the hot electron ring.

An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.

It is shown that drift dissipative instabilities can occur in the frequency regime Ωi ≪ ω ≪ Ωe. These instabilities are associated with the electron-acoustic and lower-hybrid waves.

The energy loss rate, Ė, of test ions injected with velocity V into a Maxwellian electron-ion plasma in the presence of an external magnetic field, is studied. Most of the integrals appearing in the expression for Ė are evaluated analytically and the remaining integrals are evaluated numerically for various values of the parameters η = Ωe / ωe, x = V/ve, r = Te/Ti, and the angle of injection θ. It is shown that the effect of the magnetic field is rather small except for η > 1, the temperature ratio is important for small x (x ≤ 0·2), and the injection angle is not important.

Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

A new theory is developed for the transport of energy across a strong magnetic field. The mechanism is micro-convection by sheared fluid elements, and it proves to be much more effective in heat transport than classical conduction. The equivalent thermal conductivity is calculated for the electron gas in a cylindrical plasma carrying an axial current. When the plasma pressure can be neglected, this conductivity is about 400 times greater than the classical value under certain typical conditions.

The motion of electrons and ions in a system which consists of a uniform rotating magnetic field and a steady uniform magnetic field which is aligned with the axis of rotation is re-examined. Stable orbits are identified and explicit expressions for these orbits are provided. The more realistic situation of motion in the non-uniform self-consistent fields appropriate to a cylindrical plasma equilibrium maintained by the rotating field is investigated. Again, stable orbits are found. The stability of orbits in this more complex situation is examined using an equivalent potential concept.

A new approach to the solution of the MHD equilibrium problem is outlined.