The global stability of closed plasma configurations is related to the dynamical principle of least constraint and the spacetime and gauge symmetries of the flow fields. This leads to an entirely new concept of MHD stability which is more basic than stability predictions which rely on a linearized perturbation analysis. The predictions of the theory are compared to recent experimental results obtained in studies of the stability of plasma confinement geometries. The theory predicts the violent ‘instabilities’ of these systems which are currently attributed to other mechanisms. Several pertinent details of the theory which are widely misinterpreted are discussed and clarified.

A method for obtaining a class of generalized solutions of the system of quasilinear equations has been developed for the case where the wave vector k and the velocity v of the particles are oriented in a general direction with respect to the magnetostatic field. The method is demonstrated on the case of the quasilinear relaxation of an ion beam penetrating a cold magnetoplasma.

The consequences of the quasilinear equations are explored. Particular attention is paid to the differences between the one-dimensional and the two- and three-dimensional cases, and to the differences between the cases of discrete and continuous wave-number spectra. The possibilities of and problems associated with including damped waves are treated. The relation between conservation laws and the ‘resonance approximation’, in which the limit of zero growth rate for the unstable waves is taken at finite times, is clarified. Numerical solutions for the one-dimensional case with finite growth rate are presented.

A unified treatment is given of low-frequency wave propagation in a weakly ionized magnetoplasma from the fluid equations in which ion inertia is retained. An analysis is made of the instabilities which arise due to the influence of drift of the electrons relative to the ions for three cases: (a) Parallel drift, E∥B, (b) Hall drift, E∥B, and (c) Diamagnetic drift, ∇n⊥B. In all cases an ion acoustic instability is found while additionally, for (c), there is a drift instability for strong magnetic fields. The instability boundaries in parameter space are delineated. Furthermore, for a transversely bounded plasma, the roots ω(kz real) and kz(ω real) of the dispersion relations are discussed and related to experimental observables. The results are applied to an interpretation of wave propagation and instability on a cylindrical positive column for which all three types of drift are simultaneously present. The relation of this work to the inertialess theories of the current-convective and crossed-field instabilities is also discussed.

The influence of collisions on the universal instability in a fully ionized in- homogeneous plasma is investigated by means of a simplified Fokker-Planck kinetic equation. For the Fokker-Planck model yields results qualitatively similar to the Bhatnagar-Gross-Krook model, but the two models give different collisional effects in the case where b ≥ 1. Further it is shown that collisions in general enhance the temperature gradient instability in a plasma when b ≪ 1 and reduce it when b ≥ 1.

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized, Maxwellian electrons. The linear dispersion relation is derived for waves in a perpendicular shock such that the most important sources of instability are the E × B and ∇B electron drifts. For the case of cold ions, propagation perpendicular to the applied magnetic field, and the E × B drift alone, a numerical analysis of frequency vs. wave-number is presented. The effects of the ∇B drift are also considered, and it is shown that the maximum growth rate can be larger than the maximum growth rate for the zero magnetic field ion acoustic instabifity under comparable conditions.

This paper presents an analysis of the linear dispersion relation for electrostatic waves in a Vlasov plasma of unmagnetized, Maxwellian ions and magnetized, Maxwellian electrons. The electrons undergo E × B and ∇B drifts, and the electron β is small. For propagation in the perpendicular direction, maximum growth rates can be substantially larger than those of the zero magnetic field ion acoustic instability. For propagation outside a few degrees from the perpendicular the dispersion characteristics are essentially those of the ion acoustic instability.

Whitham's averaged Lagrangian method is used to yield a relativistically covariant formalism for wave packets in a weakly inhomogeneous (and time dependent) medium. Provided the physics of the medium can be based on a Lagrangian density, a procedure of expansion and averaging is available which gives separate Lagrangians for the dynamics of the background and of the waves. The Euler—Lagrange equations then give immediately the equations of motion for the background, including non-linear reaction of the waves, and the dispersion relation, equations for ray tracing, conservation of wave action and non-linear coupling coefficients, for the waves. Many of these results can be interpreted in an illuminating way by considering the corresponding expansion of the canonical four-dimensional stress tensor.

The loading resistance of a coil-plasma system operated near the lower hybrid resonance in hydrogen and argon has been measured. The results are consistent with the predictions of a theoretical model that includes finite plasma effects.

The motion of a test particle in a plasma whose average properties vary along one direction in space, but are independent of time, is considered. A method is given which enables this problem to be treated similarly to existing theories for a homogeneous plasma.

An isotropic Vlasov plasma occupies an infinite space, the upper half of which (y > 0) is a dielectric. A transverse disturbance is incident normally on the face of the dielectric. The waves that are excited in each half of the space are obtained. It is shown that this result can be extended to cover the refiexion problem of any normally incident disturbance in a plasma defined by a dispersion relation Di(w, k). A few examples are considered; in particular transverse waves in a plasma streaming normal to the boundary where Čerenkov instability can occur.

In this note we comment and extend the results of a previous analysis in which the non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma was considered. The evolution of a monochromatic wave of small, but finite amplitude is studied by expanding the dependent variables as well as the independent variable tin the form of asymptotic series; an ordering parameter e proportional to the initial amplitude of the electric field is introduced. The expansion of the independent variable in such a series allows us to eliminate secular terms from the part of the distribution function which does not depend on the free-streaming terms. This, in turn, allows us to determine corrections to the complex frequency a. Results of a previous note on non-linear Landau damping for an initially Maxwellian. distribution function are confirmed, but it is indicated that they apply to values of time up to a value τ1 rather than for all times. One can proceed to larger values of time in the manner of the multiple time-scale method. In particular it is found that the Landau damping is increased with respect to the linear value only initially during the first time scale.

Two expressions for the power radiated by a charged particle in a homogeneous magnetoplasma are derived, using a method similar to that of Kolomenskii, Eidman and Liemohn. The first expression is identical with that of Eidman. The reason for the correctness of Eidman's result for dispersive media, in spite of his complete neglect of dispersion in the derivation, is explained. Liemohn, by taking dispersion into account at only one stage of the derivation, obtains a result which disagrees with the present one, often by many orders of magnitude, as illustrated by computations.

The second expression is derived by several authors by different methods; it is more suitable for computations than the first one. The radiation bands and their limiting frequencies are discussed systematically.

In the case of a free-particle plasma with no self-consistent field and with collisions described by the LenardBernstein operator we give an exact solution of the temporal echo problem.