The dispersion relation of linear waves in a non-relativistic, collisionless and homogeneous magnetized plasma is solved by numerical methods. Both electrostatic and electromagnetic waves with frequencies from below the ion gyrofrequency to above the electron gyrofrequency are studied for all angles of propagation. Modes occurring in a cold plasma as well as waves dependent on thermal effects are included. Dispersion surfaces, that is plots of frequency versus wave vector components, are presented for some plasma models. This presentation shows all interesting waves clearly and reveals how different modes are related. The dispersion surfaces can be used as an aid, for example, when comparing wave observations and theory, and they may also help to avoid confusing nomenclature.

The problem of the wave fields excited by a gap source at the edge of an inhomogeneous, magnetized plasma with a pair of lower-hybrid resonance layers present and bounded by conducting walls is solved. The approach used is that of a solution as a sum of multiply-reflected extraordinary mode and ion-thermal resonance cones as an alternative to the guided-wave mode approach. This is achieved by dividing up the plasma into cross-sections where WKB solutions are valid, and into lower-hybrid resonance layers where asymptotic methods are employed and connexion coefficients between each region are obtained. A diagrammatic scheme for writing the solution is introduced which can in principle be used to write down the solution for any problem of this general type once the connexion coefficients across a resonance layer have been determined via asymptotic analysis. This allows a determination in great detail of the structure and properties of the resonance cones in our model and the way they transform across the back-to-back hybrid layers. Evanescent resonance cones are found to exist in the high-density region between the hybrid resonance layers and tunnel through to the other side, maintaining their general structure if the layer is relatively thin.

Global conservation constraints satisfied by the Vlasov-Maxwell equations are used to obtain a nonlinear bound on the unstable electrostatic fluctuation energy that can develop for non-relativistic non-neutral electron flow in a planar diode with an axial applied magnetic field. It is shown that the Heimholte free energy is a minimum for the thermal equilibrium reference state. The nonlinear bound on unstable fluctuation energy that can develop for general initial conditions is calculated for the case of flute perturbations with no axial dependence. To determine the lowest upper bound on fluctuation energy consistent with conservation constraints, the density, temperature and drift velocity of the reference state are chosen to minimize the nonlinear bound. The analysis assumes that the net flux of particles, momentum, and energy, vanish identically at the cathode and at the anode.

The Zakharov-Kuznetsov equation describing Korteweg–de Vries waves and solitons in a strong, uniform magnetic field is rederived taking space stretching to be isotropic. This equation is then used to investigate nonlinear waves and solitons for long-wave instabilities. A solid angle of instability develops around the plane perpendicular to the magnetic field. For weakly nonlinear waves this angle is very narrow: widening as the amplitude of the nonlinear wave is increased. The soliton wave is unstable for all directions other than parallel to the field. Previous results of other authors, limited to solitons and perpendicular propagation are recovered. Calculations are illustrated by polar diagrams for the perturbations. Some broader implications are pointed out.

A statistical procedure is applied for constructing an entropy functional associated with a collective Vlasov equilibrium described by a given coarse-grained current and charge distribution. The functional is not at a maximum if the magnetic or electrostatic equilibrium is not unique. This property connects the principle of maximum entropy with bifurcation theory and marginal stability analysis.

This paper deals with the evolution of a small initial perturbation superimposed on a plane whistler wave due to self-modulation in the case of propagation along the external magnetic field.

Nonlinear evolution of a large-amplitude relaxation oscillation in an unstable plasma diode is investigated by a computer simulation using a particle model. The oscillation is closely related to double-layer dynamics accompanied by a negative potential dip on the low-potential tail. A vortex is formed in the electron velocity phase space during the potential evolution, which causes a topological rearrangement of the phase space in the high-potential plasma.

The solution of the Fokker-Planck equation for the distribution function of heavy ions in a background of electrons is studied. It is found that quite broad physical conditions on the distribution function (such as the positive requirement and the existence of all velocity moments) are sufficient to eliminate any ambiguity in the time-independent steady-state solutions and to determine a discrete spectrum of the time-dependent Fokker–Planck operator. The more physical case of a Maxwell-Boltzman electron distribution function is treated using the small mass ratio expansion. First-order mass ratio corrections are calculated. A plasma heating application-is suggested.

The stability of collisionless reconnecting modes which are driven by a current density gradient is analysed. We consider an inhomogeneous plasma embedded in a sheared magnetic field with finite density and temperature gradients and employ a kinetic description for the inner boundary layer. Appropriate approximations reduce the resulting integro-differential system of equations to a pair of coupled second-order differential equations. In contrast to previous results, the differential operators acting on the field components do not exhibit definite symmetry. Matching is performed numerically to the outer ideal MHD region without regard to symmetry. The asymmetric part of the solution affects the mode frequency and growth rate to the extent that the radial amplitude of the perturbed magnetic field has a significant variation within the singular layer. Stability properties with respect to relevant parameters are investigated.

This paper gives an extensive characterization of the range of validity of the Compton and Raman approximations to the exact free electron laser dispersion relation for a cold, relativistic electron beam propagating through a constantamplitude helical wiggler magnetic field. The electron beam is treated as infinite in transverse extent. Specific properties of the exact and approximate dispersion relations are investigated analytically and numerically. In particular, a detailed numerical analysis is carried out to determine the range of validity of the Compton approximation.

It is shown that the flattening of current sheets which has been observed near neutral X-points in numerical simulations of ideal MHD flow in two dimensions can be obtained from an asymptotic expansion of the dynamical equations. This asymptotic expansion suggests that exponential self-similar flattening proceeds forever and that there is no finite time singularity for ideal two-dimensional MHD flows. The equation for the spatial structure of the self-similar solution is reduced, via a hodograph transformation, to a nonlinear wave equation involving interactions with distant parts of the fluid and therefore non-universal features.

A new fluid-theory derivation of the time-dependent ponderomotive force is presented in the oscillation-centre representation. We show that the velocity renormalization adopted in this paper is equivalent to the oscillation-centre representation and is the velocity required so that the mean density obeys the continuity equation exactly. We also show that previous fluid theory results may be recovered by adopting a different velocity renormalization and by redefining the ponderomotive force.

The motion of a plasmoid (plasma-field entity) across an inhomogeneous magnetic field distribution of which the direction and strength change along the penetration trajectory has been studied. The bulk velocity decreases when the plasma element penetrates into a region of increasing magnetic field. The critical magnetic field intensity where a plasmoid is stopped or deflected is found to be the same critical field as that which has been observed in laboratory experiments for a non-rotating B-field distribution. The polarization electric field induced inside a moving plasma element has been determined for both low-β and high-β plasmoids. The momentum density vector of a plasmoid is deflected in the – B × ∇B and – B × (B. ∇)B directions as it penetrates into an inhomogeneous B-field distribution. This kinetic model has been applied to the impulsive penetration of solar wind plasma irregularities impinging on the earth's geomagnetic field with an excess momentum density. As a consequence of impulsive penetration, a plasma boundary layer is formed where the intruding plasmoids are deflected eastward. Magnetospheric plasma is dragged in the direction parallel to the flanks of the average magnetopause surface. Diamagnetic effects of these impulsively penetrating plasmoids into the magnetosphere are also briefly discussed.

We analyse high-frequency electrostatic solitary surface waves that propagate along a plasma cylinder in the presence of a constant axial magnetic field. The width of such a solitary wave, which is found to be inversely proportional to its amplitude, is expressed as a function of the magnitude of the external magnetic field.

The effect of resistive dissipation on the propagation of an MHD disturbance in a non-uniform plasma is examined. The present analysis, based on a boundarylayer technique, shows the existence of resistive normal modes with complex eigenfrequencies. The real part of the eigenfrequency is associated with an oscillatory behaviour and defines the location in space of the layer where resistivity is important. The dissipation mechanism is responsible for the damping of the wave, in contrast with previous works in which the ideal MHD theory was used.

The unstable domain in the (k, Ø) plane for oblique modulation of ion-acoustic waves, in a two-electron-temperature plasma, is investigated using the KBM perturbation technique. It is shown that, in a collisionless plasma, the maximum growth rate for the modulational instability, for large carrier-wave amplitudes (a0 ≳ 0·1), exceeds the electron Landau damping rate for sufficiently oblique modulation.

We investigate the low-frequency azimuthal oscillations on a non-neutral magnetized electron column of very low density. A perturbation analysis of the slow mode of the rigid rotator equilibrium is developed to illustrate the nature of large-amplitude fundamental-mode oscillations. The results of this theoretical analysis show two important characteristics: firstly, as the perturbation amplitude is increased the wave form ceases to be purely sinusoidal and shows period doubling. Secondly, above a certain threshold, all harmonics of the wave grow and the wave breaks. The results of the former are compared with a simple electron beam experiment and are found to be in good qualitative agreement.

The instability of low-frequency waves in a cold plasma mixed with hot electrons is investigated using the first-order CGL equations for electrons. It is assumed that in an equilibrium state the electrons consist of two components, cold electrons and hot electrons with bi-Maxwellians. It is shown that low-frequency waves with right-hand polarization can be generated by the hot electron temperature anisotropy and the existence of cold electrons.

The plasma expansion into the wake of a large rectangular plate immersed in a single-ion, collisionless, streaming plasma has been investigated in the laboratory. Several characteristics of the process involved in ‘plasma expansion into vacuum’ that have been predicted theoretically were observed, including the creation and motion of a rarefaction wave disturbance; the creation and motion of an expansion front; and the acceleration of ions into the wake at speeds above the ion-acoustic speed. The expansion was limited to early times; i.e. a few ion plasma periods, by the combination of plasma drift speed and vacuum chamber size. This prevented detailed comparison with self-similar theory, but results are in good agreement with numerical simulations and other laboratory experiments for the early time expansion. The conclusion is that the plasma expansion process is the dominant wake filling mechanism in the near wake of a body, whose potential is approximately the plasma space potential.

The propagation of small-amplitude hydromagnetic waves in a cold plasma mixed with hot ions is investigated using the first-order CGL equations for ions. It is assumed that in an equilibrium state the ions consist of two components, cold ions and hot ions with bi-Maxwellians. Propagation properties of hydro-magnetic waves are analysed by use of phase speed and refractive index surfaces, polarization and the amplitude ratio between perturbed density and magnetic field. It is shown that the existence of cold ions affects the properties of hydro-magnetic waves through finite frequency corrections only when the temperature anisotropy exists; and that the critical angle, at which the polarization sense changes from right-handed to left-handed as well as from left-handed to right-handed, can exist for intermediate and slow waves.