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.

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.

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.

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.

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

Ion-acoustic solitons in a three-component plasma which consists of electrons and positive and negative ions have been investigated experimentally. When the concentration of negative ions is smaller than a certain value, positive or compressive solitons are observed. At the critical concentration, a broad pulse of small but finite amplitude propagates without changing its shape. When the concentration is larger than this value, negative or rarefactive solitons are excited. The velocity and the width of these solitons are measured and compared with predictions of the Korteweg-de Vries equation which takes the negative ions and the ion temperature into consideration. Head-on and overtaking collisions of the rarefactive solitons have been observed to show that the solitons are not affected by these collisions.

The process of excitation of the Alfvén wave is studied by means of the qualitative method of quantum mechanics.

External injection of magnetic helicity into a plasma may be possible through the introduction of appropriately polarized electromagnetic waves. A concept of steady-state current-drive is presented, based on the validity of conservation of helicity (appropriately defined for finite frequency processes). It is shown that such external injection of helicity can maintain a steady-state current by compensating the volt-seconds consumed through plasma resistivity. Such a mechanism, if experimentally successful, is particularly interesting at high densities because the efficiency of the process does not depend on plasma density, as opposed to other radio-frequency current-drive techniques.

This paper calculates, on a kinetic basis, the dispersion relation and field polarization for waves propagating linearly through a homogeneous magnetoplasma when thermal velocities are far less than the phase velocity. Approximations are brought in only as necessary and their physical significance explained. The result is an improved derivation of the Sen–Wyller generalization of the Appleton–Hartree formula for velocity-dependent collision frequency. Further generalization to several charged species is made, and the dispersion relation is also considered in terms of the angle between the ambient magnetic field and the group (rather than phase) propagation direction. Special case reduction to the Appleton-Hartree formula is confirmed. Complications concerning the limit of weak spatial dispersion are discussed. The analysis is restricted to weakly ionized plasmas in which the charge to neutral particle mass ratios are small, collisions are weak, and the wave vector is predominantly real.

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

Finite Larmor radius corrections have been considered in the effects of strong magnetic fields on stimulated Raman scattering. A nonlinear dispersion relation describing the various channels of decay has been derived from the Vlasov-Maxwell equations and frequencies and growth rates determined for the decay of incident laser light in the extraordinary mode into scattered extraordinary mode radiation and electron Bernstein waves. A relativistic one-and-a-half dimensional particle code has been used to simulate the scattering process and the results from the numerical experiments have been compared with those obtained analytically, the agreement being generally good. Growth rates of the Bernstein waves are substantial when sufficiently strong magnetic fields are present in hot plasmas. Under these conditions the kinetic analysis shows that, in contrast to the predictions of fluid theory, the scattered light emitted from densities well below the quarter-critical layer can have a frequency less than ½ω0 where ω0 is the laser frequency. In an unmagnetized plasma this occurs only when the plasma has a finite temperature.