A theoretical analysis of the anomalous skin effect in cylindrical plasma is carried out for a model where the radial electron-density distribution is of Gaussian form. It is shown that there are major qualitative differences between the results for cylindrical and those for plane geometry. Calculations of the electromagnetic field distribution over the plasma cross-section show that the present theory is in satisfactory agreement with experiment.

The dispersion relation for a collisionless moving electron plasma when the directions of motion and wave propagation are normal to the magnetic field is analyzed. It is shown that the ordinary wave remains unaffected, but the extraordinary wave shows a different behaviour, especially at small phase velocities. It has different cut-off frequencies, propagates for all frequencies from zero to infinity, changes the sense of polarization accompanied by anomalous dispersion and does not show any resonance.

Propagation of high-frequency electromagnetic waves in a weakly inhomogeneous magnetized plasma is investigated. We suppose the density gradient to be perpendicular to an external magnetic field, and the waves to be incident obliquely upon the plasma from vacuum. We find that the transmission coefficient of the ordinary wave through the plasma resonance is approximately equal to one in a fairly wide range of angles of incidence γ near the value γ0 = arcsin (Ωc/)(Ωo + Ω) ½. The transmitted ordinary wave is fully transformed into an extraordinary wave at higher densities. Then it propagates back to the region of a smaller density, and is fully transformed into the Bernstein modes in the vicinity of the hybrid resonance. Complications connected with the evanescent layer, which arise when the high-frequency energy is transmitted into the plasma in the form of the extraordinary wave, can thus be removed by using the ordinary wave with the angle of incidence chosen appropriately.

The influence of a steady axial magnetic field on the anomalous penetration of low frequency electromagnetic fields into a cylindrical plasma column is investigated by considering a plasma with a Gaussian electron density distribution. For this model, a complete solution is obtained for Boltzmann's equation coupled to Maxwell's equations, and the fields calculated exactly. The results show dramatic changes of the internal fields for small changes of the applied magnetic field when the average Lamour radius of the electrons is of the order of the plasma radius.

Ionizing shock waves may involve a non-zero transverse electric field in the non-conducting upstream region. The possibility of this field means that two extra parameters are involved in ionizing shock transitions, in addition to the usual three MHD shock parameters. The present paper investigates the question of existence or absence of structurally determined relationships between the five parameters. The results show that ionizing shock waves can be categorized into three types, depending on the nature of their downstream singular points in a three-dimensional phase space. Thus, if shock Mach number, Alfven number, and upstream magnetic field angle are given, type 2 shooks are characterized by a unique transverse electric field in both magnitude and orientation, type 3 shocks allow one degree of freedom to the electric field but specify a relationship between the magnitude and orientation, and in type 4 shocks both electric field parameters are free to range between certain limits. These structural conditions correspond exactly to previously investigated evolutionarity conditions based on wave perturbations, the interpretation of which has been incomplete due to a lack of knowledge of the possibility of skew shocks. In light of the author's subsequent work on skew shocks and the new general three-dimensional results, a complete map of the behaviour of ionizing shock waves is now possible, and the present article attempts to construct its essential features. Earlier works are reviewed and clarified in reference to this general framework.

The electromagnetic streaming instability yields substantial growth for propagation at large angles to the beam. Transverse Landau damping suppression of the mode is calculated for a variety of beam parameters. The saturated stage of the instability (bunching in position space) can produce large electric fields oscillating at the plasma frequency in the vicinity of the beam. These fields can cause further ionization, and define the final channel radius. Comparison with experiment is satisfactory.

The structure and jump relations across a one-dimensional ionizing magnetohydrodynamic detonation wave with transverse electromagnetic fields are studied. It is shown that the downstream point in a three-dimensional phase space, constructed from the gas velocity, magnetic field and burned fraction of gas, is of a singular nature and leads to a unique solution. In the zero viscosity, infinite transitional electrical conductivity limit, the ‘fast wave’ degenerates into a pre-compression ionizing shock followed by a perfectly-conducting deflagration zone, and the ‘slow wave’ degenerates into an ordinary gas dynamic pre-compression shock followed by a deflagration zone in which the transition to perfect conductivity occurs. In both cases, a relationship is derived connecting the electric field (which cannot be arbitrarily imposed) and both the upstream variables and parameters describing the ionization transition point. This relationship must be appended to the Rankine–Hugoniot jump relations and a Chapman-Jouguet condition (or its equivalent) to provide a unique relationship between the assumed unknown shock-speed and the downstream state as a function of the assumed known upstream state.

The ionization temperature is found to affect the jump and determines the electric field developed upstream. It is found that the Hugoniot consists of two branches: a ‘normal’ one which retains the character of an ordinary detonation Hugoniot, and an ‘anomalous’ one which does not. Although both branches represent detonations endowed with a transition structure, it is suggested that ‘anomalous’ detonations are either unstable or non-evolutionary. The evolution of the topology of the Hugoniot, as a function of the upstream magnetic field and ionizing temperature, is studied and correlated with Chapman-Jouguet propagations. Results are presented for the Chapman-Jouguet jump values and detonation speeds, as functions of dimensionless parameters that represent the upstream magnetic and electric field. Relationships between this upstream electric field and ionization temperature is derived and found to differ according as ionization precedes or follows ignition.

A theory of the amplitude modulation of plasma waves is developed by applying the Karpman-Krushkal theory of quasi-monochromatic wave propagation analysis of the nonlinear wave-particle resonant effect leads to the modified nonlinear Schrüdinger equation with a non-local nonlinear term, which has been independently derived by Ichikawa & Taniuti on the basis of a reductive perturbation approach. The effect of the non-local nonlinear term is described explicity by investigating the modulation instability of an ion plasma wave.

The propagation of slow surface waves in an inhomogeneous plasma is investigated. Both ‘axial’ and ‘radial’ density gradients n(r) and those of the static magnetic field B0 are taken into account. It is demonstrated that the axial in- homogeneities n(z) and B0(z) result in the dependence of the natural surface- wave frequencies on the ‘axial’ co-ordinate z. The dependence ωSW(z) affects the phase velocity νph = ωswsol;K where K iS the propagation constant. So, in the case of surface-wave excitation by a charged particle beam in an ‘axially’ inhomogeneous plasma, the Cherenkov resonance ωSW= KV0 between the beam and the surface waves breaks, thereby reducing the growth rate of unstable oscillations. This phenomenon might be considered as the stabilization of the beam by the ‘axial’ density gradient. It is also shown that the ‘radial’ gradients n0(r) and B0(r) essentially affect the surface-wave natural frequencies as well. Dispersion equations, expressions for the natural frequencies and growth rates are obtaind, taking into account the gradients of the density and the static magnetic field.

We describe a family of exact nonlinear solutions of Vlasov's equations; the linear counterpart being circularly waves. An exact solution for a sub-group of initial conditions is given. The plasmas treated are multi-species, infinite and homogeneous, embedded in a uniform magnetic field.

A numerical method for simulating the temporal evolution of an ionizing MHD detonation, is presented, together with flow profiles for various combinations of imposed magnetic field and ionization temperature in the limit of large downstream conductivity. The propagation speeds asymptotically approach the values predicted by the jump relations and the MHD Chapman–Jouguet condition. The downstream flow approaches a self-similar solution. The wave evolution is discussed for situations where the Chapman–Jouguet and jump relations admit either no solution or multiple solutions.

The field of a small (Hertzian) dipole excited on a fixed frequency in warm electron plasma streaming atsuperthermal velocity is approximated electrostatically. The plasma is described by a hydrodynamic model, without collisions or magnetic field. The mutual impedance for two such dipoles is studied, to determine the geometrical structure of the field, and in particular to locate the Cherenkov cone of slow plasma waves excited by the source.

Equilibria of magnetoplasma with planar symmetry are presneted. Among the equilibria illustrated are configurations of plasmas confined inside a cylindrical wall and plasma in a double-inverse-pinch device.

The inhomogeneous sheath that surrounds a probe immersed in a weakly collisional magnetized plasma is investigated from the microscopic point of view, in the case when the probe is cylindrical and parallel to the magnetic field. Arbitrary surface effects of the probe (such as absorption, reflexion and emission of particles) are taken into account. The sheath is described with a model based on the solution of a boundary-value problem for the self-consistent Boltzmann—Maxwell—Poisson equation. The spatial variation of the magnetic field is discussed. Typical results of numerical computations concerning the structure of the sheath and the currents collected by the probe are given and discussed.

Theoretical development and numerical simulation of the two-dimensional electrostatic guiding-centre plasma with positive total interaction energy are presented. Equilibrium statistical mechanics predicts that no spatially homogeneous thermal equilibrium state exists for this system. This non-existence is associated with the phenomenon of ‘negative temperatures’. Quasi-stable, spatially inhomogeneous states are shown to form, and are characterized by macroscopic spatially-separated vortex structures.

The two-pole and resonance distribution approximations to the plasma dispersion function are discussed and compared.

Previously derived shock solutions for a perfectly conducting perfect gas are used to compute shock polars for the one-dimensional unsteady and two- dimensional non-aligned shock representations. A new special-case shock solution, having a downstream particle velocity relative to the shock equal to upstream Alfvén velocity, is obtained, in addition to exhaustive analytical classification schemes for the shock polars. Eight classes of one-dimensional polars and twelve classes of two-dimensional polars are identified.

Electromagnetic waves propagating perpendicular to an external magnetic field in a non-uniform anisotropic plasma can become unstable due to the excitation of either resonant ion instability or resonant electron instability. The former instability can exist in the absence of both the temperture anisotropy and the temperature gradients, whereas for the excitation of resonant electron instability the presence of at least one of them is necessary. An off-resonance drift cyclotron instability can also get excited if the temperature gradients are much stronger than the magnetic field gradients.

We have measured the level of density fluctuations 〈δne2(K)〉 for ‖K‖ ∼ 1/λD as a function of the angle between k and the current within a collisionless shock. The cut-off angle is in good agreement with that predicted for current-driven ion wave turbulence and one-dimensional heating of the ions. This agreement provides further evidence that ion-wave instability is responsible for the observed turbulence within the shock.

The multiple water-bag model can be used to describe a uniform warm plasma as accurately as one wishes. Moreover, it makes boundary-value problems in such a plasma tractable. As a special case, the problems of the influence of a point charge on a spherical grid and of the mutual influence between two spherical grids are solved. From these results, the self-impedance of a double-sphere dipole antenna is deduced. If the spheres are widely separated it exhibits a resonance at the plasma frequency, whereas if the spheres are close there is an anti-resonance at this frequency. The mutual impedance of a quadrupole probe comprising two double-sphere antennae is also studied, and is found, usually, to be not very sensitive to the finite radius of the spheres. For determining the electron temperature of the plasma, this last device seems better than a double-sphere antenna alone.