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.

Small oscillations of a dense, equilibrium plasma in a strong current channel aro considered in the approximation of two-fluid hydrodynamics of ideal charged liquids. It is shown that chute-type radial oscillations are the ones most likely to affect the system's stability. The instability induced by spontaneous excitation of these oscillations results in a spallation of the diffuse equilibrium state into separate densely compressed current channels. The present investigation of the oscillations near the stability threshold enables one to formulate the stability criterion for the pinch system. It is shown that Bennett-type equilibrium distributions rapidly become unstable with a rise in the current, while the equilibrium distributions for the plasma compressed up to the electron degeneration, are stable, by a considerable margin. The theoretical conclusions on the pinch decay into separate current channels are in agreement with the available experimental data.

An analytic study is made of the electrostatic mode structures which exist between the upper-hybrid cut-off and the plasma resonance in a plasma in which the zero-order density gradient points along the magnetic field. In general the solutions consist of long-wavelength cold modes which are converted to short-wavelength Bohm-Gross modes near plasma resonance. However, there exist certain discrete angles of propagation at which finite solutions exist that can be described solely in terms of cold plasma theory. The relevance of these processes to resonant absorption experiments in the auroral ionosphere is considered. A brief study is made of the changes produced by a finite angle between the density gradient and the magnetic field. The possibility of finding analogous low-frequency structures is also investigated.

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.

The propagation of electromagnetic waves in a plasma-filled cylindrical waveguide in the presence of a constant external magnetic field is investigated using warm plasma theory. It is found that the waves cannot be separated into transverse magnetic and transverse electric modes; only hybrid modes are propagated. Dispersion relations are derived for zero, finite and infinite magnetic fields. Frequency shifts for the wave propagation in the case of a small magnetic field are calculated.

The theme of the paper is the relation between the so-called Z mode and the upper-hybrid wave in a magnetized plasma. First, certain problems as to reflexion and transmission of upper-hybrid waves at quasi cut-off (that is, cut-off predicted within electrostatic approximation) are stated and solved by singular perturbation technique. Then the theory is extended to a problem concerning generation and trapping of upper-hybrid waves in magnetic field aligned electron density irregularities. First a single density depression is considered, and then the formalism is further extended to a system of many parallel density depressions. The study was motivated by problems in the theory of artificial small-scale ionospheric irregularities occurring in radio wave experiments.

We consider, in the framework of dissipative MHD, the general problem of instability of magnetic neutral sheets in the presence of velocity shear. Both resistivity and viscosity are included in the treatment. We show that velocity shear and/or viscosity introduce different orderings with respect to resistive tearing modes and that the classical tearing modes represent a singular case. Possible orderings for growth rates are discussed and a specific example containing the effect of velocity shear is treated in detail.

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.

Parallel whistler-mode propagation in a hot anisotropic plasma at frequencies near the electron gyrofrequency is considered by using analytical methods and a simple graphical technique, without any special restrictions on the value of the imaginary part of the plasma dispersion function argument. An exact criterion for the possibility of whistler-mode propagation in the vicinity of the electron gyrofrequency is derived. In particular it is pointed out that whistlers in this frequency interval can propagate only in a very hot and rarefied plasma submerged in a strong magnetic field. These whistlers can only be damped, the modulus of the decrement of the damping cannot exceed 1·1 times the electron plasma frequency. The refractive index remains close to unity.

It is shown that a modified electron-acoustic wave exists in a plasma with distinct hot and cold electron components. The frequency of this wave depends strongly on the cold electron number density. Solitons associated with the modified electron-acoustic waves are also discussed.

The propagation of the fast magnetosonic wave is studied, taking into account the effect of the two-ion hybrid layer. Using a one-dimensional model, which includes density and magnetic field gradients, the wave equation is solved in the cold plasma approximation. The existence of radial eigenmodes confined between the two-ion hybrid layer and the low field side wall is predicted. Comparison with experimental data obtained on the TFR tokamak confirms the theoretical conclusions. Toroidal eigenmodes are observed even in the mode conversion regime when the antenna is on the low magnetic field side.

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 structure of deflagrations in one-dimensional flow is examined in detail. It is shown that the rule that deflagrations be weak or Chapman-Jouget must be obeyed unless a non-hydrodynamic discontinuity occurs. Such flows are shown to be unique and stable, once the downstream expansion is specified. It is shown that non-hydrodynamic discontinuities, if strong, are accompanied by a compression leading to a weak termination. The application to plasmas produced by laser irradiation of a solid is investigated and the flow structure in the presence of flux limitation evaluated.

The ponderomotive force generated by random Alfvén waves in a collisionless plasma is evaluated taking into account mean magnetic and velocity shear and is expressed as a series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of random velocity field. The effect of microscale random Alfvén waves through ponderomotive and mean electromotive forces generated by them on the propagation of large-scale Alfvén waves is also investigated.

We consider the nonlinear interaction of three high-frequency waves and lowfrequency density perturbations in a sharply bounded plasma. The coupled equations are presented in a general and convenient form. To demonstrate the usefulness of our method we derive explicit expressions for the threshold of a number of possible instabilities in semi-infinite and cylindrical plasmas.

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 excitation of the whistler mode waves propagating obliquely to the constant and uniform magnetic field in a warm and inhomogeneous plasma in the presence of an inhomogeneous beam of suprathermal electrons is studied. The full dispersion relation including electromagnetic effects is derived. In the electrostatic limit the expression for the growth rate is given. It is found that the inhomogeneities in both beam and plasma number densities affect the growth rates of the instabilities.

In the second part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the linear theory of part 1 to include the effect of collisional energy transfer from the electrons to the ions. The eigenvalue problem which gives the spectrum of the wave modes that occur in a beam of finite width is formulated and solved for the case of a square beam profile. From the resulting dispersion relation, we derive the unstable wavenumber band and the maximum spatial growth rate. An approximate solution of the dispersion relation is obtained for the case of a thin beam which illustrates how the stabilizing influence of energy transfer to the ions affects the unstable spectrum. In addition, some numerical solutions of the dispersion relation are presented for the cases of ionospheric modification by a power satellite microwave beam and by an ionospheric HF heater.

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.