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.

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.

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.

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 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 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.

In the third part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the lineary theory of part 1 to include the effect of ambient drift motion perpendicular to the plane of the axis of the beam and the magnetic field. We show that the amplitude of the density perturbation satisfies a third-order hyperbolic equation, when this effect is included, and we apply Riemann's method to obtain its solution in integral form. This solution shows that a state of stationary self-focusing is established within the beam after a time equal to the transit time for a perturbation to drift across it. The form of the axial growth in the stationary state is derived from an asymptotic evaluation of the integral representation for large axial distances. It is found that the axial growth increases across the beam starting from zero at the edge through which plasma enters the beam and reaching its maximum attainable value at or before the opposite edge, depending on the magnitude of the drift velocity. The maximum growth decreases as the drift velocity increases and only occurs at the rates deduced in parts 1 and 2 when the beam width is several times larger than the scale length which describes the decay of a density perturbation within the beam due to the combined effect of drift longitudinal ambipolar diffusion, recombination and the stabilizing influence of perturbations to the electrical conductivity. The factor by which the amplitude of a convected density perturbation is reduced relative to the value it would have in the absence of drift motion is evaluated and the results are applied to the case of ionospheric modification by a transmission from the proposed solar power satellite systems.

In the fourth part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we examine the spatial nonlinear development of the instability, assuming that a stationary state of the type described earlier has been established. Our treatment considers the interaction of the pump wave with the Stokes side-band waves and the density perturbation corresponding to the most unstable linear mode. We show that the system of equations describing their interaction possesses three invariants. These invariants are used to reduce the problem to a single differential equation for the axial behaviour of the amplitude of the density perturbation. The form of the invariants differs according as the inclination of the beam to the magnetic field is above or below the critical value defined earlier. Above the critical orientation, the amplitude of the density perturbation can be expressed algebraically in terms of the amplitudes of the pump and side-band waves. We show that this case is integrable in terms of the Jacobean elliptic function dn and we use the results to find the saturation level. Below the critical orientation, the response of the plasma becomes non-local, above a certain threshold power. The algebraic relation is then replaced by a differential equation which results in a significantly more complicated differential equation for the amplitude of the density perturbation. A particular solution of this equation is found for a special choice of initial conditions and from this the saturation level is found. The results of these calculations are applied to the problem of ionospheric modification by microwave transmissions from the proposed solar power satellite systems.

In the fifth part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the nonlinear theory of part 4 to include the effect of cubic nonlinearities. These terms describe the stabilizing influence of perturbations to the electrical conductivity. We assume that a stationary state of the type described earlier has been established and consider the spatial nonlinear interaction of the pump wave with the Stokes side-band waves and the density perturbation corresponding to the most unstable linear mode. We show that the system of єquations describing their interaction possesses three invariants. These invariants are used to reduce the problem to quadratures and an implicit solution is obtained in terms of incomplete elliptic integrals of the first and third kinds. From this solution we derive explicit expressions for the saturation level and the nonlinear growth length. The results are applied to the problem of ionospheric modification by microwave transmissions from the proposed solar power satellite systems.

The development of anisotropy in an initially isotropie spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops through the combined effects of an externally imposed d.c. magnetic field and viscous and resistive dissipation at high wavenumbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wavenumbers.