We analyse the growth rate of obliquely propagating whistler mode waves in a cold plasma that also contains some hot electrons in a bi-Maxwellian distribution. Approximate analytic expressions for the growth rate are derived explicitly. They are represented by elementary functions only, consisting of a Landau damping term and a cyclotron instability term. They are found to be valid for a wide range of wave normal angles. Landau damping in the oblique propagation does not always become larger even if the wave normal angles increase. The necessary conditions for the minimal parallel growth are Ω > 0.5Ωe and T≥> 2T∥ in the bi-Maxwellian hot plasma. This method is applied to calculations of the net growth along the ray paths of obliquely propagating non-ducted whistler mode waves in a model magnetosphere.

In this paper we have studied the refraction of a hydromagnetic shock wave in an aligned field, when it encounters an interface between two streams of gases at different mach and Alfvén numbers. The hodograph mapping technique is employed in all the discussions. Both regular and irregular refractions are considered for the fast and slow shocks, but in the case of the fast shock, the discussions have been restricted to the first type. A brief account of the refraction of transverse shocks is also given. A detailed discussion is not necessary because of the similarity between this problem and that of the type 1 fast shock.

We have investigated how the presence of an electromagnetic beam and a static magnetic field influences the ion-acoustic solitons in a plasma. A modified KdV equation is derived in which the electromagnetic field plays the role of a source term. By using the perturbation analysis technique, it is shown that a homogeneous electromagnetic beam does not destabilize the ion-acoustic solitons; it reduces the amplitude, but not the velocity, of the solitons. However, any inhomogeneity in the electromagnetic field intensity does destabilize the ion-acoustic solitons; albeit not to an appreciable extent for typical cases.

Resistive instabilities in a low-β incompressible cylindrical model are investigated in a weakly sheared magnetic field. No boundary layer assumptions are made. Previous analytic results are found to fail badly when resistivity becomes too large, causing peaking in the growth rate dependence upon resistivity, and when the resonant surface approaches the axis, causing stabilization. The m = 1 tearing mode is investigated and found to lack the cut-off of higher m numbers. Finite Larmor radius effects have expected stabilizing properties, but produce a new, delocalized instability.

This work presents a systematic investigation and comparison of electromagnetic ion-cyclotron (e.m.) and electrostatic ion-cyclotron (e.s.) instabilities in uniform mixed warm and cold plasmas for magnetospheric-like plasma parameters. The following main aspects are included: Analytical: (i) we derive simple approximate expressions for the maximum growth rate, γmax for the quasi-electrostatic instability in the regime ωr » …p, к┴ » к∥ (к∥ ≠ 0) with the protons being described by mixed loss-cone and cold populations and with inclusion of electromagnetic coupling effects due to electrons; (ii) we analyse another regime in which electrostatic instalilities first increase with addition of cold plasma and decrease only after having reached a maximum, namely a regime with ωr » …p, к = к≠; (iii) we summarize the corresponding analytical results for parallel propagating electromagnetic ion-cyclotron unstable waves and discuss their validity range.

We consider the effects of resistive dissipation on energy absorption by spatially localized Alfvén waves which form a part of the continuous spectrum of ideal magnetohydrodynamics (MHD). We demonstrate that the strong absorption rate found in ideal MHD is unaltered for plasma resistivities of the order found in tokamaks, thus implying the possibility of effective heating of these machines by Alfvén waves.

The influence of a static electric field on electron oscillations of (i) a cold beam of electrons and (ii) a hot non-drifting plasma is investigated. The importance of the relative strength of the field is emphasized. In the weak field limit the oscillations are adiabatic, manifested by the existence of adiabatic invariants, preservation of eigenmodes and absence of reflexion. If the field is strong, however, interesting new features, such as mutual coupling of eigenmodes and wave reflexion, appear. Possible stability properties of a monotonic electrostatic transition (shock, double layer) are also discussed.

The generation of magnetic fields by currents driven by the electron pressure gradient in non-uniform plasmas is considered. The equations for field generation and energy balance are derived under the MHD approximation. It is shown that there exists a class of waves, thermal magnetic waves, which propagate along surfaces of constant density. The properties of such waves are examined. In addition, a class of self-similar solutions are presented. These represent an unstable growth of magnetic field in localized plasma regions, i.e. magnetic hot spots.

A variational method is presented to derive the electromagnetic response for waves of a model plasma with arbitrary β in a magnetic field whose curvature simulated by a gravitational field. The variational method is particularly well suited for deriving the electromagnetic local dispersion relation and differential equations of long-wavelength modes. In particular, the result is applied to finding the critical β needed for stabilization of low-frequency drift waves with density and temperature gradients.

A stationary collisionless and neutral plasma flowing along magnetic lines of force (B-lines) is considered and the variation of electric potential along the B-lines is described. A steep magnetic field aligned gradient of electric potential is generated at a certain location whenever plasma moves along the lines of force.

The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. We emphasize this improved renormalization. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion.

Kinetic theory of the self-modulation of a quasi-monochromatic ordinary wave propagating across an external magnetic field is presented. Explicit expressions of the dispersion and the nonlinear coupling coefficients are given for a Maxwellian plasma. In the limit of zero-temperature, a Karpman–Kruskal linear stability of the O-mode envelope is discussed.

We study nonlinear effects associated with large amplitude electron plasma waves propagating at an arbitrary angle to the external magnetic field. It is shown that the nonlinear coupling of high-frequency plasma waves with static density perturbations leads to a convective instability. The growth length of the latter is obtained. The evolution of the wave electric field is also investigated.

We have described previously the evolutionary process of magnetic field-line reconnexion by a localized enhancement of resistivity. In this paper, it is demonstrated by numerical experiment that the evolution is eventually checked, with the system attaining a quasi-steady state. On the basis of the quasi-steady configuration, established from an initially antiparallel magnetic field, we can now clarify the MHD properties that are characteristic of the diffusion, field reversal and external regions, respectively, and then the mutual dependence among them. Especially, the physical processes in the diffusion region are noteworthy, since the ultimate cause for the present reconnexion process is the bending of the field lines towards the magnetic neutral point, which results from the locally enhanced resistivity assumed in the diffusion region. The present numerical results generally agree with the analytical results for the steady reconnexion, although some discrepancies exist owing to the differences of the postulated basic situations between them. It is pointed out that changes in flow properties across the boundary of the field reversal region agree well with those required for a slow mode compression wave and that the dominant process in the external region corresponds to a fast mode expansion.

The structure of MHD switch-on shocks propagating along a magnetic field into an upstream partially ionized plasma is studied experimentally and theoretically. Detailed measurements of density, temperature and magnetic field are presented, and compared with a model based on the fluid equations for electrons, ions and neutral atoms. The main feature of the model is that dissipation of shock energy occurs primarily through ion collisions with neutrals. According to the model, at low upstreain ionization levels, ions and neutrals are preferentially heated above the electrons. At high ionization levels, the electrons are more strongly heated. This is found to be in agreement with the shock structures obtained for 4 switch-on shocks, differing in the level of upstream ionization.

A number of reconnexion concepts and experiments are briefly reviewed in order to re-examine the present interpretation of these experiments. In particular, we offer explanations as to why some experiments appear to develop Petschek modes, tearing modes, or netural current sheets. The explanations require an understanding of the proper role of magnetic Reynolds numbers, the limits of the frozen-in concept, and the importance of natural importance of natural boundary conditions. We find that netural current sheets usually from in experiments with highly symmetrical (and therefore unnatural) boundary conditions. The classical tearing mode develops from perturbations of a neutral current sheet. In less constrained geometries multiple neutral points may appear but the classical tearing mode theory needs modification to explain these cases rigorously. A Petschek mode develops in even less constrained systems although the theoretical description is highly idealized. We offer explanations as to why some experimenters appear to find neutral current sheets in quadrupole fields and examine the usefulness of concepts derived from neutral current sheet theory.

In contrast to the electronic heat conduction losses which for a tamped thermonuclear micro-explosion are minimized by a spherical target shape, the adiabatic temperature rise can be larger for a non-spherical implosion geometry, whereas for a given plasma volume and density the bremsstrahlung losses are independent of the particular geometry. The enhancement of the adiabatic temperature rise results from the ‘scissors effect’ in non-spherical implosions by which a cavity wedge can assume a larger geometric implosion velocity than the physical implosion velocity of the cavity wall. The net effect of the enhanced adiabatic temperature rise by the 'scissors effect' and enhanced electronic heat conduction losses for non-spherical cavity shapes results in an optimal non-spherical implosion geometry. For the special case of an imploding oblate ellipsoid the optimal eccentricity is derived from an exact analytical solution. The predicted effect leads to a reduction in required beam power density, permitting less beam focusing than is necessary for spherical targets, which is of special importance for electron- and ion-beam induced micro-explosions, and may even make possible the attainment of thermonuclear temperatures by chemical explosives.

The effect of thermal ions on the convective properties of the electromagnetic proton cyclotron instability is investigated. It is shown that when Ap < 1, where Ap is the proton anisotropy, cold ions, with relative specific charge mj/Zj mp ≥ 1, stabilize the convective growth of the instability. When Ap >1, the effect of thermal ions is to enhance the convective growth of the instabifity in the range where the real part of the frequency, ωr, is smaller than the ion gyrofrequency, Ωj. The maximum enhancement, corresponding to an optimum concentration of heavy ions, is shown to be a constant independent of the species. However, for each species, even for Ap > 1 (except for protons), there is always a range of values of Ap such that the species will stabilize the system. Heavier ions are shown to be more effective in enhancing the convective growth of the instability, in the sense that, the heavier they are, smaller relative concentrations are required to reach the constant value mentioned above. For sufficiently heavy species, the required concentration to optimize the convective growth, is independent of the species.

The gravitational instability of a two-component plasma has been studied here to include simultaneously the effects of neutral gas friction, finite ion Larmor radius, magnetic resistivity and Hall currents. The viscosities of the two components of the plasma have also been taken into account. The mode of the transverse as well as the longitudinal wave propagation have been discussed. The dispersion relations have been obtained for both these cases and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. For the transverse mode of propagation, it is found that the growth rate of the unstable mode increases with magnetic resistivity and with the ratio of the densities of two components. The influence of the magnetic resistivity is, therefore, destabilizing on this mode of wave propagation. The viscosities of the two components are found to have a stabilizing influence on the growth rate in this case since it is found that the increase of hte viscosity effects reduces the growth rate. For the longitudinal mode also it is found that the effects of viscosities as well as that of neutral gas friction are stabilizing. The magnetic resistivity does not affect the growth rate since the equation determining the growth rate is found to be independent of this effect.

A modified form of the Bogoliubov plasma cluster expansion is applied to the derivation of a divergence-free kinetic equation from the BBGKY hierarchy. Special attention is given to the conditions under which the Landau kinetic equation may be derived from this more general formulation.