The microinstabilities of a high-pressure plasma moving along a magnetic field with a non-uniform velocity profile are investigated. A similar problem was studied earlier by Dobrowolny on the basis of hydromagnetic equations with an oblique viscosity tensor. The present paper, unlike Dobrowolny's work, gives a kinetic analysis. Perturbations with transverse wavelength both larger and smaller than the ion Larmor radius are considered. The analysis indicates that there is a large family of microinstabilities of the ‘drift’ type whose mechanism differs from the classical Kelvin–Helmholtz instability.

We derive dispersion formulae for the transverse waves propagating through a collisionless magneto-active plasma in the direction of the magnetic field valid for relativistic as well as non-relativistic temperatures, and compare them with those of earlier works. Wave propagation under various limiting conditions of temperatures and magnetic field are discussed.

In part 1 of this work, we have found a ‘critical curve’ which separates the unstable self-modulation regime from the stable one for a Gibbs ensemble of interacting modes. On this critical curve, the correlation length diverges and scaling invariance occurs; in particular, the Langmuir correlation spectrum is proportional to k-2. Simple laws have been derived for the neighbourhood of the critical curve. However these derivations are based on equilibrium statistical mechanics and the results are obtained with a Hartree approximation which has not been checked. So, in this second part, we elaborate a direct statistical theory of Zakharov's equations completed by excitation sources and dissipations. In spite of infra-red divergences and a large fluctuation level, large-scale properties are derived in the neighbourhood of the critical curve, by the renormalization group method. The laws obtained in part 1 are slightly modified; however, the same spectrum is obtained.

A three-dimensional nonlinear Schrüdinger equation for an electrostatic ion cyclotron wave coupled to an ion-acoustic wave in a collision-free plasma consisting of cold ions and two-temperature electrons is derived using the reductive perturbation method. It is shown that a range of wavenumbers corresponding to the instability of a plane electrostatic ion cyclotron wave against a two-dimensional modulation depends on the ratio of temperature of hot and cold electron components.

The equations of MHD equilibrium are solved by including plasma pressure and current in a large aspect-ratio ordering scheme for the calculation of toroidal, l = 3 stellarator vacuum fields. The extended ordering unifies the low-beta equilibrium theory for tokamaks and l = 3 stellarators, and allows solutions to be obtained simply for arbitrarily prescribed pressure and current density profiles. Expressions are given for the equilibrium magnetic field and the equation for the flux surfaces is calculated, including the effects of l = 3 shaping and toroidal displacement. These results are used to calculate equilibria for the parameters of CLEO stellarator, and we examine the role of an externally applied vertical field in reducing pressure-induced flux surface distortion and destruction.

Convective instability of a plasma slab (contained between two metal walls) subject to a longitudinal external magnetic field is studied. The results show that (i) increase in the ionization rate Z causes a reduction in the stability of the plasma; (ii) the instability persists in the limit k ⇒ 0.

The electromagnetic instability of a relativistic electron beam penetrating an infinite plasma is analyzed. The purpose of this paper is to determine the effect of collisions within the plasma upon the growth rate of the Weibel-type electromagnetic instability. The dispersion relation including the effect of collisions is solved analytically and numerically. It is found that collisions can enhance the growth rate of the electromagnetic instability in the case of low plasma temperature.

The theory of electrostatic plasma turbulence is considered. The basic equations for the dynamics of the hierarchy of the moment equations are derived and the difficulty of the closure problem for strong plasma turbulence is discussed. The characteristic functional in phase space is introduced and its relations to the correlation functions are described. The Hopf functional equation for dynamics of the characteristic functional is derived, and its equivalence to the hierarchy of the moment equations is established. Similar formulations were carried out in velocity-wave vector space. characteristic functional are considered and their relationships are studied. An approximate solution for Hopf's equation for the nearly normal turbulence is obtained which is shown to predict diffusion of the mean distribution function in velocity space.

The properties of certain wave modes excited in a weakly ionized plasma placed in an external d.c. electric field are analyzed from the standpoint of the linearized kinetic equation, the electron steady-state distribution function being taken in the form of the extended Margenau–Davydov and, in particular, Druyvesteinian. The presence of absolute stability cones formed by certain propagation directions is found. The corresponding critical values of the electron drift, destabilizing each of the modes considered, is also evaluated for a plasma with a Druyvesteinian distribution.

Ideal MHD equilibria with an ignorable space variable are investigated. It is shown that only three classes of these symmetric equilibria exist: the systems with a straight, a (cylindric) helical, and a circular magnetic axis.

Many different problems, associated with the propagation of electromagnetic waves in an inhomogeneous isotropic plasma and governed by second-order differential equations, are reformulated so as to be brought within the scope of a common analytical procedure. Refiexion coefficients, energy considerations, approximation procedures, slab refiexion, and other theorems are considered, the investigations of different physical processes all being attributable to one underlying mathematical method involving integrals, whose integrands contain quadratic products of the field variables and their derivatives in two different arrangements.

A class of magnetostatic solutions is obtained for the magnetic field and current in a toroid. The solutions are characterized by nested toroidal flux surfaces whose cross-sections are concentric circles. The model distribution of the magnetic field and current allows a correct calculation of the typical self-induced magnetic force exerted by a current interacting with its own magnetic field in a toroidal configuration.

Recently a spatially uniform expression for the time asymptotic binary correlation function of a Landau-stable plasma was derived from the BBGKY hierarchy equations. In this paper, the high-frequency (Vei ≪ ‖w‖ ≪ ωpe) electrical conductivity of a spatially homogeneous, unmagnetized Lorentz plasma

is calculated from this expression; the result is compared with those obtained from other convergent collision integrals.

The models of Vekshtein, Ryutov & Sagdeev (VRS), describing a marginally stable turbulent plasma sustaining an electric current, are shown to be incomplete by their neglect of the equations determining the spectral densities of the driving modes. An exhaustive study of these models including a detailed determination of the frequencies, spectral densities and turbulent energy densities, shows that, strictly speaking, there exists no self-similar turbulent state (SSTS). However, an approximate SSTS can be constructed, based on the finding that the tail of the spectral densities behaves self-similarly.