The hydrodynamic theory of drift Kelvin-Helmholtz instabilities is discussed. It is shown that the hydrodynamic approach gives, in the region of its applicability, the same results as the kinetic one. Previous studies on the hydrodynamic theory of drift Kelvin-Helmholtz instabilities are analysed. It is shown that certain parts of these studies are incorrect. Reasons for this are discussed.

The stability of localized solitary wave solutions of simultaneous nonlinear Schrödinger equations describing different types of interacting waves in a plasma has been investigated. It is found that the stability depends on the nature and strength of the interaction potential between the two waves. The possible results of interactions between two colliding solitary waves have been discussed using the conservation laws.

In this paper we generalize the formalism developed by Balescu and Paiva-Veretennicoff, valid for any kind of weak turbulence, for the determination of all the transport coefficients of an unmagnetized turbulent plasma, to the case of a magnetized one, and suggest a technique to avoid finding the inverse of the turbulent collision operator. The implicit plasmadynamical equations of a two-fluid plasma are presented by means of plasmadynamical variables. The anomalous transport coefficients appear in their natural places in these equations. It is shown that the necessary number of transport coefficients for describing macroscopically the magnetized turbulent plasma does not exceed the number for the unmagnetized one. The typical turbulent and gyromotion terms, representing dissipative effects peculiar to the magnetized system, which contribute to the frequency-dependent transport coefficients are clearly exhibited.

Using the Bhatnagar–Gross–Krook collision model, the effects of charge-transfer and elastic ion-neutral collisions on the crossfield beam-driven ion-acoustic instability in a double plasma device are studied. Elastic collisions cause a slowing of the beam, while charge exchange gives rise to an exponential decay in ion beam density. The resultant damping of the instability is calculated and compared with experiment.

Expressions for the current response operators of first and second order are calculated for a fluid plasma with isotropic pressure terms. The unperturbed state is an arbitrary space and time dependent solution of the basic equations. The response operators are given in a form which shows explicitly the mathematical structure behind the approximate conservation of wave energy in resonant wave interactions. The coefficients in the coupled mode equations are expressed in terms of these response operators.

A uniformly-streaming compressible and infinitely-conducting plasma is confined by a magnetic field aligned with the stream. The system is disturbed by introducing magnetic dipoles into the field. A Fourier-transform method is used to determine the displacement of the interface between the streaming plasma and the magnetic field within the framework of a ‘shallow-water’ approximation. For the case of a subsonic plasma stream, stationary waves appear on the interface upstream of the dipoles, and it is found that (i) these stationary waves are possible only if the gravity effects on the plasma are weak enough; (ii) the effect of surface tension at the interface is to reduce the amplitude and increase the wavelength of these waves. For the case of a supersonic plasma stream, however, stationary waves at the interface are not possible.

Analytic forms for the MHD continuous spectra in axisymmetric tokamak equilibria are derived using an expansion scheme in powers of the small inverse aspect ratio. Resulting formulae for the shear Alfvén continuum have been evaluated for the shear Alfvén wave heating experiment on the Tokapole II device at the University of Wisconsin-Madison. Mode coupling, induced by toroidicity or non-circularity, is shown to occur, in first order, on and near rational surfaces for particular poloidal and toroidal mode numbers. The coupling is shown to produce gaps in the spectrum, analogous to the gaps which appear in the energy spectrum of a single electron in a periodic potential lattice.

This paper is concerned with the Boltzmann collision integral for the one-particle distribution function of a test species of particle undergoing elastic collisions with particles of a second species which is in thermal equilibrium. A previous paper studied this expression as a function of the mass ratio for the two species of particle when the test particle distribution function was isotropic in velocity space; this work generalizes that analysis to anisotropic distribution functions by expanding the distribution function in tensorial spherical harmonics. First the limit of zero mass ratio is considered: this simplifies the calculation dramatically. There is no contribution to the collision integral from the zeroth-order spherical harmonic in this limit. Then the main calculation shows how to find the terms arising from the existence of a finite mass ratio as an ascending power series in this quantity, and evaluates for each spherical harmonic the next term, linear in mass ratio. This is checked for two special cases: that of an isotropic distribution function, when the expression reduces to Davydov's form, and that arising from a cross-section inversely proportional to the collision velocity, when a comparison with the exact solution of the associated eigen problem can be made. As in the isotropic case, an exact representation of the collision integral as an expansion in mass ratio must include some terms non-analytic in this quantity and vanishing more quickly than any positive power: it is shown how these arise in the present formalism. The formulae derived here have applications to the transport theory of electrons and light ions in a predominantly neutral gas as governed by the Boltzmann equation.

The filamentation and collapse of Langmuir waves in a weak magnetic field are analysed in two particular cases of low-frequency acoustic perturbations: (i) adiabatic perturbations which correspond to subsonic collapse, and (ii) nonadiabatic perturbations which correspond to supersonic collapse. Here the existence of Langmuir filaments and Langmuir collapse in a weak magnetic field are due to nonlinear interaction of high-frequency Langmuir waves (which make small angle with the external magnetic field) with low-frequency acoustic perturbations along the magnetic field.

The behaviour of the crossfield current-driven ion-acoustic instability in the presence of a sheared magnetic field and a density gradient is investigated theoretically in the limit in which growth due to inverse Landau damping is small. The shear damping rate is found and the critical shear length shown to vary as (mi/me)⅓ and as ((VD–CS)/CS)–⅔.

Petschek's model of compressible reconnexion developed in part 1 is extended to include an additional transverse magnetic field. Part of the incoming Poynting flux is degraded into kinetic energy at an intermediate wave (rotational) discontinuity. Yet more is degraded into heat and kinetic energy at a slow shock lying downstream of it. Everywhere downstream of the rotational discontinuity, the transverse magnetic field exceeds its upstream value. As a result, the total release of magnetic energy from the antiparallel components of the incoming magnetic field calculated in part 1 is decreased by a factor lying between a half and unity. The weak radial inhomogeneity exemplified by the ‘local’ similarity solution is determined by consideration of the fast and slow magneto-acoustic and Alfvén waves emitted at the neutral point. The Alfvén waves lead to a weak singularity in the vicinity of the rotational discontinuity, while a similar singularity is found in the vicinity of the outflow axis of symmetry associated with an entropy wave.

An analytical theory for the time evolution of the distribution function, energy and current of an assembly of electrons submitted to a quasi-sinusoidal stochastic field is given. To the first order, energy and current are obtained using Sturrock's stochastic acceleration theory. The calculation of the transition probability enables us to get the distortion of the distribution function, and to recover the preceding first-order results. To the second order, collisions are taken into account, in the framework of the two-dimensional theory. The turn-on time for the current is evaluated. The results obtained are compared with the numerical results of Karney & Fisch.

Generalized expressions for the rates of change of the momentum, energy and thermal anisotropy of fast, charged particle beams interacting with non-Maxwellian multi-species plasmas are derived. The results hold for the case of spherically symmetric systems and, therefore, are relevant for inertial confinement fusion schemes driven by fast charged particle beams and for various astro-physical situations. The calculations are based on the Fokker-Planckformalism. The effects connected with the departures from the Maxwellian distribution functions are expressed in terms of their fifth moments, , which reflect the role of the non-Maxwellian tails. The familiar stopping power expression holding for Maxwellian targets is recovered as a particular case.

The generation, structure and propagation of one-dimensional ionizing MHD shock waves in helium under a pressure of 100 mTorr are investigated with the help of numerical simulation. The normal magnetic field varies within 3 to 10 kG and the longitudinal magnetic field varies up to 2·5 kG. The model includes the kinetics of ionization and photo-processes. If a solid conducting piston is a source of perturbation, it may give rise to generation and further development of an MHD switch-on wave. Its evolution at an advanced stage depends weakly on the source. The curves for the dependence of the shock speed on time and the driving magnetic field as well as the profiles for the main quantities are presented. A possibility of comparison with real experiments is discussed. Algorithms based on Godunov's sliding meshes and the imbedding methods are used for numerical simulation.

The linear growth rate of the crossfield current-driven ion-acoustic instability is obtained for any equilibrium particle velocity distribution function of the type . Quasi-linear theory is then used to investigate the saturation of the instability. Several associated features, namely, particle diffusion in velocity space, anomalous resistivity, energy distribution and electron and ion heating rates are evaluated for a Maxwellian distribution. Finally, a brief comparison is made with the heating rates associated with the electron cyclotron drift instability.

It is shown that the asymptotic evolution of a finite-amplitude Alfvén wave propagating parallel to the uniform magnetic field in a warm homogeneous collisionless plasma is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the ion finite Larmor radius (FLR) effects in the momentum equation and the Hall current and electron pressure corrections to the generalized Ohm's law. In the cold plasma limit the equations reduce to those available in the literature. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in the solar wind.

The heat conductivity of a laser-created plasma heated by inverse bremsstrahlung absorption is investigated in the vicinity of a self-similar state (SSS), taken as reference state. Under certain conditions, the slowly varying macroscopic quantities obey true, local hydrodynamical equations and a well-defined, positive, heat conductivity exists. The latter is strongly time-dependent through the unperturbed temperature. Its value, compared to the classical heat conductivity at the same temperature, shows a reduction of about 20%. It is shown that, for high intensities and/or long wavelengths, the linear heat conduction theory necessarily breaks down, even if the temperature gradient is very small.

The Hα resonant scattering diagnostics applied to the tokamak UNITOR is described. The measurements yield the density distribution of excited hydrogen atoms as a result of plasma-wall interaction processes and background plasma parameters. Special regard has been given to the influence of recycling processes.

Starting from the two-fluid model hydrodynamic equations, a dispersion relation is obtained for wave propagation through a two-temperature plasma perpendicular to the direction of the spatially uniform external magnetic field B0cosω0t and several excitation conditions are deduced.

Nonlinear ion-acoustic waves in magnetized plasmas are investigated. In strong magnetic fields they can be described by a Korteweg-de Vries (KdV) type equation. It is shown here that these plane soliton solutions become unstable with respect to bending distortions. Variational principles are derived for the maximum growth rate γ as a function of the transverse wavenumber k of the perturbations. Since the variational principles are formulated in complementary form, the numerical evaluation yields upper and lower bounds for γ. Choosing appropriate test functions and increasing the accuracy of the computations we find very close upper and lower bounds for the γ(k) curve. The results show that the growth rate peaks at a certain value of k and a cut-off kc exists. In the region where the γ(k) curve was not predicted numerically with high accuracy, i.e. near the cut-off, we find very precise analytical estimates. These findings are compared with previous results. For k≥kc, stability with respect to transverse perturbations is proved.