The conservation equations for a suspension composed of an ionized gas and small solid dust particles are formulated and solved numerically. Such flows can be found downstream of strong normal shock waves propagating into dusty gases. The solution indicates that the presence of the dust has a significant effect on the post-shock flow field. Owing to the dust, the relaxation zone will be longer than in the pure plasma case; the equilibrium values for the suspension pressure and density will be higher than in the dust-free case, while the obtained values for the temperature, degree of ionization and velocity will be lower. The numerical solution was executed for shock Mach numbers ranging from 10 to 17. It was found that the thermal relaxation length for the plasma decreases rapidly with increasing shock Mach number, while the thermal relaxation length for the suspension mildly increases with increasing M. The kinematic relaxation length passes through a pronounced maximum at i M = 12·5. Throughout the investigated range of Mach numbers, the kinematic relaxation is longer than the suspension thermal relaxation length.

The properties of Alfvén solitons are examined (solitons propagating parallel to the magnetic field in a magnetized plasma) in the case when the plasma possesses a finite pressure. Starting from a two-fluid system of equations, the reductive perturbation method is used to derive a derivative nonlinear Schr ödinger equation, which is solved by a pseudo-potential method. An envelope soliton is found which possesses a width –amplitude relationship. The same functional form for the envelope of the magnetic energy density is obtained regardless of the value of the plasma &bgr;.

A pair of modified Zakharov equations coupling the high-frequency Langmuir oscillations to the low-frequency ion-acoustic perturbations in a turbulent, collisional plasma with a neutral background is derived. The time evolution of the coupled ion-acoustic–Langmuir solitons show that the electron–ion and electron–neutral collisions damp the Langmuir oscillations and let the ion density perturbations radiate away. On the other hand, the ion–neutral collisions damp the ion density perturbations letting the Langmuir oscillations flow out. In the case of ion viscosity, however, both the ion density perturbations and the Langmuir oscillations radiate away one after the other. In these processes, electron–ion and electron–neutral collisions seem to dominate over the other two.

We present a general formulation for treating the linear stability of inhomogeneous plasmas for which at least one species is described by the Vlasov equation. Use of Poisson bracket notation and expansion of the perturbation distribution function in terms of eigenfunctions of the unperturbed Liouville operator leads to a concise representation of the stability problem in terms of a symmetric dispersion functional. A dispersion matrix is derived which characterizes the solutions of the linearized initial-value problem. The dispersion matrix is then expressed in terms of a dynamic spectral matrix which characterizes the properties of the unperturbed orbits, in so far as they are relevant to the linear stability of the system.

An approximate dispersion relation is obtained for quasi-longitudinal whistler mode propagation in the hot anisotropic plasma. The influence of plasma temperature and anisotropy on whistler energy focusing along the magnetic field and whistler trapping in the magnetospheric ducts are considered for the case when the whistler wave normal angle is not equal to zero.

The conservation equations appropriate to a steady, one-dimensional flow of dusty ionized argon were solved numerically. The specific effect of each of the physical parameters of the dust upon the flow properties in the relaxation zone was studied. It was found that increasing the dust particle mass causes an increase in both the kinematic and thermal relaxation lengths. In addition to these changes, the flow field inside the relaxation zone is also affected. An increase in the dust mass (caused either by an increase in the dust density or its diameter) causes an increase in the plasma velocity, temperature and electron number density and a decrease in its density and pressure. Similar effects are encountered when the specific heat capacity of the dust is changed. An increase in the emissivity of the dust causes an increase in the plasma density and pressure and a decrease in its velocity, temperature and electron number density. Increasing the emissivity of the dust results in a decrease in the relaxation zone length.

The solution of the linearized Vlasov equation is given for an arbitrary equilibrium Hamiltonian in which there is only one non-ignorable co-ordinate. The solution written in terms of integrals with respect to time which only extend over the bounce period of an equilibrium orbit in its equivalent one-dimensional potential. A closed-form solution and a solution based on a Fourier expansion are given. Explicit formulae are presented for Cartesian and cylindrical co-ordinates.

We derive the dispersion formulae for electromagnetic waves including relativistic kinematics and a corresponding Maxwellian equilibrium distribution function without any approximations and having anisotropy in the streaming velocity. For non-relativistic temperatures, waves propagate when the streaming velocity is much smaller than the thermal velocity of the species, with varying thermal modes.

The mean electromotive force and ponderomotive force generated by nonlinear random Alfvén waves propagating along the mean magnetic field and linear random Alfvén waves propagating in arbitrary directions in a collisionless plasma are calculated by use of Fourier analysis methods. It is shown that the a-effect can exist in the interaction between two different waves and that the magnetic turbulent diffusivity can be negative depending on the energy spectrum functions of the initial values of the magnetic and velocity perturbations. The results are applied to the substorms in the Earth's magnetosphere.

An expression is derived for the ponderomotive force acting in a cold collisionless magnetized plasma in a high-frequency electromagnetic field. Some related topics, such as the magnetic moment and solenoidal currents induced by the HF field are considered. A microscopic approach is used. The results are in complete agreement with the general expression for the ponderomotive force in a liquid medium with frequency dispersion obtained earlier by Washimi & Karpman by means of phenomenological considerations.

In this third of a series of papers on the stability of Vlasov equilibria, the dispersion functional technique developed in part 1 is applied to the multi-species Vlasov plasma and to the Vlasov-fluid model. An alternative form of the dispersion functional is derived for the Vlasov-fluid model in which magnetohydrodynamic and kinetic aspects of the problem are separated explicitly. A necessary and sufficient condition is derived for stability with the Vlasov-fluid model. Stability of the multi-species Vlasov plasma is discussed and a necessary and sufficient condition for stability near a marginal point is derived. Explicit formulae for quantities occurring in the dispersion functional are given in cylindrical co-ordinates for the Vlasov-fluid model when there is one nonignorable co-ordinate in the equilibrium. The dispersion functional for a multi-species Vlasov plasma is shown to be related to the ponderomotive Hamiltonian.

A magnetically confined two-fluid plasma is considered in which the Ohmic heating of the electrons by a current driven parallel to an applied magnetic field is balanced by bremsstrahlung and equipartition to the ions. It is found that for a steady state the applied electric field must be below a critical value which in absence of bremsstrahlung is given by where the electrical conductivity is and the total pressure is p. Under this condition it is found that there are two /Futions for Te/Ti which satisfy the steady electron energy balance equation in a homogeneous, fully ionized plasma. One of these /Futions always has values above the critical value of Te/Ti (= 132 in absence of bremsstrahlung) for the onset of the electrothermal instability in a fully ionized gas. Inclusion of electron thermal conduction transverse to the magnetic field (with Hall parameter ) yields a wavelength for maximum growth of the instability of about , where ae is the electron Larmor radius. The steady non linear profiles showing current filamentation have been calculated. Runaway electrons and ion-acoustic instabilities can occur in the spatial maximum of the current density and electron temperature. Inclusion of bremsstrahlung loss reduces the value of Te/Ti for the onset of the instability, and at Te = Ti yields a maximum ion temperature obtainable by Ohmic heating in a stable plasma.

Thirteen moments are taken of the collision term in the Boltzmann–Fokker– Planck equation for a multi-species, multi-temperature, hot plasma, following the method first developed by Grad for neutral gases. The collision integrals are evaluated for each colliding species pair. These integrals give, in particular, the rate of exchange of momentum and energy produced by collisions. The set of integrals may be combined with moments of the remaining terms in the Boltzmann equation to give thirteen moment equations for each species of particle. To complete the calculation, extensive use was made of the symbolic computer language REDUCE.

A systematic study is made of the dynamical properties of the charge density fluctuations in strongly coupled two-component plasmas. The time-correlation function of the partial density fluctuations is described with the use of the memory function formalism. A second-order memory function is approximately expressed in terms of its self-part by taking into account the total momentum conservation law. After assuming a Gaussian time-dependence for the self-part, the excitation spectrum of the charge density fluctuation is calculated for the semi-classical hydrogen plasma, and is in fairly good agreement with the molecular dynamics calculation due to Hansen & McDonald. It is found that the collisional effects play an important role in the strongly coupled system.

A theory of whistler wave propagation in axially symmetric density ducts is developed. Both density crests and troughs are considered. The duct width is assumed to be large compared with the parallel wave length. All considerations are based on the Maxwell equations. A number of effects that are not included in the ray theory and (or) the Schrödinger-type equations are elucidated. Among them is whistler detrapping from a density crest at ω < ½ωH. An analytical theory of the detrapping is developed and the corresponding wave attenuation rate in the duct is calculated.

In the first part of this work a higher-order solution of the anharmonic oscillator equation describing the nonlinear rippled equilibrium state of magnetically focused, partially neutralized electron beams is given. Thus, using the method of harmonic balance, we derive a ripple-&litude solution of the form

where ø=ω1t+β0,ω1 being the nonlinear proper frequency and β0 a phase shift depending on the initial conditions. In the second part of the work we carry out a stability analysis of the nonlinear equilibrium state found in the first part with respect to long- and short-wavelength surface space-charge perturbations. In the framework of a local approximation the wave equation for the rippled beam is found to be a Hill type of equation which contains harmonic terms up to cos 3kSz (ks is the wavenumber of the ripple). This equation is solved by a resonant-mode coupling method; coupling of fast-fast, slow-slow and slow-fast waves is considered. The growth rates and band widths for different possible wave couplings are derived and compared.

Wave excitation by an inhomogeneous suprathermal electron beam in a homogeneous magnetized plasma is investigated. Not only is the beam density non-uniform, but the beaming electrons also have a sheared bulk velocity. The general dispersion equation including both electrostatic and electromagnetic effects is derived. Particular attention is paid to the whistler mode. It is found that the density-gradient and velocity-shear effects are important for waves with frequencies close to the lower-hybrid resonance frequency.

We consider the stability against small perturbations of a class of exact wave solutions of the equations that describe an unmagnetized relativistic cold electron plasma. The main feature of these nonlinear waves is a transverse circularly polarized electric field with periodic amplitude modulation in the longitudinal direction. Floquet's theory of linear differential equations with periodic coefficients is used to solve the perturbation equations and obtain the instability growth rates.

We investigate nonlinear resonances and the averaged potential in a bounded non-isothermal plasma, placed in a constant magnetic field and a parallel external a.c. electric field. The treatment assumes one component MHD. It is assumed that a standing Alfvén wave exists before the electric field is switched on.

Certain unfamiliar terms in renormalized plasma turbulence theory are interpreted in terms of the familiar physics of the Balescu–Lenard collision operator. Specifically, it is argued that the so-called polarization parts of the operator which renormalizes the particle propagator are related to fluctuations of the Fokker–Planck coefficient which describes polarization drag, and to fluctuations of the effective dielectric function of the medium.