A procedure is outlined for obtaining a high degree of quiescence in a magneto- plasma.

A single particle is subjected to the combined action of a static uniform magnetic field and an electromagnetic wave. The equations of motion are solved using the perturbation method up to second order. In the results, two different types of second-order effects appear: (i) the always present non-resonant effects, resulting in a ponderomotive drift and a nonlinear cyclotron frequency shift, and (ii) the resonant effects appearing at the half-integer harmonics of the gyrofrequency and leading to perpendicular heating and diffusion.

A unified picture of the structure of steady, one-dimensional shock waves in partially ionized argon, in the absence of external electric or magnetic field, is presented. The investigation is based on a two-temperature, three-fluid continuum approach, using the Navier–Stokes equations as a model and including non-equilibrium ionization. Quasi charge neutrality and zero velocity slip are assumed. The analysis of the governing equations is based on the method of matched asymptotic expansions and results in the following three layers: (1) a broad thermal layer dominated by electron thermal conduction, (2) an atom-ion (A-I) shock structured by the heavy particle (atoms and ions) collisional dissipative mechanisms and (3) an ionization relaxation layer (IRL) wherein electron- atom inelastic collisions dominate. Solutions have been obtained for the first two orders with respect to a small parameter, which is the ratio of energy fluxes due to heavy particle viscous dissipation and electron thermal conduction. Whereas only electron temperature and electric potential show any marked variation in the thermal layer, the changes in all the variables in both the A-I shock and the IRL are significant.

Inclusion of electron thermal conduction terms in the governing equations has been observed to introduce numerical instabilities in the analysis of the IRL. They are circumvented by adopting a regular perturbation scheme with respect to a local small parameter, which has been identified to be the ratio of the freestream degree of ionization to the nondimensional characteristic temperature for first ionization. Numerical results show that the effect of electron thermal conduction on the IRL profiles is significant. Results in the form of tables and figures are presented for five sets of equilibrium free-stream conditions.

The stability of the solar wind against the whistler mode is analyzed. It is shown that the solar wind can become unstable owing to this mode after a distance of 100 R from the sun. The minimum value of the relative velocity (Ur) between ∝-particles and protons for the excitation of this instability is the proton thermal velocity αi. The maximum growth rate at 200 R occurs for the values of the parameters kρi = 0·3,(T┤/T∥)i = 0·3 and Ur/αi = 0·5.

Ionization wave frequency spectra and their spatial distribution along argon and neon plasma positive columns are detected by microwaves in the 8–18 GHz frequency band. The plasmas are created at medium pressure by d.c. discharges in narrow tubes. Detection takes place in a rectangular waveguide on the microwave fields reflected and transmitted by plasma columns which are placed transversely across the waveguide in different positions and at several values of the discharge current. The frequency of the microwaves is adjusted for a parametric resonance condition with respect to Langmuir's electron frequency. The properties and dispersion relations of these waves are derived from a linear theory developed by K. W. Gentle, in which, for discharge operation below the Pupp limit, metastables are also included in the ionization and species conservation equations. An estimate of the total collision frequency is derived from a simplified two-fluid model valid essentially near the Pupp equilibrium limit.

A general self-consistent framework is developed for the calculation of transport coefficients in a collisionless, weakly turbulent plasma. These coefficients characterize the response to a perturbation away from a quasi-steady turbulent state, which is assumed to exist as a result of the stabilization of the linear instabilities. It is shown that a purely hydrodynamical description does not exist for plasmas: the macroscopic picture must include non-conserved quantities, which lead to the plasmadynamical (or ‘two-fluid’) picture of the system. The number of independent transport coefficients, necessary for the macroscopic characterization of the plasma, is correspondingly increased as compared with a two- component mixture of two ordinary fluids. The typical turbulent contributions to the transport coefficients are clearly exhibited.

The energy of hydrodynamically unstable plasma waves is re-examined. The modified Landau–Lifshitz factor Re (∂/∂ω) (ω∈) recently proposed is shown to involve several difficulties when energy and momentum conservation are considered.

Nonlinear magneto-acoustic waves in a turbulent plasma are simulated by collisional MHD equations. Damping of these waves due to electrical conductivity arising from micro-instabilities and collisional viscosity are analyzed. Numerical investigation of competing effects due to non-linearity and dissipation has been carried out. It is found that finite amplitude perturbation leads to the formation of a shock in both the slow and the fast mode propagation. Collisional viscosity plays an important role in the damping of nonlinear magneto-acoustic waves in the astrophysical and space plasmas.

We consider the effect of trapped electron instability turbulence on the dynamics of a typical mode. We find its effects are turbulence induced additional collision frequencies for the trapped electrons which are stabilizing. The resulting saturation level is found to be considerably smaller than previous estimates.

Magnetosonic solitons may be given smooth increasing profiles by assuming the presence within the wave of a current distribution Jy(x) of trapped ions perpendicular to Bz(x) and the wave velocity Vx. Suitable ions are found immediately upstream of perpendicular, collisionless shock waves and these are coincident with the often observed ‘foot’ in magnetic field profiles of moderately supercritical shocks. By modelling Jy(x) we apply the theory to previous experiments where Jy(x) is observed, and are able to reproduce reasonably, and thus explain, the profiles in the foot. Insight into a number of features of fast shocks is obtained.

The complete second-order theory of the multiple water-bag model is developed for one-dimensional collisionless electrostatic waves, in terms of the initial value problem. Nonlinear frequency spectra are obtained in Van Kampen's formulation, and a new pole, already predicted by R. W. B. Best, appears for hot plasmas. This theory is successfully checked by a full numerical experiment of the Vlasov–Poisson system.

Resonant excitation of Alfvén waves by fast particles in a finite pressure plasma in a non-uniform magnetic field is studied. Plasma compressibility in the wave field is determined both by the curvature of the magnetic lines of force and finite Larmor radius of fast particles. A general expression for the instability growth rate is obtained and analyzed; the applicability of the results obtained in the previous paper has also been studied. The finite pressure stabilization of the trapped particles instability has been found. The bounce-resonance effects are analyzed.

Using the two-fluid approximation, we summarize properties of linear waves in an unbounded magnetized relativistic plasma by a parameter-space diagram of wave phase velocity: a relativistic plasma pond.

In this paper we consider relativistic interaction of an overdense plasma with very intense electromagnetic waves. Nonlinear coupling of dispersive waves in the presence of an ambient magnetic field is investigated. Lorentz transformation together with rotations of the co-ordinate system are employed to obtain analytic solutions. Two cases with variable gamma factors are treated in detail: in one case the magnitude of the electric field remains constant in the transformed frame; in the other no restriction is made to the electric field, but the total stream velocity vanishes in the transformed frame. Numerical illustrations of various modes for these two cases are depicted graphically.

This paper is concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized electron–ion plasma. These nonlinear waves are of fixed profile, superluminous, period.ic and transverse. The small perturbations are assumed to propagate in the same direction as the nonlinear wave. A Lagrangian method is used to derive the perturbation equations. The analysis is carried out in the frame where the nonlinear waves are space independent and then the results Lorentz transformed to the laboratory frame. Part 1 refers to circularly polarized waves. In this case it is possible to integrate the equations and obtain an algebraic dispersion relation in the form of an eighth order polynomial equation in the frequency. The analytical and numerical solution of this equation, for a wide range of variation of the parameters involved, reveals the existence of a very unstable mode. Particular attention is given to very large wave amplitudes for which the plasma behaves like an electron–positron plasma; in this case the growth rate of the unstable mode can be as high as the frequency of the nonlinear wave.

The tracing of the geometrical optics rays in toroidal geometry and in the electron-cyclotron frequency range has been done numerically. The results presented are relevant to the extraordinary-mode propagation and conversion at the upper-hybrid resonance layer. High-density regime refraction effects, together with strong bending of the warm Bernstein rays along the toroidal direction and resonance-cone structure generation, are the main features of the numerical output.

The potential energy of an ideal static MHD plasma is minimized using the invariants of motion as variational constraints and assuming a general symmetry (dependence on two space variables only). For simplicity only the plasma-on- the-wall case is considered. The first variation yields a generalized Shafranov equation, the second the desired stability criterion. It is found that equilibria with a longitudinal current increasing monotonicaily towards the boundary are always stable with respect to symmetric modes. For equilibria with an outwardly decreasing current a sufficient criterion (for symmetric modes) is derived, which only requires the solution of a linear eigenvalue problem. The theory is applied to the straight circular cylinder and to the axisymmetric torus.