The first critical fast Mach number is rigorously defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed. Above the first critical Mach number, resistivity alone is unable to provide all the dissipation needed for the required Rankine-Hugoniot shock jump. A survey of the dependence of the first critical Mach number upon upstream plasma parameters is needed to guide studies of the structure of collisionless shocks in space. We vary the upstream plasma beta, the upstream shock normal angle, and the ratio of specific heats for the plasma. The first critical Mach number depends sensitively upon upstream plasma parameters, and is between 1 and 2 for typical solar wind parameters, rather than the often quoted value of 2·7, which is valid for perpendicular shocks propagating into a cold plasma. We introduce the suggestion that the flux of superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the first critical Mach number. Our parametric survey indicates that this hypothesis might be most conveniently tested using interplanetary shocks.

The propagation of an electron-acoustic wave in a plasma consisting of two types of ion and two temperature electrons has been investigated in the linear and nonlinear regimes. The presence of the second species of ion modifies the characteristics of the wave. The analysis has been done for both the finite amplitude and the small amplitude case of the electron-acoustic solitary wave. The ion temperature ratio and the electron density ratio rather than the relative ion density are the effective parameters which govern the amplitude of the electron-acoustic soliton.

An analysis of profile modifications in laser-plasma interactions in the presence of an externally applied constant d.c. magnetic field is presented. By considering the case of circular polarization for the incident laser light, the flow velocities and the shelf densities in the incident as well as the evanescent regions are calculated. For left-handed circular polarization, the flow velocity in the incident region is enhanced by the magnetic field, whereas the opposite occurs for right-handed circular polarization. On the other hand, the shelf density in the evanescent region is always supercritical for the former case, and for the latter case it can be either subcriticai or supercritical, depending on the strengths of the incident laser intensity as well as the external magnetic field.

A phase integral (WKBJ) theory of damped modes in a resistive cylindrical plasma column is developed. The theory predicts several phenomena observed previously in numerical studies: (i) the complex frequency ω has a point spectrum lying on a locus which is approximately independent of the resistivity, and which intersects the ideal continuum only at its end points (at angles of 45° and 30°); (ii) the qualitative features are independent of current profile and m–number, provided |k.B| is monotonic and strictly positive; and (iii) the two branches of the spectral locus joining the two end points of the ideal continuum correspond to precisely defined ‘internal’ and ‘wall’ modes, and bifurcate from a ‘global’ mode at a certain complex frequency which can be predicted from the topological features of the Stokes diagram in the complex radial position plane. In order to derive consistent connexion formulae for reflexions from the wall, the magnetic axis, and from turning points, we reduce the resistive hydromagnetic equations to a scalar wave equation, uniformly valid over the entire plasma to two orders in an expansion in the square root of the resistivity. Good numerical agreement is found between eigenvalues from the full equations, the reduced equation, and from the WKBJ method.

Theoretical analysis for the stability of a diffusion dominated positive column between coaxial cylinders in the presence of an axial magnetic field is carried out under the assumptions of quasi-neutrality of charges and no sheath at the walls. Self-consistent infinitesimal perturbations of plasma density and electric potential, which satisfy the linearized governing equations to the same degree of approximation are used to derive the dispersion relation. The perturbations associated with aximuthal modes m ≤ 0 are stable for any gap size and plasma parameters. The stability of non-axisymmetric perturbations is studied for different gaps. It is found that the presence of inner cylinders increases the stability of a magnetized positive column and m = 2 defines the region of stability when the ratio of the radii of the inner and outer cylinders is less than 0·5. In the case of narrow gaps, higher and higher modes are excited. The minimum non-dimensional axial electric field at which the magnetized positive column between coaxial cylinders becomes unstable for different gaps is also determined.

An original method for calculating and representing the excitation coefficients of longitudinal electron waves is applied to the case of a hot, collisionless, homogeneous and isotropie plasma with a bi-Maxwellian velocity distribution function. Using a Van Kampen treatment we introduce a ‘wave density’ distribution which is represented graphically. When hot electrons are added to a plasma of cool electrons the Landau mode is distorted and its damping increases with the hot/cold temperature ratio θ. The Landau mode separates into two modes for θ ≥ θ0 where θ0 increases as the hot/cold density ratio α decreases. We show that no wave seems to be able to propagate at frequencies below the plasma frequency. Using an abrupt cut-off in the hot electron distribution function, we recover the results for a Maxwellian plus water-bag distribution.

Using the stationary phase method, a simple asymptotic analysis of a two-dimensional model of the coupling of the cold-plasma magnetosonic wave excited by an ion-cyclotron resonance heating (ICRH) antenna is presented. Such an analysis allows quick evaluation of the basic characteristics of the ICRH antenna radiation pattern and shows how the power spectrum radiated by the antenna and plasma dispersion properties combine to produce the power flux distribution observed in the far-field region. The results of the present simplified analysis are found to be in reasonably good agreement with more sophisticated coupling codes. This development thus serves as a simple analytic tool for quick investigation of the most fundamental features of coupling for antenna design studies. With a view to spectrum shaping for improved heating and tokamak RF current drive, the case of a phased antenna array is also analysed.

General expressions are derived for the energy density of electromagnetic waves in a cold collisionless magnetoplasma. Random as well as coherent waves are considered.

A diffusion equation for magnetic field lines of force in a turbulent magnetic field, which describes both the random walk of a single field line and how two nearby lines separate from each other, has been obtained using standard statistical techniques. Starting from such an equation, a closed set of equations for the moments may be obtained, in general, with suitable assumptions. From such a set of equations the Kolmogorov entropy may be explicitly calculated. The results have been applied to the most interesting examples of magnetic field geometries.

Two continued fraction expansions for the plasma dispersion function are given. The first is a very simple expansion for which error estimates can be obtained and which provides better approximations as the modulus of the argument increases. The second, while not so simple, provides whole range approximations.

The nonlinear propagation of a circularly polarized, electromagnetic wave in a collisional, infinite, magnetized plasma is considered. The presence of collisions leads to spatial variation in the amplitude of the wave field which gives rise to a time-independent ponderomotive force. The ponderomotive potential for a left (right) circularly polarized wave attains a maximum at the ion (electron) cyclotron frequency. In the vicinity of the cyclotron frequency it is shown to be always positive. A decrease in both the particle density and the real and imaginary parts of the complex wavenumber is shown to result from the effect of the ponderomotive force.

In this paper a new approach to the approximate solution of the MHD equilibrium equation is described. The axisymmetric equilibrium equation is first transformed to a time-independent Schrödinger equation and then solved by the Ritz method in a suitable rotational co-ordinate system, the validity of the solution being not limited to large aspect-ratio configurations. The zeroth-order approximation is analytically computed and the relationship between the poloidal beta and the shift of the magnetic axis is derived. To the same order, the adiabatic compression of the plasma ring is studied and a non-dimensional compression chart is obtained. Results of numerical computations of the higher orders are also reported.

The investigation of the kinetic cross-field streaming instability, motivated by the research of collisionless shock waves and previously studied by Wu et al., is discussed more fully in the present work. Since, in the ramp region of a quasi-perpendicular shock, electrons can be preferentially heated in the direction transverse to the ambient magnetic field, it is both desirable and necessary to include the effect of the thermal anisotropy on the instability associated with a shock. The present study has found that Te⊥ > Te‖ can significantly enhance the peak growth rate of the cross-field streaming instability when the electron beta is sufficiently high. Furthermore, the present analysis also improves the analytical and numerical solutions previously obtained.

The effects of a d.c. magnetic field on stimulated Raman sidescatter from laser-produced plasmas is studied. For exact sidescatter along the magnetic field, the Raman instability separates into two distinct decays in which the scattered light is either a right (RHCP) or left (LHCP) circularly polarized electromagnetic wave. Growth rates of the instabilities can be enhanced in the former case but are diminished in the latter. The magnetic field induced effects are greatest near the quarter critical density where frequency shifts can be especially significant, being equal to ± ¼Ωc for decay into RHCP and LHCP waves, respectively.

In the aforementioned paper we obtained an equation for non-linear Alfvén waves in a finite-β plasma, and investigated envelope soliton solutions thereof. The purpose of this note is to point out an error in the derivation of the soliton envelopes, and present corrected expressions for these solitons.

The error arises from our assumption of translational invariance of both the envelope and phase of an envelope soliton expressed in equations (16) and (17). Rather, the phase is related to the amplitude by where y ≡ x — VEt is a comoving co-ordinate, and all other quantities are defined in the above paper.