The stimulated backscattering of electromagnetic ordinary waves from extraordinary waves propagating normal to a magnetic field in a plasma of finite length is studied. A pair of coupled differential equations for the amplitudes of the backscattered and scatterer waves is derived from Maxwell's equations and the moment equations for an inhomogeneous magnetized plasma. Solution of the coupled equations for a homogeneous plasma yields an expression for the growth rate of the absolute instability as a function of plasma length and damping rates of the product waves. The convective regime in which only spatial amplification occurs is discussed. A numerical study of the effects of the magnetic field on Raman and Brillouin backscattering is presented.

Self-similar solutions of the magnetogasynamic equations are derived which describe the resistive decay of a plane current sheet in a compressible plasma. Such current sheets are thought to provide the magnetic energy storage in solar flares. They also occur at the boundaries between regions containing different magnetic-field directions in interplanetary space, and at the interface between the solar wing and the earth' magnetic field. It is shown that the resistive decay of a current sheet in a compressible plasma must involve plasma motion. The convective effects associated with this motion are incorporated in the analysis; the inertia effects are not. The electrical and thermal conductivities are taken to be constant, but the analysis may easily be generalized to include realistic temperature and magnetic field dependences of these quantities. Radiative and viscous terms are not included. The ordinary differential equations resulting from the similarity hypothesis are solved numerically, yielding curves of the plasma density, temperature, and velocity, as well as of the magnetic and induced electric fields, as functions of the similarity variable. The non-dimensional groups of importance are: y, the ratio of specific heats at constant pressure and constant volume; Kx, the ratio of thermal to resistive diffusivity; β∞, the ratio of plasma pressure to magnetic pressure at large distances from the current sheet. The first of these ratios is kept constant and equal to 5/3, corresponding to a monoatomic gas. The behaviour of the solution when the other two ratios are varied is investigated. The plasma velocity at large distances from the current sheet does not vanish in these solutions. It is always directed toward the sheet. However, when the diffusivity ratio K∞ is small, plasma flow away from the centre of the sheet also occurs in two narrow regions, one on each side of the centre. As a result of the reversals in the flow direction, the density then displays a relative minimum at the centre of the sheet with two outward travelling maxima adjacent to it. The plasma temperature at the centre of the sheet becomes very large for small K∞ and β∞ The expansion of the sheet becomes explosive and inertia effects can no longer be neglected. The physical meaning of these results is discussed and directions for further research are outlined.

Magnetoacoustic waves were generated in an argon plasma by passing an RF current through a solenoid antenna surrounding the plasma column. The complex impedance of the antenna was measured as a funcion of wave frequency in order to investigate the column geometric resonances and to obtain estimates of ion density and electron temperature. Although this technique yielded reliable estimates of the ion number density, the wave &litudes near resonance were found to be anomalously low and reliable temperature measurements could not be obtained.

A solution to the Grad–Shafranov equation is obtained by expanding the MHD equilibrium functions in half-integer powers of the poloidal flux, about the magnetic axis. The poloidal angle dependence of the expansion coefficients is solved for, from a sequence of ordinary linear differential equations with constant coefficients. Flux conservation is achieved after calculating the inverse rotational transform, by requiring it to be invariant during the pressure rise.

The stability problem of the double layer (electrostatic shock) is investigated using a simple model of the plasma. It is shown that local Penrose-stability in general is insufficient for global stability, owing to the existence of linerly unstable trapped Langmuir modes in the density cavity. An additional requirement for stability is that the thickness of the layer must be smaller than a critical value, which in the case of a strong layer (eΔπ/κTe ≫ 1). and for the particular model being used, is of the order (eΔπ/κTe)½ λD. Various qualitative features of the instability mechanism are discussed in terms of normal mode coupling, and quantitative results, such as mode frequencies, growth rates etc., are obtained by means of a conventional perturbation approach, which, in addition to the results expected from coupled mode theory, also shows the existence of two purely decaying modes, appearing for a sufficiently thin, stable layer. The double layer formation process is briefly commented on, and some distinguishing features of the instability in this regard are pointed out.

The general coupling coefficient for three electromagnetic linear modes of an inhomogeneous and relativistic plasma is derived from the oscillation-centre viewpoint. A concise and manifestly symmetric formula is obtained; it is cast in terms of Poisson brackets of the single-particle perturbation Hamiltonian and its convective time-integral along unperturbed orbits. The simplicity of the compact expression obtained is shown to lead to a new insight into the essence of three-wave coupling and of the Manley–Rowe relations governing such interactions. Thus, the interaction Hamiltonian of the three waves is identified as simply the trilinear contribution to the single-particle (new) Hamiltonian, summed over all non-resonant particles. The relation between this work and the Lie-transform approach to Hamiltonian perturbation theory is discussed.

Structures of the current layer between two magnetized anisothermal plasmas are studied on the basis of a kinetic formulation. It is shown that the structure of the current layer is dominantly controlled by the hotter species of the plasmas. The thickness is characterized by the ion gyroradius if the ion temperature is much greater than the electron temperature. The structure is, in general, insensitive to the asymptotic potential difference and the relative flow velocity between plasmas on the two sides.

The stability of cylindrical flux surfaces in the presence of finite resistivity and parallel ion viscosity is reconsidered, and in particular the increment in the logarithmic derivative Δ(Q) over the inner dissipative region. Correction of the viscosity coefficient removes the branch-point behaviour at large growth rates reported earlier. Numerical results for real Q in the high-beta hard-core pinch are supported by mathematical analysis to show that parallel ion viscosity renders Δ(Q) positive definite provided D < 0, with a positive minimum increasing with temperature. This stabilization is associated with coupling of the parallel plasma motion in the presence of magnetic field curvature. The viscous compressible value of Δ(Q) is somewhat less than its inviscid compressible counterpart at small real Q, so that relative to purely compressible theory parallel ion viscosity can be slightly destabilizing.

Soliton formation at the upper hybrid frequency has been discussed recently on the basis of warm two-fluid theory. In this paper we report the results of a reductive perturbation theory analysis of the Vlasov equation describing the nonlinear modulation of electrostatic waves in a warm magnetized plasma. This approach allows a treatment of soliton formation with scale lengths of the order of, or less than, the electron Larmor radius rL for both upper hybrid and Bernstein waves. A three-dimensional generalized nonlinear Schrödinger equation has been found. Contributions to the nonlinear frequency shift derive from three distinct processes. One contribution describes the generation of the second harmonic governed by (ω + ω) → 2w where ω is the frequency of the electrostatic carrier; a second arises from the self-interaction between the high-frequency waves (ω + ω → ω + ω) while the third contribution describes the nonlinear coupling between the carrier and the slow background plasma motion.

Propagation orthogonal to the magnetic field is studied and leads to a simplified nonlinear Schrodinger equation with cubic nonlinearity, predicting soliton formation at the upper hybrid and cyclotron harmonic frequencies. Expressions for the nonlinear frequency shift coefficient are presented for the upper hybrid and Bernstein modes in the low temperature limit and the relative strengths of the three competing nonlinear processes are compared. For krL ≥ 1·0, numerical analysis shows the dominant nonlinearity to be that arising from the nonlinear wave-particle interaction. The stability of the soliton solution is determined by the relative signs of the dispersion and the nonlinear frequency shift coefficient. Some properties of upper hybrid and Bernstein solitons are examined. In particular the variation of the normalized dispersion and nonlinear frequency shift coefficient with the basic plasma parameters (krL)2 and (ωpe/Ω, is presented, where (ope, fi are the electron plasma frequency and electron gyrofrequency respectively. Regions of instability are identified for both upper hybrid and Bernstein modes. The connection between reductive perturbation theory and previous warm fluid theories is also established.

The problem of a monochromatic plane electromagnetic wave incident from a vacuum onto a plasma slab is considered. The method of solution is based on the representation of the disturbance in the plasma layer as that generated by an appropriate current source in the complementary regions into which, for the purpose of the representation, the plasma is conceived to extend. The normal incidence case is treated first for both the specular reflexion and the absorption boundary conditions, with the extension to oblique incidence following in a later section of the paper.

Observations show a second harmonic spectrum which is broadened and shifted towards the low-frequency side of the true harmonic. A theoretical description of this effect is given based on the assumption that plasma waves generated by resonant absorption at the critical surface are coupled to a series of side-bands via an ion sound wave, and the resultant broadening of the plasma wave spectrum is reflected in the second harmonic emission. If the ion sound wave is propagating outwards, it is shown that, for suitable parameters, a large number of side-bands on the low-frequency side can be excited, giving a spectrum in good agreement with experimental results.

Parametric decay of magneto-acoustic oscillations in a cylindrical plasma column is considered, including the Hall effect and the effects of finite resistivity. Growth rates for axisymmetric modes in decay instabilities are derived and applied to the problems of parametric excitation of Alfvén waves and supplementary heating of plasmas. It is shown that both the slow (ion cyclotron) and fast (compressional) modes may be parametrically excited. The threshold &litudes for nonlinear dissipation of pump field energy are calculated and briefly discussed.

The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrödinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrödinger equation are re-examined and found to be more restrictive than previously stated.

We consider the diffusion of a magnetic field in a stationary medium where the electrical conductivity along field lines (σ∥) differs from that across them (σ⊥), and by showing that in the limit σ⊥/σ∥ → 0 the fields remain force-free, some unusual features of force-free evolution are clarified.

This paper considers nonlinear interaction between three monochromatic waves in a hot non-uniform electron plasma. With the aid of coupled mode theory the interaction of three longitudinal waves is studied and a specific case of the interaction of two longitudinal waves and one perpendicular wave is derived for the limiting case of long wavelength. Furthermore, the non-uniformity involves generalization of the theory of the interaction of two transverse waves and one longitudinal wave of a previous contribution.

The propagation of a linear wave packet in a generally dispersive, but non- absorbing, medium is considered. By an extension of the principle of stationary phase to higher inverse order in time, an approximation is derived that encompasses both the main signal propagating at the group speed, and the precursors that precede and follow it.

In this note we investigate the stability of large-amplitude longitudinal relativistic plasma waves. We find that they are secularly stable, that is, small perturbations grow in time proportional to time but not exponentially with time. Similar results have recently been obtained for transverse waves by Romeiras (1978)

A theory for the free expansion of a plasma with two electron temperatures is presented. It is shown that in the case of a laser-produced plasma expansion the ions separate into a fast and a slow component, and that the number of fast ions is particularly sensitive to the hot to cold electron temperature ratio. If the electron temperature ratio is ≳ 10 then the quasi-neutral self-similar solution breaks down. The regions in the rarefaction expansion where the quasi-neutrality assumption fails are discussed.

This paper provides an analysis of the propagation characteristics of ion cyclotron waves in a magnetized plasma whose density varies in a direction perpendicular to the ambient magnetic field. It is shown that the component of the wave energy flux across the density stratification is conserved except at a critical level (which is associated with a resonance singularity in the wave equation) at which the jump in the wave energy flux is balanced by wave absorption by the plasma. The relationship of this behaviour with field line resonance is briefly discussed, as is its possible relevance to ULF waves propagating in the vicinity of the earth's plasmapause.

Convective instability of a weakly ionized plasma contained in a narrow gap between two metal cylinders is studied considering non-axisymmetric waves. The case with the applied magnetic field in the azimuthal direction due to a central electrode is treated. The results show that the non-axisymmetric waves are more stable than their axisymmetric counterparts.