Cross-modulation in plasma is an electromagnetic wave interaction in which the modulation of one ‘disturbing’ wave is imposed nonlinearly on the transport properties of the medium, and thence onto a second, ‘wanted’ wave propagating linearly through it. This analysis is restricted to weakly ionized plasma with allowance for ambient magnetic field, as in the lower ionosphere. A kinetic description is used, based on the Boltzmann equation for the electrons, with electron-molecule collisions described by Boltzmann's collision integral. Because of the small mass ratio this simplifies to a differential form. The perturbation of the electron velocity distribution function f(v, t) due to the disturbing wave is calculated up to terms quadratic in wave amplitude, which are the lowest order to show the effect. The part of the term quadratic in wave amplitude at zero times the fundamental frequency, and isotropic in velocity space, which represents the perturbation in electron energy distributions, is selectively enhanced by an inverse factor of mass ratio, since the excess energy imparted by the wave to the electrons is transferred collisionally to the molecules at a rate inversely proportional to mass ratio. Modulation of the wave induces modulation of the electron energy distribution. A more general expansion scheme, in velocity-space spherical harmonics, is also presented. To calculate the dispersion relation for the second, ‘wanted’ wave, the linear part of the disturbing wave analysis is adapted, and the amplitude of the wanted wave is given in the WKB approximation as a phase integral of the refractive index along the ray path; this contains moments of the electron energy distribution and is modulated. The predictions of older semi-empirical theories, that the effect is enhanced when the fundamental frequency of the disturbing wave is close to the electron gyrofrequency, and that the second harmonic of the modulation is also imposed on the wanted wave, are confirmed. The wanted wave is predominantly amplitude-modulated, and only amplitude modulation of the disturbing wave is picked up; phase modulation is not transferred. There is no cross-modulation if the collision frequency is independent of collision speed, when contributions from all parts of velocity space cancel.

The stability of a viscous and heat-conducting plasma is considered, with temperature and density gradients arranged so that the resulting pressure is homogeneous, as suggested by some experiments on laser-plasma interactions. Gravity and magnetic field effects are ignored throughout. A non-dissipative fluid is considered first. Under the assumption of an Epstein profile for the equilibrium temperature, the dispersion curves for the propagation of sound waves are determined using a relaxation technique applied to a second-order spheroidal boundary-value problem for mode numbers 1,…, 5: it is found that these modes may be destablized by inhomogeneity. The dynamics of vorticity is analysed in the framework of the WKB approximation, which allows reduction to a fourth-order boundary-value problem: this is tackled in the ‘quasi-classical’ limit by solution of the relevant Bohr-Sommerfeld eigenvalue problem. Convective flows arise in the classically accessible layers and evanesce outside. For the same Epstein temperature profile as above, two such layers are formed, in agreement with observation. Given the growth rate of the unstable flow, the modified Rayleigh number, the width of the convective layer and the temperature drop across it are calculated as functions of the transverse wavenumber and for mode numbers 1–5. Conversely, given the modified Rayleigh number, the growth rate is calculated. The modified Rayleigh number and the growth rate thus found have a minimum and a maximum respectively as functions of the wavenumber of the perturbation. These can be taken as the most favourable values for convection to develop. The value of the wavenumber at which these extrema are attained can be used to determine the aspect ratio of the convective cells.

An analysis is presented of linear stability against tearing modes of a current sheet formed between two oppositely magnetized plasmas forced towards each other in two-dimensional steady stagnation-point flow. The velocity vector in this flow is confined to planes perpendicular to the reversing component of the magnetic field. The unperturbed state is an exact resistive and viscous equilibrium in which the resistive diffusion outwards from the current sheet is exactly balanced by the inward motion associated with the stagnation-point flow. Thus the behaviour of the tearing mode can be examined even when the resistive diffusion time is comparable to or smaller than the growth time of the instability. The linear ordinary differential equation describing the mode structure is integrated numerically. For large Lundquist number S and viscous Reynolds number Re the Furth-Killeen-Rosenbluth scaling of the growth rate is recovered with excellent accuracy. The influence of the stagnation-point flow on the tearing mode is as follows: (i) long-wavelength perturbations are stabilized so that the unstable regime falls between a short-wavelength and a long-wavelength marginal state; (ii) for sufficiently low Lundquist number (S < 12.25) the current sheet is completely stable to tearing-mode perturbations; (iii) the presence of high viscosity reduces the growth rate of the tearing instability. This effect is more important at small wavelength. Finally, application of the results from this study to the problem of solar-wind plasma flow past the earth's magnetosphere is briefly discussed.

Some properties of the frequency spectrum of magnetic fluctuations in a tokamak two-species plasma are investigated. We start from the nonlinear resistive ballooning kinetic equation. A method based on the fluctuation-dissipation theorem of thermodynamics is employed. The frequency range |ωDe|/ω>|ω*e| is considered. The dependence of magnetic fluctuations on frequency and various macroscopic parameters is discussed. The influence of magnetic fluctuations on plasma thermodynamics is investigated.

Using the magnetohydrodynamic model, the evolution of a resistive plasma can be represented as a relaxation through a sequence of force-free equilibrium states. We show, by extending existing work, that this process is equivalent to magnetic field diffusion in a strongly anisotropie static conductor. The latter evolution is easier to simulate numerically, and is carried out for laboratory based plasmas confined in cylinders and toroids. We obtain a variety of universal equilibrium profiles that are consistent with experiment and relaxation theory and that predict the existence of states arising in reversed-field pinches. The existence of a critical axial flux is predicted about which there exist stable modes of operation corresponding to high and low current. We also show the existence of a critical aspect ratio at which it is most desirable to build toroidal devices. This corresponds to the value at which maximum current, for a fixed driving field, can be generated.

A plasma with a boundary transition layer of variable depth in the presence of a powerful electromagnetic field is considered. It is shown that a displacement of the boundary will grow, and will propagate as a nonlinear surface wave in the direction in which the depth of the transition layer decreases.

Coherent low-frequency oscillations whose frequency is lower than the ion plasma frequency are generated by a mesh grid with negative d.c. bias in a double-plasma device. The frequency is inversely proportional to the one-quarter power of the grid voltage under a fixed plasma density, and is proportional to the ion plasma frequency when the grid bias is kept constant. With potential profiles near the grid, which are measured by an emissive probe, the transit time of ions is numerically calculated. The inverse of the transit time agrees well with the oscillation frequency. The oscillation is considered to be excited by a klystron bunching effect of incident ions towards the ion-rich sheaths.

The motion of a particle driven by a slow RF wave inside crossed electrostatic and magnetostatic fields is examined. A time-scale separation exists in the synchronous frame, moving at the slow-wave phase velocity, where all fields appear static in time and the cyclotron motion is much faster than the guidingcentre drift. The averaging of the periodic gyromotion is performed systematically with canonical transformations up to second order in the smallwave amplitude. The first-order guiding-centre drift follows the equipotential surfaces of the transformed electric field. The second-order effects, due to the field-line curvature, and/or the nonlinear variation in the wave phase velocity, cause departures from the parapotential flow. The topology of the trajectories depends on the departure of the drift velocity from synchronism with the wave. Various flow topologies corresponding to different values of the control parameters are examined.

An exact solution for the thermal (Xe) or particle (D) diffusivities is derived (up to a constant factor) for the diffusive model in terms of the Fourier coefficients of the perturbed Te (or ne) signals. The common assumptions of constant ne and Xe (or D) generally used in the standard analytical or semi-analytical solutions are not required, since their radial dependences are taken explicitly into account. The effect of a damping (sink) term in the heat equation can also be implemented easily.

The image approach, used extensively to treat bounded unmagnetized plasmas, is extended to the case of an arbitrary homogeneous and non-magnetic medium. A general dispersion relation for electromagnetic surface waves on a plane plasma-vacuum interface is thus obtained, subject only to the suitability of the chosen boundary conditions. The boundary conditions used here are those of Barr and Boyd. It is emphasized that this dispersion relation is applicable to magnetized plasmas. The general dispersion relation is applied to the special case of an isotropie medium, and the dispersion relation of Barr and Boyd for an unmagnetized plasma is reproduced. A major assumption in the image approach is that the semi-infinite bounded medium can be described by the infinite-medium response. The validity of this assumption and of the boundary conditions is discussed. Two conditions are deduced that must be satisfied for the image theory to be self-consistent. It is argued that these can be satisfied in all situations for which the assumed boundary conditions are appropriate.