A pseudo-spectral three-dimensional Strauss-equations code is used to describe internal disruptions in a strongly magnetized, electrically-conducting fluid, with and without an externally applied, axial electric field. Rigid conducting walls form a square (x, y) boundary, and periodic boundary conditions are assumed in the axial (z) direction. Typical resolution is 64 × 64 × 32 and the maximum Lundquist number is approximately 400. The dynamics are dominated by a helical current filament which wraps itself around the axis of the cylinder; parts of this filament can sometimes become strongly negative. The ratio of turbulent kinetic energy to total poloidal magnetic energy rises from very small values to values of the order of a few hundredths, and executes ‘bounces’ as a function of time in the absence of the external electric field. In the presence of the external electric field, the first bounce is by far the largest, then the plasma settles into a non-uniform quasi-steady state characterized by a poloidal fluid velocity flow. At the large scales, this flow has the shape of a pair of counter-rotating bean-shaped vortices. The subsequent development of this fluid flow depends strongly upon whether or not a viscous term is added to the equation of motion. Inclusion of viscosity tends to damp the flow and leads to pronounced subsequent bounces suggestive of sawtooth oscillations, though the first bounce remains substantially the largest. By means of a three-mode (Lorenz-like) truncation of the Strauss equations, the evolution of the largest spatial scales alone may be examined. Some time-dependent solutions of the low-order truncation system suggest qualitative agreement with fully resolved solutions of the Strauss equations, while other solutions exhibit interesting dynamical-systems behaviour which is thus far unparalleled in the fully-resolved simulation results.

Dimensional analysis is used to predict the functional relationships amongst the characteristic variables of the ablation of a cold dense fluid by an imposed external heat source. From these relations, self-similar limiting forms are identified and evaluated. Numerical simulation is used to investigate the interpolation between these limits. Self-similar forms generalizing well-known existing solutions of relevance to laser-plasma are demonstrated and include a general proof of Nemchinov's hypothesis for the heating of small targets of limited mass.

Kinetic theory, including ion Larmor radius effects, is used to analyse the Alfvén wave heating of cylindrical plasmas using axisymmetric waves excited by an antenna at frequencies up to the ion cyclotron frequency. At the Alfvén resonance position, the compressional wave is mode converted to a quasi-electrostatic wave (QEW) which propagates towards the plasma centre or edge depending on whether the plasma is hot or warm. The energy absorbed by the plasma agrees with the MHD theory predictions provided the QEW is heavily damped before reaching the plasma centre or edge; if it is not, then QEW resonances may occur with a consequent increase in antenna resistance. The relation between ion cyclotron wave resonances and QEW resonances in a hot plasma is shown. The behaviour described above is demonstrated by numerical solution of the wave equations for small and large tokamak-like plasmas. WKB theory has been used to derive useful expressions which quantify the QEW behaviour.

The effect of toroidal geometry upon the distribution function of weakly RF-heated minority ions in a tokamak plasma is considered. An analytic scheme to solve the corresponding bounce-averaged Fokker-Planck equation is developed and explicit solutions are given in the limits of high and low velocities. It is found that trapped-particle effects may significantly reduce the RF-induced anisotropy in the distribution function.

Recent laboratory measurements of plasma expansion in a plasma wake experiment are compared with analytical expressions which approximate the plasma expansion model of Crow, Auer & Allen. Good quantitative agreement was found between the data and theory for the velocity and position of the ion expansion front. These results provide an important insight into the behaviour of the expansion early in its development.

Second-harmonic generation of an extraordinary wave is investigated in the domain of phase synchronism with the pump wave. The conversion efficiency parameter is calculated for various values of the magnetic field, electron plasma density, angle of propagation and slab thickness.

The magnetic fields associated with plasmas frequently exhibit small-amplitude MHD fluctuations. It is useful to have equations for the magnetic field averaged over these fluctuations, the so-called mean field equations. Under very general assumptions, it is shown that the effect of MHD fluctuations on a force-free plasma can be represented by one parameter in Ohm's law, which is effectively the coefficient of electric current viscosity.

Lie group transformations are found which allow the removal of background inhomogeneity and non-steadiness from the nonlinear Schrödinger equation for the envelopes of HF waves. Background profiles are determined for which this removal can be realized.

The linear stability of steady flow of an inhomogeneous, incompressible hydromagnetic fluid is considered. Circle theorems which provide bounds on the complex eigenfrequencies of the unstable normal modes are obtained. Sufficient conditions for stability follow in a number of special cases.

With an infinite system of balance equations, derived from the Boltzmann equation, conductivity expressions are obtained in the form of three-term recurrence relations leading to continued fractions. Without collisions, only Landau damping causes attenuation. Its modification by collisions is illustrated for some simple collision models.

Relativistic electron beams propagating in plasma broaden as electric and magnetic fields scatter them. We calculate the beam spreading expected from errors in the ambient magnetic field, and from both electrostatic and magnetic waves generated by the beam itself. All these effects can be important in contemplated experimental regimes. Beam expansion can serve to set limits on the strength, size and phase velocity of caviton waves. Beam-driven magnetic waves can scatter beams effectively even if applied field errors are small. This can affect schemes for transport of beams in inertial fusion, and plasma heating schemes.

The theory of resonant electron diffusion as an effective saturation process of the auroral kilometric radiation has been formulated. The auroral kilometric radiation is assumed to be amplified by the synchrotron maser instability that is driven by an electron distribution of the loss-cone type. The calculated intensity of the saturated radiation is found to have a significantly lower value in comparison with that caused by the quasi-linear diffusion process as an alternative saturation process. This indicates that resonant electron diffusion dominates over quasi-linear diffusion in saturating the synchrotron maser instability.

The boundary term in the energy integral (105) is superfluous and should be dropped. If we use the Jacobian relation (86) to transform the dummy variables of integration from ψ, θ, to x, y (recalling that B = Bmax = const. at the ends), we see that this term reduces to the integral of a fixed function of x and y over a fixed region of the (x, y) plane. In other words, it reduces to a pure constant.