The quantum Boltzmann collision operator is expanded to yield a degenerate form of the Fokker–Planck collision operator. This is analysed using Rosenbluth potentials to give a degenerate analogue of the Shkarofsky operator. The distribution function is then expanded about an equilibrium Fermi–Dirac distribution function using a tensor perturbation formulation to give a zeroth-order and a first-order collision operator. These equations are shown to satisfy the relevant conservation equations. It is shown that the distribution function relaxes to a Fermi–Dirac form through electron–electron collisions.

It is found on the KT-5C tokamak that an edge fluctuation can be excited using a pair of floating Langmuir-probe pins. This fluctuation propagates along the magnetic field, with its amplitude decreasing drastically when it is off the magnetic field line, which is similar to the results obtained from experiments on the TEXT tokamak. Moreover, our experimental observations indicate that the excited fluctuation propagates with the electron directional motion, and is mainly manifested in an electron density fluctuation. Physically, this excited fluctuation could be considered as modulation of the external electric field by electrons, and is carried by the electron directional motion wherever it goes. These results are in good agreement with the proposed ballistic model that can be derived by solving the linearized Vlasov equation.

An intense short laser pulse or a millimetre wave propagating through a plasma channel may act as a wiggler for the generation of shorter wavelengths. When a relativistic electron beam is launched into the channel from the opposite direction, the laser radiation is Compton/Raman backscattered to produce coherent radiation at shorter wavelengths. The scheme, however, requires a superior beam quality with energy spread less than 1% in the Raman regime.

In an experiment carried out in a linear, unmagnetized plasma, evolution and propagation of nonlinear, rarefactive ion–acoustic pulses have been investigated. The nonlinear rarefactive pulse is observed to undergo fissioning as it propagates. Measurements of the ion velocity distribution function within the pulse indicate strong modifications of the distribution functions at velocities in the neighbourhood of the ion acoustic speed. Wave–particle interaction is thus shown to play an important role in the observed behaviour. Large-amplitude rarefactive pulses, while showing multiple fissioning, also exhibit a large-amplitude, low-frequency (≈30 kHz) oscillatory tail, downstream of the main pulse. The oscillatory tail is unlike the expected Airy function that normally accompanies a weakly nonlinear rarefactive pulse. The observations suggest the existence of ion-hole-like structures on the downstream side. The mechanism of the excitation seems to be through modification of the ion phase space due to trapping of ions in the negative potential well of the rarefactive pulse.

The wavelengths and attenuation coefficients of dipolar left and right-hand circularly polarized waves in a radially inhomogeneous axially magnetized plasma column are computed by means of step approximation of the radial plasma density profile. A comparison with theoretical results assuming radial plasma homogeneity shows that the radial plasma inhomogeneity is significant for wave propagation. In particular, it facilitates the occurrence of backward waves and increases by up to one order of magnitude the wave attenuation coefficient compared with a homogeneous plasma column having the same average plasma density.

We present a covariant theory of photon acceleration in time-varying plasmas. This is a ray-tracing model for frequency upshift of waves interacting with relativistic plasma perturbations, such as ionization fronts and plasma wakefields. This theory explores the formal analogy between a photon in a plasma and a relativistic particle with a finite rest mass. The covariant ray-tracing theory is applied to the case of photon acceleration by a modulated wakefield. Threshold criteria for transition to chaos are derived.

A stability criterion for axisymmetric modes of ideal MHD equilibria without wall stabilization is derived for linear profiles with vanishing current density at the edge. Using perturbation theory, the critical half-axis ratio of the elliptical cross-section is computed for finite aspect ratio.

Transverse focusing or filamentation of weakly nonlinear Alfvén waves propagating in a dispersive medium is studied using an amplitude-equation formalism. Special attention is devoted to the small-β regime, where kinetic effects are weak and Alfvén-wave trains are unstable to convective filamentation. It is shown that, according to their initial duration, focusing wave packets can collapse in a finite distance or, conversely, the focusing can be arrested by the development of magnetosonic waves, which in both cases may lead to the formation of sharp acoustic fronts. This effect, which dominates the usual longitudinal steepening, provides an efficient mechanism to heat the plasma without requiring large-amplitude waves. It can significantly contribute to the acceleration of the solar wind.

Using a kinetic model for low-frequency dust acoustic waves (DAW) in a dusty plasma, we have examined the effects of a dust-size distribution on their propagation and damping. Both Landau damping and damping due to dust-charge variation are included. We consider Gaussian and power-law dust-size distributions. In accordance with earlier results of Melandsø et al., we find that the dust Landau damping dominates at short wavelengths. At wavelengths longer than the Debye length λD0, the dust-charge variation is generally dominant. It is always dominant for the power-law size distributions that we have studied. We also find that if the upper and lower size limits of the dust are chosen so that the average dust size remains constant, regardless of the power-law exponent γ, the wave properties are practically identical to those of a monosize distribution of the average dust size. For a Gaussian dust-size distribution, Landau damping may be the dominant damping mechanism if the dust plasma is tenuous (P[Lt ]1) and the width of the distribution is large.

Expressions for the linear response tensor are derived using a covariant forward-scattering method for unmagnetized relativistic thermal distributions restricted to one-dimensional (strictly parallel) and two-dimensional (strictly perpendicular) motions. The freedom to make Lorentz transformations is used to generalize the strictly perpendicular distribution to a counterpart of the nonrelativistic Dory–Guest–Harris (DGH) distribution.

The linear response tensor for a relativistic counterpart of a bi-Maxwellian distribution is calculated in closed form for a magnetized plasma. The method used involves the following steps: (1) a covariant form of the response tensor for an arbitrary distribution of particles is derived using both a forward-scattering method and a covariant version of Vlasov theory; (2) the response tensor is evaluated for a strictly perpendicular, thermal distribution using a method due to Trubnikov; (3) the parallel distribution is built up by applying a Lorentz transformation to sum over a weighted, continuous distribution of parallel speeds. A convenient starting point for a detailed investigation of waves in such a plasma is the small-gyroradius approximation to the general expression for the response tensor, and the relevant approximation is derived and discussed briefly. The expansion of the general expression for the response tensor in Bessel functions in given in an appendix.

The transverse part of the linear response tensor is evaluated for a highly relativistic thermal electron gas, starting from Trubnikov's response tensor for an arbitrary temperature. Three contributions to the response tensor are important. The diagonal components are dominated by an unmagnetized term, which gives the familiar dispersion k2=w2p0, where wp0 is the proper plasma frequency. The difference between the diagonal components is larger in magnitude than the off-diagonal components, implying that the natural modes are nearly linearly polarized. This leads to a generalized form of Faraday rotation in which linear polarization is partially converted into circular polarization at a rate per unit path length ∝λ3 (λ=wavelength).

Parametric instabilities of upper-hybrid oscillations trapped in a plasma density depletion across an ambient magnetic field are investigated. Approximate dispersion relations are derived, which lead to the identification of two parametric instabilities of the localized upper-hybrid bounded wave structure. Both are related to trapped upper-hybrid oscillation resonances. The first is a decay to a frequency of a trapped wave resonance, downshifted from the applied frequency, where the downshift must be slightly larger than the lower-hybrid frequency. The second instability can exist when the applied frequency is slightly below the arithmetic mean of the frequencies of two trapped oscillation resonances; then the antiStokes component of one is in resonance with the Stokes component of the other. Both slab and two-dimensional geometries are considered.