Equilibrium of non-neutral clouds in a toroidal vessel with toroidal magnetic field is demonstrated in the presence of a toroidal current, finite mass and finite pressure. With a toroidal current, it is shown that in a large-aspect-ratio conducting torus the equilibrium is governed by competition between forces produced by image charges and image currents. When (where Er and Bθ are the self electrostatic and self magnetic fields of the cloud), the confinement is electrostatic and plasma shifts inwards; when the confinement is magnetic and plasma shifts outwards. For there is no equilibrium. With finite mass or finite pressure, it is shown, in a large-aspectratio approximation, that the fluid drift surfaces and equipotential surfaces are displaced with respect to each other. In both cases the fluid drift surfaces are shifted inwards from the equipotential surfaces.

The coupling coefficients for resonant three-wave interaction of magnetosonic and Alfvén waves, derived by means of kinetic theory, are presented. The calculations allow for anisotropic background temperatures. The results are compared with previous ones from fluid theory.

The collisional relaxation of various plasma distributions that are initially far removed from thermal equilibrium is investigated numerically using a Fokker–Planck code. It is shown that self-similar and kappa distributions do not remain self-similar or kappa, and that this is due to the velocity dependence of the effective collision frequency. For the relaxation of an isotropic two temperature plasma it is shown that a constant-temperature three-component distribution function is a plausible model for analytical calculations. Investigation of the relaxation of bi-Maxwellian plasmas resolves some discrepancies that have arisen from earlier studies.

A new theoretical model to study surface wave–particle interaction in a cylindrical plasma has been developed. This model is based on linear resolution of the Vlasov equation, with the specular reflection hypothesis. Expressions for the breakdown time of the linear solution and for the rate of increase of kinetic energy per electron, as a function of the critical parameters, have been obtained.

The collisionless Vlasov–Poisson system in the drift approximation is examined for the existence of maximum-entropy nonlinear coherent solutions in the steady state. Two major nonlinear effects are taken into account. The first is the velocity-space trapping of particles, leading to closed trajectories in phase space. The second is the physical-space trapping of particles, leading to closed trajectories in the plane perpendicular to the magnetic field. The regions of validity of these nonlinearities are discussed and their relative importance demonstrated. Numerical solutions of the equations describing the nonlinear stationary states in one and two dimensions are presented.

The hydrodynamic echo on the surface helicon-type modes radiated to vacuum in a magnetized plasma with steepened density profile is investigated. It is shown that perturbations induced by an initial pulse at the plasma boundary are modulated by a later applied second pulse of different wavelength, to yield a non-vanishing echo signal, which can be radiated to vacuum. The angle of the radiation and the density of the energy flow of this signal are determined.

The convection mode in a collisional plasma is investigated, with the inclusion of electromagnetic effects. It is shown that a dissipative instability can occur. The relationship to several well-known modes as well as applications to typical low-temperature plasmas are discussed.

A generalized Lorentzian (kappa) particle distribution function is useful for modelling plasma distributions with a high-energy tail that typically occur in space. The modified plasma dispersion function is employed to study the instability of ion-acoustic waves driven by electron drift in a hot isotropic unmagnetized plasma modelled by a kappa distribution. The real and imaginary parts of the wave frequency ω0 + ιγ are obtained as functions of the normalized wavenumber kλD, where λD is the electron Debye length. Marginal stability conditions for instability are obtained for different ion-to-electron temperature ratios. The results for a kappa distribution are compared with the classical results for a Maxwellian. In all cases studied the ion-acoustic waves are strongly damped at short wavelengths, kλD ≫ 1, but they can be destabilized at long wavelengths. The instability for both the kappa and Maxwellian distributions can be quenched by increasing the ion-electron temperature ratio Ti/Te. However, both the marginally unstable electron drift velocities and the growth rates of unstable waves can differ significantly between a generalized Lorentzian and a Maxwellian plasma; these differences are also influenced by the value of Ti/Te.

We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.

A representation of the physical fields as functions on (k, ω, r, t) phase space can be based on Gaussian windows and Fourier transforms. Within this representation, we obtain a very general formula for the second-order nonlinear current J(k, ω, r, t) in terms of the vector potential A(k, ω, r, t). This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasmas, including the effects of inhomogeneous turbulence, wave convection and refraction.

A perfectly conducting hot plasma in thermodynamic equilibrium is studied without taking account of the effects of collisions and viscosity. The medium is inhomogeneous, unbounded, axisymmetric and subject to a magnetic field B0 parallel to the axis of symmetry of the cylinder. Plasma equilibrium is investigated using a magnetohydrodynamic model, and the system of equations is closed with an equation of state corresponding to the adiabatic law for an ideal gas. Transformation groups are applied to generate asymptotic selfsimilar solutions for the density, pressure and magnetic field magnitudes on the equilibrium, and thus to obtain the spatial dependence of the invariant solutions since the temporal variable is eliminated. From consideration of the nature of these solutions, necessary conditions for equilibria in finite inhomogeneous media are obtained. Results are given for inhomogeneous media with finite conductivity. The degrees of inhomogeneity for pressure and density and their relations with dimensionless constants, arising from the group parameters, provide information on certain drastic changes in equilibrium temperature profiles.

Stimulated emission of ordinary plane-polarized electromagnetic waves propagating in the axial direction by a relativistic or non-relativistic electron beam is investigated using a new quantum kinetics based on the Dirac equation. The momentum and energy conservation laws and the time-reversal invariance of the transition probability are used explicitly to calculate the gain without expanding the transition rate as a power series in ħ. It is found that electroncyclotron masing occurs when the longitudinal temperature differs greatly from the transverse temperature for any beam energy. This electron-cyclotron masing is an individual-electron effect, which is not related at all to the phase bunching.

The effect of finite spectral width on the modulational instability of Alfvén waves described by the derivative nonlinear Schrodinger equation is investigated using a method developed by Alber to derive a transport equation for the spectral density. The dispersion relation for a monochromatic wave is regained for a delta spectrum. It is shown that the growth rate and domain of modulational instability diminish as the spectral width increases for both the Gaussian and uniform spectrums.