The asymptotic solution of the system of Vlasov and Maxwell equations for a plasma slab with a given current distribution is derived for weak absorption and weak equilibrium density inhomogeneity, but without the usual restriction that the perpendicular wavelengths be larger than the Larmor radii of the thermal particles. The equilibrium magnetic field is homogeneous. No model equations or phenomenological assumptions are introduced, except that the interaction of the components of the electric field parallel and perpendicular to the equilibrium magnetic field (corresponding to the ordinary and extraordinary waves in a homogeneous plasma) has been neglected. The electric field in vacuum is determined by a condition on the analytical form of the Fourier transform of the field that must necessarily also apply to the exact solution. The example presented to illustrate the results considers the emission at the harmonics of the electron gyrofrequency of a population of fast electrons in a plasma with cold ions; the theoretical results are in a very good qualitative agreement with experiment.

The reductive perturbation method is employed to investigate the excitation of ion-acoustic solitons in an ion-beam—plasma system consisting of warm ions and isothermal electrons through which a warm ion beam is propagating. Korteweg—de Vries and Korteweg–de Vries-type equations are obtained for the first- and second-order perturbed potentials respectively. The renormalization method is used to remove the secular terms. It is found that both the amplitude and the width of the soliton are strongly affected by the ion temperatures as well as the velocity of the ion beam. An alternative method is used to make a comparison with the solution obtained by the perturbation method.

The derivative expansion perturbation method is applied to investigate the modulation of nonlinear ion-acoustic waves in a weakly relativistic warm plasma. At the second order of perturbation theory, a nonlinear Schrödingertype equation for the complex amplitude of the perturbed ion density is obtained. The coefficients in this equation show that the condition of modulational stability is modified by the relativistic effect as well as by the finite ion temperature. The association between the small-wavenumber limit of the nonlinear Schrödinger-type equation and the oscillatory solution of the Korteweg-de Vries equation obtained by reductive perturbation theory is considered. Different limits are considered in order to compare with previous work.

We derive the analytical solution of the Boltzmann equation for the stationary electron distribution function that is reached in a plasma generated on the application of a uniform very high-frequency electric field in an atomic gas. The theory includes all excitation transitions: ionization and electronic transitions. The analytic solution is also extended to continuous discharges with low electric field or high pressure in the gas. Then the electron rate coefficient for excitation of the first state (which is the most significant) is calculated analytically. We apply the results to the modelling of very high-frequency argon discharges and to high-pressure continuous discharges in argon and in sodium. The results are compared with numerical results of Ferreira and co-workers for argon and of LaVerne for sodium: in both cases we find good agreement between numerical and analytical approaches.

The equations of motion of a test particle in a stochastic magnetic field and interacting through collisions with a plasma are Langevin-type equations. Under reasonable assumptions on the statistical properties of the random processes (field and collisional velocity fluctuations), we perform an analytical calculation of the mean-square displacement (MSD) of the particle. The basic nonlinearity in the problem (Lagrangian argument of the random field) yields complicated averages, which we carry out using a functional formalism. The result is expressed as a series, and we find the conditions for its convergence, i.e. the limits of validity of our approach (essentially, we must restrict attention to non-chaotic regimes). Further, employing realistic bounds (spectral cut-off and limited time of observation), we derive an explicit formula for the MSD. We show that from this unique expression, we can obtain several previously known results.

We investigate the charge-dispersive effects on a sheath of monosized dust particles in equilibrium. This is done through describing the dust particles by using equations in (x, v) space (kinetic space) that include terms originating from the charge distribution of the dust particles. The charge-dispersive terms are assumed to be completely determined by the local charging processes. We find that the effects due to these terms are opposed by the ordinary gradient terms in the current equation in kinetic space, and they are therefore smaller than first expected. We also identify kinetic effects that are not included in the usual expression for the dust charge in hydrodynamic space.

Experiments using a biased multiblock limiter in the KT-5C tokamak show that positive biasing is more effective than negative biasing in modifying the edge electric field, suppressing fluctuations and improving plasma confinement. The biasing effect varies with the limiter area, the toroidal magnetic field and the biasing voltage. By positive biasing, the edge profiles of the plasma potential, the electron temperature and the density become steeper, resulting in a reduced edge particle flux, an increased global particle confinement time and lower fluctuation levels of the edge plasma.

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2 velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space—time-varying Eulerian correlation are derived solely in terms of plasma parameters. it is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.