This paper uses incompressible visco-resistive MHD to study the propagation of linear resonant waves in an inhomogeneous plasma. The background density and magnetic field are assumed to depend only on one spartial Cartesian coordinate, and the magnetic field is taken to be unidirectional and perpendicular to the direction of inhomogeneity. The equation that governs the component of the velocity normal to the plane formed by the direction of the inhomogeneity and the magnetic field is derived under the assumption that the coefficients of viscosity and resistivity are sufficiently small that dissipation of energy is confined to a narrow dissipative layer. The solutions to this equation are obtained in the form of decaying normal surface modes with wavelengths much larger than the characteristic scale of the inhomogeneity. The effect of non-stationarity inside the dissipative layer is taken into account, and valid solutions are found even when the ratio of the thickness of the dissipative layer to the inhomogeneity length scale is of the order of or smaller than the ratio of the inhoinogeneity length scale to the wavelength. These solutions are the generalization of the solutions obtained by Mok and Einaudi, which are only valid when the first ratio is much larger than the second. The rate of wave damping is shown to be independent of the values of the viscosity and the resistivity. However, the behaviour of the solutions in the dissipative layer depends strongly on the viscosity and the resistivity. In the case that the effect of dissipation dominates the effect of non-stationarity, the solutions behave in the dissipative layer as found by Mok and Einaudi. When the effect of dissipation is steadily decreased in comparison with the effect of nonstationarity, the solutions become more and more oscillatory, and their amplitudes grow very rapidly in the dissipative layer. Eventually, when nonstationarity dominates dissipation, the amplitudes of the solutions become so large in the dissipative layer in comparison with those outside the dissipative layer that practically all the energy of the perturbations is concentrated in the dissipative layer.

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.

We consider the microscopic sources of toroidal and poloidal flow in confined magnetoplasmas and the effects of such flows on macroscopic stability. The central difficulty is satisfactory modelling of kinetic theory effects so as to permit their robust introduction into magnetohydrodynamic (MHD) codes. It is tentatively concluded that poloidal rotation, but not toroidal, is responsible for the computed stabilization and return to axisymmetry.

The stability of an MHD tangential discontinuity is studied in an incompressible plasma where viscosity is taken into account at one side of the discontinuity. When the shear velocity is smaller than the threshold value for the onset of the Kelvin-Helmholtz (KH) instability, two surface waves can propagate along the discontinuity. There is a critical value for the shear velocity, which is smaller than the threshold value for the onset of the KH instability. When the shear velocity is smaller than the critical value, the two surface waves propagate in Opposite directions. When the shear velocity is larger than the critical velocity, the two waves propagate in the same direction, and the wave with smaller phase velocity is a negative-energy wave. Viscosity causes this negative-energy wave to be unstable, and the instability increment is proportional to the viscosity coefficient.

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 thermal mean-field equilibrium of a translation-invariant, unbounded one- component guiding-centre plasma is studied by analytical techniques. A variational principle is constructed. It is shown that only radial symmetric, decreasing density profiles occur. Prescribing the total number of gyro centres N ∈ (0, ∞), the energy E ∈ (E0, ∞) and the canonical angular momentum M ∈ (0, ∞]) uniquely determines a profile. Metastable or unstable profiles do not exist. A simple algebraic relation between N, M, the guiding-centre temperature β−1 and the characteristic Larmor frequency ω is derived. This explains Williamson's computer-based observations.

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.

A semi-analytical approach is proposed for computing the non-local response of a toroidal plasma to an electromagnetic perturbation. Although the perturbed distribution function as well as the absorbed power are also computed, the focus is on the associated quasi-linear diffusion operator. Different decorrelation models allow one to recapture the well-known ideal collisionless plasma result where the wave–particle energy exchange is exactly at resonance, as well as the more realistic plasma response where the interaction region is widened. The choice of the independent variables also allows one to carry out all computations except the integration of the guiding-centre motion analytically.

A composite interstellar model consisting of stars and optically thin radiating plasma is considered in order to investigate the thermal instability arising from possible radiation and other heat-loss mechanisms. The stellar dynamics is governed by the Vlasov equation, while the gas is supposed to be a hydromagnetic plasma, described by the MHD equations, with a density- and temperature-dependent heat-loss function. It is shown that while with cold stars the system is in general unstable irrespective of thermal effects of the plasma, with warm stars having a Maxwellian distribution the thermal plasma considerably influences the stability of the composite system. It is also shown that the otherwise stable composite (with warm stars) configuration may become unstable in the presence of a radiating plasma because of coupling between the heat-loss mechanisms and stellar populations.

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.

A new mechanism is suggested that draws non-resonant thermal electrons into a higher-velocity range, where they can be effectively accelerated by waves. We argue that the acceleration of a small number of pre-existing resonant particles influences the dynamics of the bulk plasma and results in a macroscopic electric field. The solution for the spatial dependence of this electric field is obtained, and it appears to be a new type of electrostatic shock, which forms only in the presence of background turbulence. This field enriches the region of resonant particles with thermal electrons, which leads to a build-up of an excess of accelerated particles. The number of accelerated particles is calculated. This mechanism appears as a good candidate to explain electron acceleration in the foot of quasi-perpendicular shocks.

A general treatment of ion resonance instability for a non-neutral plasma column is performed using a macroscopic cold-fluid-Maxwell model. The azimuthal motion of the plasma components has an important influence on the behaviour of the instability. When the electrons are in slow rotational equilibrium, the instability occurs in both slow and fast ion rotational equilibrium. However, there is stability when the electrons are in fast rotational equilibrium except that the l = 1 mode becomes unstable and independent of plasma rotation. The kink (l = 1) mode only occurs when the plasma column boundary exceeds a certain threshold value that depends on the ratio of the plasma frequency to the cyclotron frequency.

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.

The study of the diffusion of magnetic field lines is based on a stochastic model with a Hamiltonian structure. A Liouville equation can then be associated with Hamilton's equations representing the magnetic line. This allows a statistical description of all observable quantities. In particular, the mean-square displacements (MSD) of a field line and the mean-square relative distance (MSRD) of two lines are considered. Equations for these quantities are obtained by applying the direct-interaction approximation (DIA) to the stochastic Liouville equation. The running diffusion coefficient is derived from the MSD equation. The status of the temporal and spatial Markovian approximations in the DIA is discussed. The MSRD's evolution establishes the existence of a clumping effect between two lines, which eventually leads to gyrotropization of the system. A clump life length is defined. In both cases the equations of motion are shown to be identical to the equations obtained within the Langevin treatment of magnetic fluctuations. This shows the equivalence between the DIA and the Corrsin approximation performed in the Langevin approach.

A new model for collisional transport in a tokamak plasma is analysed. This model is obtained from Grad's 2-fluid 13-moment equations by estimating the order of magnitude of the various effects and neglecting those that are small. The model includes small particle flows, pressure anisotropy and temperature variation within flux surfaces. A formal solution is calculated that satisfies the model equations to O(me/mi). These solutions are found to evolve on a time scale Temi/me ≈ 50 ms.

Lie symmetries, conservation laws, and Lagrangian and Hamiltonian formulations of the triple degenerate, derivative nonlinear Schrödinger (TDNLS) equations for weakly nonlinear dispersive, magnetohydrodynamic (MHD) waves are derived. The equations describe how Alfvén waves propagating parallel to the background magnetic field B interact with the magneto-acoustic modes near the triple umbilic point where the fast, slow and Alfvén mode phase speeds coincide. The Lie point symmetries are used to derive classical similarity solutions of the equations. In particular, the similarity solutions corresponding to time translation, space translation and rotational invariance symmetries are reduced to quadrature. The dispersionless TDNLS system is of hydrodynamic type, and has three families of characteristics analogous to the slow, intermediate and fast modes of MilD. The Riemann invariants corresponding to each of these families are obtained in closed analytic form. Examples of solitary wave and periodic travelling wave solutions are investigated by plotting the contours of the Hamiltonian H(v, w) in the (v, w) phase plane, where the canonical variables v and w correspond to the normalized transverse magnetic field perturbations. An analysis of the prolongation Lie algebra is carried out in order to investigate the integrability of the equations.

The Saha equilibrium approximation and the temperature relaxation approximation to the MHD equations are investigated with regard to the analysis of the formation of nonlinear ionization non-uniformities and their evolution in a non- equilibrium MHD plasma. An analysis of characteristic relaxation times under typical plasma parameters is carried out to verify these approximations. Characteristic space scales of electron thermal conductivity and radiation are evaluated. These space scales determine the characteristic width of nonlinear ionization wave fronts, and are important for the application of numerical simulations.

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.

A gyrating electron beam propagating through a planar plasma duct can excite a whistler wave or an electron-cyclotron wave, depending on the plasma- density profile of the duct and the energy of the beam. The gyrational motion of the electron beam supplies energy to the wave. In the case of a whistler wave the interaction occurs via coupling of the fast cyclotron beam mode (ω ≈ k2vb + ωc/γ0) to the electromagnetic whistler mode through the Weibel instability mechanism, whereas for an electron-cyclotron wave the coupling is through the negative-mass instability mechanism. It is seen that there exist two diflerent beam-energy regimes for excitation of these waves. The growth rate and the efficiency of conversion for both waves are calculated for typical parameters of a gyrotron and a large-orbit gyrotron.

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.