Table of contents

The spatial evolution of a velocity-modulated ion beam is described theoretically and experimentally for a stable, ion beam-plasma system. For a sinusoidal modulation, the perturbation initially grows and then shows a periodic change of amplitude along the beam. But under certain conditions, after the initial growth and subsequent saturation, the perturbation is observed to dampen away monotonically. The initial growth is also measured with ramp and pulse modulations. The experimental results agree quite well with the so-called 'wave theory' for ion beam bunching.

A method is given for the construction of all solutions of the relativistic Vlasov equation that depend on one cartesian coordinate z and time t in the combination z-V_pt only with V_p>c. These solutions represent non-linear electromagnetic waves in a relativistic plasma without static fields, which reduce for sufficiently small amplitudes to the longitudinal and transverse waves in a uniform plasma known from linear theory. Explicit expressions will be given for the influence of wave amplitude and plasma temperature on the coupling of longitudinal and transverse wave components, the dispersion relations of longitudinal and transverse waves and the modulation of plasma density and streaming velocity. The relevance of elliptically polarized transverse waves of this type to the description of pulsar waves is discussed.

Energy absorption is assumed to take place through the generation of large amplitude plasma waves propagating outwards from the critical surface, and the effect of these waves on the particle distribution is described by a quasi-linear equation with non-linear broadening of the resonance. Instead of solving for the wave amplitude and particle distribution function simultaneously, a form for the wave amplitude is chosen from physical considerations, with a damping coefficient chosen to give conservation of energy. With this simplification results are obtained over a range of parameters, without a great deal of computational effort.

A kinetic equation for a multi-species plasma in an external uniform magnetic field is derived from the BBGKY hierarchy of equations. The equation generalizes the equation of Rostoker (1960), which assumes that the distribution function is independent of the azimuthal angle, and all previous results can be derived from it. An additional advantage is that the collision integral is obtained in a form which is free from infinite sums of Bessel functions, and this greatly facilitates calculations based on it.

A finite amplitude cylindrical ion acoustic wave develops at large distances from the exciter an oscillatory structure which resembles an Airy function but its amplitude oscillations are asymmetric. This phenomenon can be described by solutions of the linearized Kortweg-de Vries equation in self-similar variables. This equation has been solved for integral values of a parameter gamma . New solutions which can be represented as the Weyl transform of the Airy function are obtained for fractional values of gamma . The measured rate of spatial damping of the oscillations and the variation of their period with respect to distance and Debye length agree well with those predicted by these solutions.

A resonant collective process can be excited in a plasma gradient which accelerates energetic particles into the higher density region.

A theory of the generation and propagation of two and three dimensional magnetohydrodynamic surface waves due to an arbitrary as well as special oscillatory pressure distribution acting on the free surface of an inviscid electrically conducting fluid is presented. The unsteady solutions for two as well as three dimensional free surface elevation are obtained explicitly. The asymptotic behaviour of these solutions for large time and distance are determined to describe the qualitative and quantitative nature of the wave motions. The solutions consist of both the steady-state and the transient components. The latter is found to decay asymptotically for large time, and the steady-state is reached. Magnetohydrodynamic surface waves in deep and shallow fluid are dispersive in nature.

Numerical results are presented for the electrical conductivity of a structureless hydrogen plasma for weak electron-ion interaction. There is good agreement with measured conductivity in a fully ionized plasma at temperatures approximately 20000K from which it is concluded that the electron-ion mechanism is the dominant one limiting the conductivity under these conditions. The numerical differences between the conventional conductivity formula and the resistivity formula based on the total force-force correlation function are small in the present application.

The drift motion of a collisionless plasma is measured in a curved magnetic field. A large drift is observed when the plasma is isolated from electric conductors. In a stationary state where the plasma is in contact with the conductors, the E*B drift is found to be very small, because a short-circuit path is formed through the conductors by the fast motion of electrons along the magnetic field.

The effect of a resonant perturbing magnetic field on heat conduction in a Tokamak, in the collisional regime, is studied theoretically. Heat flux in a Tokamak with a resonant helical field is calculated, and Bohm type transport considered.

Analytical calculations on the linear instabilities of an inhomogeneous neutral guiding centre plasma have been carried out, for a given equilibrium density profile. The perturbed potential is examined, and boundary conditions calculated. A dispersion relation is calculated, and applied to various conditions.