We have investigated the stability of the screw pinch with the help of the double adiabatic (CGL) equations including the finite Larmor radius effects through the anisotropic pressure tensor. The calculations are approximate, with FLR treated as a first-order correction to the ideal plasma equations. The dispersion relation has been solved for various values of R2 = p∥/p⊥ and α for the rale and imaginary part of the frequency (ω = ωR ± iωI) in three particular cases: (a) μ = 0, the θ-pinch, (b) μ = ∞, the Z-pinch, (c) μ = -α/m, field distubances parallel to the equilibrium field. Here μ is the pitch of the magnetic field in the pressureless plasma surrounding the main column, α is the wave number, m is the azimuthal number, p∥ and p⊥ are plasma pressures along and perpendicular to the magnetic field.

Initial growth rates are calculated for unstable modes of the Taylor type driven by temperature and density gradients in the presence of viscous and thermal diffusion. For a laser-driven plasma it is shown that, even without ablative flow, conduction can sharply reduce unstable growth, and that growth should only occur in the region of low temperature near the ablation front.

The problem of transport coefficients in statistical mechanics is reconsidered. A general method is given by which the hydrodynamical equations can straightforwardly obtained starting from the kinetic equation for the one-particle distribution function. From the statistical counterparts of the hydrodynamical equations so derived, the statistical expressions for the transport coefficients are immediately identified.

Linearized hydrodynamic modes have recently been the object of very thorough reserach from the viewpoint of irreversible statistical mechanics; in particular, the Brussels school formalism has been used by Résibois to derive the eigenfrequencies of the hydrodynamical modes, whereby operatorial equations for transport coefficients have been obtained (Résibois 1970; see also the instructive book by Balescu (1975) on this subject).

The statistical theory of the transport coefficients which was formulated in a previous paper (Vasu, 1976) is exemplified here by the case of a two-fluid plasma in a magnetic field. In addition, a general method is given which allows us to calculate frequency dependent transport coefficients; this method is a natural extension of the paper mentioned above. In the static limit, the transport coefficients obtained for the two-fluid plasma in a magnetic field are similar to those reported by Braginsky (1963) although there are some numerical differences. The frequency dependent transport coefficients obtained here include important resonant and time lag effects.

The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.

Wave-wave coupling is investigated for spatially growing waves in a cold beam-cold plasma system. Numerical solutions of the wave coupling equations are obtained for various combinations of three waves as well as several interacting triplets of waves that are of experimental interest. It is found that most three wave interactions in this system are explosive if they involve the most unstable mode. The results are compared, where applicable, with analytic criteria for the unboundedness of the solutions.

Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the evolution equation of the ensemble average distribution function is significantly different from the classical diffusion equation in velocity space. The average turbulent collision operator involves the usual spatial and temporal autocorrelation of the stochastic field, together with the correlation of this field with its spatial gradient, and the velocity derivatives are complemented by spatial derivatives

Measurements of the m = 1 growing mode of a linear screw pinch, by external dipole probes, are compared with the recorded plasma motion on streak photographs. Good agreement is found up to a maximum amplitude which depends on plasma density and growth rate.

The oscillating-two-stream instability (OTSI) is shown to be a zero-frequency absolute instability of the backward-wave parametric type. The instability is shown to be distinct from the concurrent parametric-decay-instability (PDI), even for sub-critical pump frequencies very near the critical value. The analogous ‘purely-growing Brissllouin instability’ (POBI) is shown not to exist, in a collinear interaction, with a travelling-wave pump. In fact we conclude that no such backward-wave, zero frequency, absolute instability could occur in any case where the two interacting, frequency shifted waves are on the same mode of propagation as the travelling-wave pump. Finally, the possibility of a PGBI by means of a standing-wave pump, as suggested earlier by Lashmore-Davies, is confirmed for a collinear interaction, through the identification on the Brilbum diagram of a zero-frequency, back-wave parametric interaction resulting from the coupling of Stokes and anti-Stokes light waves by the standing-wave pumb light wave.

We investigate the electromotive force produced by plasma motions which are excited by an assigned body force. Two specific enquiries are made: (i) Can the Hall term create helicity in a plasma which is isotropically forced? (ii) What is the general form of the turbulent electromotive force when magnetic shear is present in the system? It proves possible to answer (ii) for weak shear in the two cases of weak and strong magnetic field.

A general dispersion relation is derived for linear waves in a non-uniform, magnetized plasma using the polarized co-ordinate system. An equilibrium distribution function with general gradients in density and temperature (and differing parallel and perpendicular temperatures) is proposed using polarized tensors. A compact conductivity tensor is derived in terms of tensor quantities, including certain tensor moment integrals whose elements may be evaluated separately from a given problem. This is of importance in computational applications. The derivation is under the restrictions (a) small gradients, (b) the local approximation of Krall & Rosenbluth, and (c) β⊥ ≪ 1. Conditions for coupling of electrostatic and electro-magnetic modes are investigated.

Electromagnetic ray propagation is discussed for weakly nonlinear dispersive media. Specialization to periodic waves justifies the use of a self-excitation model and facilitates the construction of a complete system of ray equations. The solution describes the evolution of frequencies, propagation vectors and amplitudes along the ray path. The formalism may be extended to include the case where a velocity field exists. This is based on special relativity and the Minkowski model for the electrodynamics of moving media. It is assumed that the velocity field varies slowly in space and time. The results are relevant to propagation problems in weakly nonlinear plasmas and optical media.

The parametric resonances involving the coupling of an external harmonic electric field to the plasmadynamical (PD) modes are studied. Particular attention is devoted to the resonant triplets involving purely dissipative PD modes of zero frequency. It is shown that a new type of instability exists in this class of processes.

Weak nonlinear coupling between two polarized transverse waves in a weakly relativistic plasma is studied including the effect of dispersion. The frequency of the coupled waves is of the same order of magnitude as the electron plasma frequency. By using the multiple scale method it is shown that the slow modulation of the complex amplitudes is described by simultaneous nonlinear Schrödinger equations. Travelling wave solutions are then obtained for this system of equations by the analytical and the numerical methods. As the result of the wave-wave interaction, two envelope waves are, in general, composed of dispersive shock waves or non-periodic nonlinear wave-trains, while the usual solitary waves or periodic nonlinear wave-trains can exist as a special case. case. The results of analysis can readily be applied to other coupled waves with different polarizations in a nonlinear dispersive medium.