The non-linear dynamic behaviour of two three-wave systems in plasma with two waves in common has been studied, including the possibility of negative energy waves and also the effect of linear damping or growth and frequency mismatch. Depending on the various initial conditions solutions of different types have been discussed. It has also been shown that one of the triplets can be stabilized by the other one against explosive instability depending on the relative strength of the coupling factor.

Low aspect ratio tokamak (LART) configurations represent a promising approach to thermonuclear fusion. They require auxiliary non-ohmic power for heating, current drive and turbulent transport suppression. This paper pioneers the pre-requisite for the quantitative evaluation of these effects, namely the formulation and solution of the full wave equation for pre-heated (i.e. prior to the addition of any auxiliary heating or current drive) LARTs, the case in which mode-converted Alfvèn waves ($\omega < {\omega}_{ci}$) are used as an additional non-ohmic power source. Arbitrary aspect ratio and magnetic shear tokamaks with non-circular cross-section are properly considered; this general approach includes, as a particular case, that of low aspect ratio (spherical) tokamaks.

The problem is formulated in terms of the vector and scalar potentials (${\bf A}, \Phi$), thus avoiding the numerical pollution occurring in the case of the (${\bf E},{\bf B}$) formulation. Adequate boundary conditions at the vacuum–metallic wall interface and regularity conditions at the magnetic axis are enforced.

For the pre-heated stage, a quite general two-fluid, resistive dielectric tensor operator able to describe the anisotropic plasma response in spherical tokamaks is derived and used; except for its linear character, no geometrical limitations are imposed on it. Consistent equilibrium profiles also including effects of neoclassical conductivity and bootstrap current are used (Wilson 1994).

The wave equations are solved with the aid of a suitable $2\frac{1}{2}{\rm D}$ finite-element algorithm, taking advantage of the up-down symmetry of the problem. Illustrative solutions obtained for Culham's START device are presented and discussed; this includes a sensitivity study to the antenna parameters (geometry, frequency and wavenumbers). Finally, as one of the possible applications of these results, illustrative ensuing ponderomotive forces and the non-inductive current drive in a START-like device are calculated.

This paper presents the cross-focusing of two intense laser beams in a collisionless plasma, taking into account the relativistic non-linearity. The non-linearity is not bound to large irradiances and this non-linearity is only a perturbation. It should be noted here that while considering the self-focusing due to relativistic electron mass variation, the electron ponderomotive density depression in the channel may also be important. Therefore, these two non-linearities may simultaneously affect the self-focusing process. In the present paper we have considered the situation when only relativistic non-linearity is important. The non-linearity due to relativistic mass variation depends not only on the intensity of one laser but also on the second laser. Therefore, one laser beam affects the dynamics of the second beam and hence a cross-focusing process takes place. The electric field amplitude of the excited electron plasma wave (EPW) has been calculated and its effect on the cross-focusing process has also been discussed. It is observed that the inclusion of a resonantly excited EPW on cross-focusing is significant and the accelerating electric field of the generated EPW becomes affected. A comparison of the theory with the recent experimental observations has also been presented.

Energy gain by an electron during its motion in the field of a fundamental ${\rm TE}_{10}$ mode excited by a microwave in a rectangular waveguide is analysed. Expressions have been obtained for the fields of the mode, angle of deflection and the acceleration gradient of the electron, when it is injected along the direction of mode propagation. A 25 keV electron gains an energy of 120.44 keV when a microwave of intensity $10^{10}$\,W\,m$^{-2}$ at frequency 6 GHz is employed to excite the mode in a waveguide of width 0.03 m and height 0.02 m. The effect of the microwave frequency and width of the waveguide is to decrease the electron energy gain for a fixed microwave intensity. However, higher acceleration gradients are obtained when the electron is injected with a larger energy.

The momentum balance equation and the balance equation for the pressure tensor of a collision-free one-species magnetoplasma are linearized and Fourier-transformed, together with Maxwell's curl equations. They are combined in an algebraic dispersion system for the average perturbation velocity of the plasma particles. To do this a set of five fourth-order projectors is introduced, constructed with the aid of a commutative ‘ring product’ of two second-order projectors. It is shown that the trace-free part of the anisotropic perturbation pressure tensor, usually ignored for the sake of simplicity in such analyses, is of the same order of magnitude as the trace of this tensor. The vanishing determinant of the dispersion system is the dispersion equation of fifth degree in the square of the refractive index.

Taylor and Cargill (2001) presented a general theory of expansion waves in MHD flows. On page 243 we defined the magnetic field in the $r$-$\theta$ plane as ${\bf B}=(B_{r}(\theta), B_{\theta}(\theta), B_{z}(\theta))$, and ${\bf V}=(V_{r}(\theta), V_{\theta}(\theta), 0)$. It has been pointed out to us that this assumption is in general inconsistent with the z-component of the momentum equation.