The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfvén and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfvén spectrum. The stabilizing effect of favourable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed.

It is pointed out that ambiguities arise in taking the resonant parts of nonlinear response tensors. A prescription is proposed and used to evaluate the resonant parts explicitly in terms of a covariant and gauge invariant formalism. Symmetry properties of the resonant parts are identified. The prescription used can be justified by analogy with a calculation based on QED where no ambiguity arises; it is also justified directly by classical arguments. In some standard treatments of nonlinear damping processes a necessary symmetry is not imposed. When this symmetry is imposed, the relations derived here imply that turbulent bremsstrahlung, as defined by Tsytovich et al., does not exist.

Electron-acoustic (EA) and ion-ion-hybrid resonance (IIHR) waves, in a multi-ion-species magnetoplasma with density gradients perpendicular to the magnetic field and the direction of wave propagation are found to be drift unstable provided the inhomogeneities exceed a certain threshold. The possibility of mode conversion between the EA and the IIHR waves is examined.

A general KdV-type equation which covers most of the known model equations for weakly dispersive waves is investigated. First, the possible stationary localized states are discussed. When perturbed longitudinally, the perturbations can be finite and complex but should be small. In the main (second) part of the paper a necessary and sufficient stability criterion for the stationary states is derived. This is performed in two steps: A variational formulation leads to an instability region, whereas the sufficient stability criterion follows from a Liapunov functional. The stability theorem is evaluated for various models including ion-acoustic waves in plasmas and lower-hybrid cones.

The application of RF heating (ICRH or LHH) to a fusion plasma creates high-energy tails on the distribution function of the heated particle species. In the presence of loss regions in velocity space, e. g. due to particle drifts in the toroidal magnetic field ripple of a tokamak, the collisional pitch-angle scattering losses may be significantly enhanced. The present work assesses the importance of such RF-enhanced losses and explicit expressions are derived for the evolution of the loss fraction. In particular, for parameters typical of PLT we find that the loss fraction could rapidly reach high values.

The propagation of an electron-acoustic wave in a plasma consisting of two types of ion and two temperature electrons has been investigated in the linear and nonlinear regimes. The presence of the second species of ion modifies the characteristics of the wave. The analysis has been done for both the finite amplitude and the small amplitude case of the electron-acoustic solitary wave. The ion temperature ratio and the electron density ratio rather than the relative ion density are the effective parameters which govern the amplitude of the electron-acoustic soliton.

Using the stationary phase method, a simple asymptotic analysis of a two-dimensional model of the coupling of the cold-plasma magnetosonic wave excited by an ion-cyclotron resonance heating (ICRH) antenna is presented. Such an analysis allows quick evaluation of the basic characteristics of the ICRH antenna radiation pattern and shows how the power spectrum radiated by the antenna and plasma dispersion properties combine to produce the power flux distribution observed in the far-field region. The results of the present simplified analysis are found to be in reasonably good agreement with more sophisticated coupling codes. This development thus serves as a simple analytic tool for quick investigation of the most fundamental features of coupling for antenna design studies. With a view to spectrum shaping for improved heating and tokamak RF current drive, the case of a phased antenna array is also analysed.

General expressions are derived for the energy density of electromagnetic waves in a cold collisionless magnetoplasma. Random as well as coherent waves are considered.

In this paper a new approach to the approximate solution of the MHD equilibrium equation is described. The axisymmetric equilibrium equation is first transformed to a time-independent Schrödinger equation and then solved by the Ritz method in a suitable rotational co-ordinate system, the validity of the solution being not limited to large aspect-ratio configurations. The zeroth-order approximation is analytically computed and the relationship between the poloidal beta and the shift of the magnetic axis is derived. To the same order, the adiabatic compression of the plasma ring is studied and a non-dimensional compression chart is obtained. Results of numerical computations of the higher orders are also reported.

The effects of a d.c. magnetic field on stimulated Raman sidescatter from laser-produced plasmas is studied. For exact sidescatter along the magnetic field, the Raman instability separates into two distinct decays in which the scattered light is either a right (RHCP) or left (LHCP) circularly polarized electromagnetic wave. Growth rates of the instabilities can be enhanced in the former case but are diminished in the latter. The magnetic field induced effects are greatest near the quarter critical density where frequency shifts can be especially significant, being equal to ± ¼Ωc for decay into RHCP and LHCP waves, respectively.

In the aforementioned paper we obtained an equation for non-linear Alfvén waves in a finite-β plasma, and investigated envelope soliton solutions thereof. The purpose of this note is to point out an error in the derivation of the soliton envelopes, and present corrected expressions for these solitons.

The error arises from our assumption of translational invariance of both the envelope and phase of an envelope soliton expressed in equations (16) and (17). Rather, the phase is related to the amplitude by where y ≡ x — VEt is a comoving co-ordinate, and all other quantities are defined in the above paper.