The problem of bifurcation of a free boundary equilibrium is reconsidered in a simple model. We find which combinations of specified parameters result in a non-unique solution and find the resulting bifurcation point. By including reversed current solutions, the model sheds some light on the equilibrium βp limit obtained in previous analytic and numerical models.

The magnetohydrodynamic properties near a two-dimensional X-type magnetic neutral line in a viscous and resistive plasma in the steady-state are investigated.

The effect of the nonlinear changes of the dispersion characteristics of highfrequency azimuthally symmetric surface waves in a plasma column is investigated theoretically. Both (ω + ω) – ω and (ω – ω) + ω nonlinear interactions of the third order (in relation to the fundamental wave amplitude) are considered here. These two types of interactions influence the wave phase velocity and the collisional damping rate in opposite ways. When ω2Pi/v2 < 1, the contribution of the (ω – ω) – ω interaction is negligible and the (ω + ω) – ω interaction results in an increase of the phase velocity and a decrease of the time damping rate. When ω2pi/v2 > 1, both interactions are involved; the (ω – ω) + ω interaction associated with the ponderomotive force becomes more important, decreasing the phase velocity and increasing the time damping rate (ωpi and v are ion plasma and electron-neutral collision frequencies, respectively).

The transmission and reflexion coefficients are calculated for the coupling of an ordinary polarized wave to the Z mode when the angle of incidence is near the critical angle.

The time evolution of weak shocks in the classical theory of shock waves may be described by Burgers' equation, which is a small-amplitude, long-wavelength, but nonlinear wave equation. The present paper derives Burgers' equation for three different hydrodynamical models of cosmic ray shocks. The main development of the paper concerns the hydrodynamical model in which Alfvénic effects are neglected. For this model it is shown that the steady-state solution of Burgers' equation is equivalent to the weak, but smooth, transition solutions of the shock structure equation obtained previously. It is shown that Burgers' equation may be regarded as a wave energy equation, in which the interaction of the wave with the background medium is taken into account. Burgers' equation is also derived for Alfvénic models in which the Alfvén waves that scatter the cosmic rays are generated by the cosmic ray streaming instability, and propagate down the cosmic ray pressure gradient, at the Alfvén velocity relative to the background fluid.

We show that under a wide range of conditions easily achievable in the laboratory, the dispersion of the radial eigenmodes of electromagnetic whistler mode waves in a cylindrical magneto-plasma is dominated by the electron inertia and becomes synonymous with the electrostatic Trivelpiece-Gould modes. A similar situation exists close to, but just below, the ion gyrofrequency.

In the Fokker-Planck approximation, a general solution of the kinetic equation for the distribution function of non-thermal α-particles in spatially uniform DT plasma is obtained. The previously published solutions are then derived as special cases. Transport equations describing diffusion of non-thermal α-particles are obtained and diffusion coefficients are calculated. To compare the hydro-dynamic and kinetic descriptions of non-thermal α-particle energy transport, the critical ignition length of the overheating instability in DT fusion plasma, determined by non-local plasma heating due to α-particle diffusion, is calculated using both approaches. The two results are in good agreement.

The dispersion of the radial eigenmodes of a cylindrical m = 1 whistler wave with Ωi; ≪ ω < Ωe ≪ ωpe is investigated for both conducting and insulating boundaries. The effects of electron inertia and resistivity on the modes are discussed.

It is shown that the combined effect of resistivity and thermal conductivity is responsible for the existence of marginal stationary modes in a cylindrical current-carrying plasma, under the influence of a shearless magnetic field. These modes occur in the tokamak approximation and for low wavenumbers. In the nonlinear theory they give rise to large-scale stationary convection.

The ion temperature history of the plasma fireball in TRISOPS IIX has been measured by comparing the time-resolved neutron yield from a D–D reaction and a D–T reaction. This measurement results in a reading of ion temperature that is independent of any assumptions of plasma density or fireball volume. The results verify and clarify previously reported TRISOPS parameters. In a separate set of measurements using a D–D reaction, the ion temperature was determined by comparisons of Doppler broadening and neutron yield. It was found that the ion temperature rises in 5 μs to 6 keV with a corresponding density of 1015 ions cm3. After 8 μs it falls rapidly to 1 keV as the density rises to 1017 ions cm–3. The 1 keV temperature is held for about 20 μs. These temperatures and densities yield an equilibration time for ions and electrons that is long compared with the duration of the experiment.

The self-focusing of whistler waves in a low-β plasma is considered. Axially symmetric solutions of the MHD and Schrödinger equations are found that describe stationary and homogeneous wave beams together with the plasma ducts in which they are trapped.

The self-focusing occurs both at ω < ½ωc and ω > ½ωc where ωc is the electron cyclotron frequency. The wave leakage which takes place in some types of duct and pre vents self-focusing from developing is investigated in detail.

Ignition of a self-sustained fusion reaction in a strong magnetic field is studied. The critical ignition dimensions and the threshold ignition energy are calculated as functions of the fuel density and the magnitude of the transverse magnetic field. A new method for producing ultra-high magnetic fields is proposed which provides at once heating of the fuel by induction currents and localization of the micro-explosion by the magnetic field. Simple analytic estimates show that a certain combination of inertial, magnetic and wall methods of plasma confinement may decrease the ignition energy below 100 kJ.

The excitation of whistler wave instability due to slow cyclotron (m = – 1) interaction in an inhomogeneous plasma penetrated by an inhomogeneous beam of electrons is studied. Expressions are obtained for the elements of the plasma and beam dielectric tensors. It is shown that the inhomogeneity in both beam and plasma number densities affects the growth rate of the instability.

If an external current pulse is applied to a diffuse plasma sheet pinch, surface wave modes are generated, which decay by collisionless damping, leaving only oscillations of the Alfvén continuum along the Alfvén resonance surface. The transverse perturbations within this surface phase-mix to zero. It is shown that perturbations induced by an initial pulse are modulated by a (later applied) second pulse of different wavelength, to yield non-vanishing second-order transverse perturbations, even though the first-order transverse perturbations have phase-mixed to zero. This analysis shows the importance of nonlinear effects in the evolution of inhomogeneous magnetohydrodynamic motions.

This paper deals with non-isothermal plasmas in which each species is described by Grad's thirteen-moment approximation. A theoretical framework, which includes a generalized Ohm's law and an ambipolar diffusion law, is used to treat energy dissipation resulting from ‘Motional’ interactions between the species. The frictional forces consist of a momentum relaxation force together with a ‘thermal force’ that occurs, in the presence of heat flow, partly because of the dependence of the collision frequencies on temperature. Detailed results are obtained for binary plasmas and for partially and fully ionized ternary plasmas. Our formalism is then compared with the technique used by Demetriades & Argyropoulos to study dissipation in thirteen-moment plasmas. The effects of thermal forces are illustrated by considering situations in which the drift contribution to the electronic relative thermal flux vector predominates over the thermal flux vector itself. Then, for binary plasmas and for ternary plasmas that are not too lightly ionized, the thermal forces increase the resistivity by a factor of about 5/2.

A method is presented for computing the class of axisymmetric current distributions flowing in a torus whose peripheral surface is a flux surface for the magnetic field produced by the current itself. The method allows the correct calculation of the ‘self-induced’ magnetic forces arising from the interaction between these currents and their own field. The general expression for the self-induced force is given and an approximate formula is presented in the large aspect-ratio limit.

Linear and nonlinear mechanisms for generating convective cells with finite but small parallel (to the external magnetic field B0) wavelength are presented. The problems of mode-coupling as well as quasi-steady nonlinear mode structures are analytically studied. Possible applications in space plasmas are discussed.

Using the Zakharov equations in their Fourier-transformed form, we consider the development of the modulational instability (MI) both for the monochromatic and the finite-width cases. In the static approximation and considering a monochromatic Langmuir wave which is coupled only to a single pair of Stokes and anti-Stokes Langmuir perturbations, we show that the resultant set of equations is integrable and we discuss the analytical solution of these equations. We show how a finite-width driver will lead to a threshold for the MI. We compare our results with those obtained by other authors.

It is shown that a finite-amplitude upper-hybrid wave can decay into a perpendicularly (to an external magnetic field B0zˇ) propagating electrostatic lower-hybrid/ion-cyclotron wave and a left-handed circularly polarized (LHCP) electromagnetic wave (along B0) or an ordinary mode radiation (across B0). Nonlinear dispersion relations and the growth rates are obtained. It is suggested that the present nonlinear instability can be responsible for the enhanced narrow band radiation which is frequently observed in the Earth's magnetosphere.

The coupling of volume, long-wavelength TM electromagnetic and longitudinal space charge (electrostatic) waves by the rippling of magnetically focused electron beams is examined analytically. The dispersion relation is obtained and then solved for these types of wave. Instability, with growth rates proportional to the relative ripple amplitude of the beam, is found and discussed.