We consider the electromagnetic field produced by an azimuthal current of arbitrary shape, external to a plasma. In particular, we study absorption of the field energy by a radially inhomogeneous plasma cylinder with double ioncyclotron resonance. We calculate the power absorbed by plasma ions for an arbitrary ion distribution function. We show that, in some regions of the plasma it is possible for the work done by the field on the currents to be negative. We also show that, if the plasma has regions with a large density gradient (e.g. a narrow transitional plasma-vacuum layer), power absorption increases sharply. We consider, too, the exciting of the natural oscillations of the cylinder by external currents. In this case, power absorption is independant of the dissipative properties of the plasma.

Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (∂ / ∂ t = 0) Vlasov– Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bzext ê 2. Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the jth component distribution function f j(H⊥, Pθ, υ 2) depends on perpendicular energy H⊥ and canonical angular momentum Pθ, exclusively through the linear combination H⊥ – ω jPθ, where ω j = const. = angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on H⊥−ωjPθg in circumstances, where the density profile or magnetic field profile is specified.

Steady magnetohydrodynamic combustion waves for a perfectly conducting, electrically neutral perfect gas in an aligned field are examined in phase space, taking into account the effects of viscosity and the thermal conduction as transport processes. Steady defiagration does not exist. Conditions to be satisfied by the initial and final states of detonation waves are derived, which may include an extension of the evolutionarity condition and the Taniuti—Resler relation to shock waves with finite width and energy release. A constraint on the shock wave is given in a conservation form. The exact solution of the final state is also given in such a way that it depends linearly on the energy supply, and may be classified completely by means of the parameters of the solution itself.

The second-order elliptic partial differential equation, which describes a class of static ideally conducting magnetohydrodynamic equilibria with helical symmetry, is solved analytically. When the equilibrium is contained within an infinitely long conducting cylinder, the appropriate Dirichiet boundary-value problem may be solved in general in terms of hypergeometric functions. For a countably infinite set of particular cases, these functions are polynomials in the radial co-ordinate; and a solution may be obtained in a closed form. Necessary conditions are given for the existence of the equilibrium, which is described by the simplest of these functions. It is found that the Dirichlet boundary-value problem is not well-posed for these equiilbria; and additional information (equivalent to locating a stationary value of the hydrodynamic pressure) must be provided, in order that the solution be unique.

A new systematic method of analysis of three-wave interactions is proposed, and applied to a description of interactions of waves (0, 1 and 2) in a homogeneous electron plasma, in which Landau damping is insignificant. Transverse, linearly polarized wave 0, which may represent an external (‘ pump’ ) wave, is assumed to be in resonance with longitudinal and transverse waves 1 and 2 already existing in a weakly-turbulent plasma. The rate (d W/ dt)j, at which energy is transferred from wave j to the others, is calculated, assuming that directions of propagation of resonating waves are restricted by conditions of three-wave resonance only. Conditions of the form (dW/dt)j = 0 constitute threshold criteria for amplification of wave j to occur. There is a brief discussion of processes during which the energy of one of the resonating waves remains constant, although energy is transferred between the other two waves. The relation between energy absorbed by the plasma and energy transferred between waves is evaluated.

The resonant interaction of three waves in a uniform hot magnetized plasma is examined. The coupling coefficients are obtained in a symmetric form from the Vlasov-Maxwell equations.

The paper compares the methods of re-normalization introduced by the Dupree—Weinstock theory of turbulence with those in the theories of Kadomtsev, Rudakov and Tsytovich. It is shown to what extent they are equivalent.

The paper considers the two scattering instabilities photon decays into photon plus plasmon (t → t' + l) and photon decays into photon plus phonon (t → t' + s) and the two absorptive instabilities photon decays into plasmon plus plasmon (t → l + l' ) and photon decays into plasmon plus phonon (t → l + s). The corresponding growth rates and thresholds are determined for a homogeneous, unmagnetized plasma. The regimes of weak and moderately strong pump fields are examined, together with the possibility of purely-growing instabilities for the decays t → t' + s and t→ l + s.

We examine stimulated Raman scattering in an inhomogeneous plasma, and demonstrate that there may be an exponentially growing decay, which owes its existence to reflexion of the electromagnetic decay wave. Unlike absolute instabilities, which depend on simultaneous vanishing of the wavenumber mismatch and its derivative, it can occur over a wide spectrum of decay wave frequencies, and may, therefore, be of greater practical importance than those instabilities.

The properties of the field and flow near a two-dimensional X-type magnetic neutral line are considered for an incompressible, inviscid, conducting fluid in the steady state. In this region the magnetic field is not ‘frozen’ into the plasma, and finite conductivity effects must be considered. In the region surrounding the X line, it has hitherto been assumed that the field lines to lowest order form systems of hyperbolae (the field components increasing linearly with distance from the null), while the fluid flow lines form systems of rectangular hyperbolae with fluid flow perpendicular to the field on the axes of symmetry of the field lines. The assumption of such a configuration was based upon a somewhat cursary consideration of the governing equations, a detailed examination never having been carried out. We present the results of such an examination, which reveal that the above configuration is not a valid solution of the MHD equations, and that, for the case studied, the field to lowest order must form a neutral sheet. The properties of the field and flow parallel to the plane of symmetry are also considered. It is found that non-uniform fields and flows may exist within the diffusion region, in support of recent convection-region studies. This work shows clearly the need for more detailed and careful consideration of such systems.

The effect of the interaction of plasma and neutral gas on the structure of switchtype shock waves propagating in a partly-ionized gas is studied. These shocks, in which the magnetic field is perpendicular to the shock front either upstream or downstream, exhibit a spiralling behaviour of the magnetic field in the shock transition region, if the Hall term is important in the Ohm's law. Observation of this behaviour for shocks propagating into a plasma with a residual neutral content of ~ 15 % has implied an anomalously high resistivity of the plasma. We show that this can be partly explained by considering the collisions of ions with the neutral atoms in a magnetic field. We show that the extra dissipation due to the increase in resistivity goes primarily to the ions and neutrals. Thus even in the absence of viscous dissipation within each species, the heavy particles can be appreciably heated in a shock propagating into a partly-ionized gas in a magnetic field.

A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfvé n, acoustic, drift and entropy modes in a partly-ionized plasma. The fundamental electromagnetic nature of the interchange mode is noted: coupling to the intermediate Alfvé n mode is strongly stabilizing for finite k2. Both ion– viscous and ion–neutral stabilization are included; and it is found that collisions destroy the FLR cutoff at short perpendicular wavelengths.

A nonlinear fluctuation—dissipation theorem is derived for a turbulent plasma. The method of dressed test particles is generalized to a nonlinearly stable plasma; the turbulent state is described by the Dupree—Weinstock formalism. A comparison with the Cook—Taylor theory is discussed.

The exact theory of a wave of fixed profile travelling with speed c/n (0 < n < 1) through a uniform, cold, collisionless, unmagnetized plasma is investigated for the case in which the electric field has a non-zero transverse component, which lies in a fixed direction. The governing equations, referred to the frame of reference in which there is no space dependence, are studied analytically in each limit n→0, n→1. and by computation for other values of n. It is shown that, for each value of n, there is, in general, just one periodic solution of an arbitrarily given amplitude; and a quantitative description of these periodic solutions is provided in graphical form. A simple ‘dispersion relation’ is obtained for large- amplitude waves.

The structure of the drift instability is examined in several density regimes. Let λ e be the total electron mean free path, kz the wave-vector component along the magnetic field, and ν ⊥ / ν ∥ the ratio of perpendicular ion diffusion to parallel electron streaming rates. At low densities (kz ν e > 1), the drift mode is isothermal, and should be treated kinetically. In the finite heat conduction regime

the drift instability threshold is reduced at low densities (v⊥/v‖<0·1) and increased at high densities (v⊥/v‖>0·1), as compared with the isothermal threshold. Finally, in the energy transfer limit (kzλe<(m/M)½), the drift instability behaves adiabatically in a fully-ionized plasma, and isothermally in a partly-ionized plasma, for an ion-neutral to Coulomb collision frequency ratio vin/vii>2(m/M)½ at Ti = Tc = Tn.

This paper studies the nonlinear coupling between an ion—acoustic wave and two Alfvén waves. On the basis of the MHD equations, this three-wave interaction is described within the coupled normal-mode theory. It is shown that a largeamplitude acoustic wave can decay into a pair of Alfvén waves in a high-β plasma. Calculations of the threshold condition and the maximum growth rate suggest that this decay process may occur both in the laboratory and in the ionosphere.

The stability of a bounded, homogeneous, neutralized plasma with counter- streaming electron beams is analysed. A water-bag model is used to describe the electron distribution in velocity space, so that finite beam temperature and a background plasma are included in the theory. For boundary conditions, the absorber– source wall (the diode boundary) and the reflecting wall are considered. For the former, growth-rate calculations indicate that the instability is a combination of charge bunching (counter-streaming) and diode circuit effect. As the diode length increases, the growth rate of all modes in the system approaches the maximum growth rate. For the reflecting wall, as the length increases, the maximum growth rate transfers to higher and higher order modes with shorter wavelength, while the growth rate of the lower-order modes goes to zero.

Ion-acoustic solitons are observed to form when a large-amplitude positive step voltage is applied to a single mesh grid. For the formation of the soliton, the sheath about the grid plays an important rôle. The number and the amplitude of the solitons are examined experimentally as a function of the nonlinear index, and are compared with theory. The observed width and the velocity of the soliton are well explained by the theory of a hot-ion fluid and Boltzmann electrons. The phase delay of two solitons by a head-on collision is also observed.

We derive dispersion formulae for the transverse and longitudinal waves propagating through a Vlassov plasma, valid for relativistic as well as non-relativistic temperatures, and compare them with those of earlier workers. We discuss wave propagation under various limiting conditions of temperature.

Using the Dupree—Weinstock perturbed-orbit model of plasma turbulence, we obtain the diffusion equation describing the evolution of the average one-particle distribution function for whistler mode turbulence. The numerical result for electron pitch-angle diffusion within this scheme leads us to conclude that the effect of the resonance broadening due to perturbed orbits on the pitch-angle diffusion coefficient is not large compared with that evaluated by the unperturbed orbit in the whistler mode spectrum with a finite width. Based on the explicitly evaluated resonance function, the effects of this broadening on the growth rate for the whistler wave are also discussed.