We explore the long-term nonlinear evolution of a tearing-mode-unstable sheared-field plasma in a turbulent environment. Two different physical configurations are modeled, and a different computational system is used for each. Results of both sets of calculations show that magnetic tearing arises spontaneously provided that the initial turbulence energy level is below the natural saturation level of the tearing instability.

We discuss briefly the relationship between our results and those of previous calculations, concluding that there are no significant unexplainable disagreements.

A numerical parametric study of the radial ambipolar electric field in a stellarator reactor has been undertaken. With the numerical neoclassical code FLOCS (Flow Code for Stellarators), which is capable of handling both ions and electrons of all relevant kinetic energies, the radial ambipolar field (Er)AMB is determined from the algebraic condition that ion and electron fluxes are equal. As expected, the potential is of the same order of magnitude as the temperature. Somewhat surprisingly at first sight, however, the potential does not change much with the temperature (in the parameter range under consideration), being somewhat insensitive to moderate variations of T. An explanation for this behaviour is presented. Finally, the radial particle fluxes, consistent with the obtained (Er)AMB, and the particle confinement time are computed.

In this paper we develop spectral laws for the small- and large-wavenumber regimes of the energy and enstrophy cascades in electrostatic turbulence and discuss how these spectra differ, owing to compressibility effects, from those for two-dimensional hydrodynamic turbulence. We also show that the compressibility effects on the scaling laws can be described as intermittency corrections formulated according to the log-normal model of Obukhov and Kolmogorov.

The presence of charged dust particles in a plasma can change its dispersion properties. From the linear response of an equilibrium dusty plasma to the propagation of small perturbations, we find an average dielectric function є(ω, k) for the system in the case when the grain space distribution is random, and ensemble averages are taken over the random variables. For the case of high-frequency plasma waves, when for the unperturbed case (cold plasma), we find that є becomes complex in the presence of the dust, leading to possible damping in a domain where Landau damping is usually negligible (ω ≫ kVT).

The time dynamics of two-wave and four-wave mixing in a collisional plasma are explored. Maxwell's equations are coupled to the governing equations of a warm collisional plasma; this is followed by linearization based on a strong undepleted pump wave and simplification by the slowly varying envelope approximation. The resulting equations are solved via Laplace-transform techniques. We predict that in the presence of collisions between the plasma charged particles and background neutrals the two-wave-mixing geometry produces spatial amplification of an applied probe wave under transient (or nearly degenerate) conditions on the frequencies. The four-wave-mixing configuration produces a response that is governed by a ratio of characteristic time constants and the average number of collisions in a characteristic spatial scale. In both configurations enhancement of the plasma response occurs when transient or nearly degenerate conditions generate a moving intensity grating that propagates at a velocity of a natural mode of the plasma. The two-wave-mixing geometry has a single such resonance condition, and the four-wave-mixing geometry has two.

We have studied wave propagation in a cold plasma, in the presence of a spatially rotating magnetic field of constant magnitude. New features introduced by this variation include streaming velocities and a plasma current in equilibrium and density fluctuations. We present only the case of wave propagation along the axis of rotation of the magnetic field. A set of ordinary differential equations for the electric field components is obtained, which may be combined into a single fourth-order ordinary differential equation with periodic coefficients. Solutions are obtained in closed form and their nature is determined in terms of the physical parameters of the System, magnetic field strength, number density and wave frequency.

Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic.

Electromagnetic-wave propagation in inhomogeneous magnetized plasmas is studied. Two different approaches to the subject are discussed and compared. Explicit expressions for the dielectric tensor components are derived following an established procedure that takes into account the effects of the gradients of plasma parameters, and are shown to possess non-resonant contributions to the anti-Hermitian parts. General and explicit expressions are also derived by following a different approach that has recently appeared in the literature, and are shown to possess satisfactory symmetry properties leading to anti-Hermitian parts comprising only resonant terms. The simple case of high-frequency waves in the ordinary mode propagating perpendicularly to the ambient magnetic field is presented as an example in order to show that the use of the dielectric tensor derived using the second method correctly describes wave absorption and/or amplification, eliminating the feature of non-resonant absorption that arises from the use of the first method.

In a weakly dissipative and weakly space-time-varying plasma the propagation of electromagnetic waves may be described by geometric optics. The local tensors governing geometric optics possess approximate symmetries, which become exact in the limit of zero dissipation. These symmetries, which are well known from explicit expressions obtained in various plasma models assuming a homogeneous background, have not previously been created satisfactorily, either with respect to their appearance or to their derivation for an inhomogeneous medium. As an example of the implications of these symmetries, the coupled mode equations for the resonant interaction between three geometric-optics modes are derived in a form such that, in the dissipationless limit, the linear part of the equations conserves wave action. When nonlinear interaction terms are included, the waves are shown to exchange wave action in accordance with the Manley—Rowe relations.

A study has been carried out of free double layers formed within the plasma volume of a low-pressure mercury-arc discharge at high current densities. The free double layer is observed to form as a visible boundary, which drifts slowly from the central section of the discharge. Current-driven instabilities are observed as the discharge current is gradually increased to a critical value, at which current limitation is observed to occur. This process, which is accompanied by high-current spikes, ceases when the free double layer becomes visible as a sharp boundary dividing the discharge column into two regions of different luminosities. The layer is observed to form in the later stages of current limitation, the onset of which occurs for a ratio of drift to thermal speed of electrons of about unity. Electrical energy is converted by the layer into kinetic energy of the charged particles. Accordingly, high-energy ions were measured by means of an electrostatic energy analyser. The multiple-sheath character of the free ‘double layer’, which is inferred from probe measurements of potential profiles, is discussed and comparisons with other space-charge structures with the same topology are made.

Local tensors determining the geometric-optics description of a Vlasov-Maxwell plasma are considered. The linear and quadratic current responses on a small-amplitude electromagnetic perturbation are given by expressions for the local admittance tensors. These explicitly exhibit symmetries that imply the linear conservation of wave action, if wave-particle interactions are neglected, and the corresponding quadratic conservation laws. Considering, for example, the resonant interaction between three geometric-optics modes the Manley—Rowe relations accordingly follow. Various extensions of the results, including consideration of higher orders in the small amplitude, strong space and time dependence of the background plasma, relativistic theory and the gyrokinetic approximation as well as some corresponding results for important fluid models, may be obtained straightforwardly either directly or by combining the results of this paper with those of previous work.

The effect of non-uniformities on the flow of electric current in weakly ionized plasmas is investigated by taking into account the ion slip as well as the Hall current. An Ohm's law for a non-uniform plasma is derived, from which the formula previously obtained by Numano, i.e. an extension of Rosa's equation, is obtainable as a special case. Making use of this new Ohm's law, the effective electrical conductivity and the effective Hall parameter are determined for isotropically turbulent plasmas. It is found that when the ion-slip effect is absent they are in good agreement with the results obtained previously.

We consider the resonant interaction between two transverse waves and one longitudinal wave in a plasma. In particular, we discuss coupling phenomena involving long-wavelength modes that have been overlooked by previous authors.

We study nonlinear effects including possible modulational instability of an intense electromagnetic pulse propagating through a fully ionized unmag-netized plasma. (The pulse is assumed to be sufficiently strong to accelerate particles to weakly, but not fully, relativistic velocities.) The envelope is shown to evolve over long time scales in general according to a vector form of the well-known cubic nonlinear Schrödinger (NLS) equation. Three distinct nonlinear effects contribute terms cubic in the amplitude and thus can be of comparable magnitude: ponderomotive forces, relativistic corrections and harmonic generation. In contrast with previous work, our calculation takes all three effects into account. Integrability and modulational stability of any given system are shown to depend on polarization, frequency, composition and temperature, and these dependences are given. We first carry out the calculation in detail for the case of zero temperature. In the special case of a cold positron-electron plasma, in contrast with the predictions of Chian & Kennel (1983), the model is strictly modulationally stable for both linear and circular polarization. We then generalize our result by giving the dependence of the nonlinear coefficients on temperature. As it turns out, finite-temperature effects are qualitatively important only near a critical frequency (<3/2ωp) just above the plasma frequency for which the group velocity is comparable to either (or both) of the sound velocities. The results have important implications for pulsar micropulse observations and possible technological applications.

This paper extends our previous results (Kates & Kaup 1989) on the nonlinear modulational stability properties of plasma electromagnetic pulses to include the presence of an ambient magnetic field B0 parallel to the direction of propagation. As before, the pulse is assumed to be sufficiently strong to accelerate particles to weakly, but not fully, relativistic velocities. The positive component may consist of either positrons or singly charged ions, and no specific assumptions or approximations are made concerning the mass ratio of the components (previous work assumed a positron—electron plasma). The plasma is assumed to be fully ionized. The effects of a finite temperature are included for generality. Using singular perturbations, we derive approximate solutions that describe the evolution of a circularly polarized pulse. The envelope is shown to evolve over long time scales according to the cubic nonlinear Schrödinger (NLS) equation. Relativistic corrections and pon-deromotive forces both contribute terms cubic in the amplitude. (In contrast with the case studied in Kates & Kaup (1989), harmonic effects vanish identically here because of circular polarization.) A positron-electron plasma without magnetic fields was shown in our previous paper to be modulationally stable, except in the case of finite temperature, where modulational instability is possible near the plasma frequency ωp. Here it is shown that, even for a cold plasma, the presence of an ambient magnetic field makes a decisive difference: modulational instability can arise within a broad range of frequencies and values of B0, in particular for a pure positron-electron plasma. For given B0 and polarization we demonstrate the existence of critical frequencies for the onset of modulational instability. This result has important consequences for observations of pulsar micropulses and possible technological applications.

We report here some corrections to the above paper.

First there are some minor typographical errors. In (6a) and (8a) the term

should be replaced by

and the term

should be replaced by

There are also two terms missing in the derivation of (6a). These result from the fact that the second-order angular drift frequency in

also yields a contribution of the same order as the other terms in (6a). One should therefore add to the right-hand side of (6a) and (8a) the terms

.