Small-amplitude ion-acoustic double layers in a magnetized plasma have been studied, taking account of Poisson's equation. Both analytical and numerical solutions are obtained for compressive and rarefactive double layers. It is found that the results are significantly different from the case when quasi-neutrality is assumed.

Dispersion relations are obtained for Alfvén surface waves in a two-ion-species cylindrical plasma with finite edge density. A simple step density profile is used. The results are compared with those obtained in a plasma surrounded by a vacuum layer. For modes with positive poloidal mode number m the finite-density edge region introduces an ion-cyclotron resonance and a waveguide cutoff in the surface-wave dispersion relation at the cyclotron frequency of each ion species. For negative-m modes a new dispersion-relation branch is introduced at frequencies just below the ion-cyclotron frequency of each species. The origin of these effects is analysed in terms of the wave types that can propagate in the regions of constant density, and their interaction with the Alfvén and ion-ion hybrid resonances in these regions. This interaction is shown to be determined by the polarization of the wave fields. The relevance of the results to the Alfvén-wave and ion-cyclotron-resonance heating schemes is discussed. The possibility that the excitation of high-m surface waves contributes to the anomalously large fraction of power that is found to be deposited in the plasma edge during ion-cyclotron-resonance heating is considered.

The stability of oblique modulation of ion-acoustic waves in a collisional plasma with one and two electron-temperature distributions is studied using the KBM method. For the case of one electron distribution it is found that collisions give rise to regions of physical instability that are otherwise stable in the absence of collisions. For the two-electron-distribution case in the presence of collisions the domains of physical instability of the wave are studied with respect to the values of the temperature ratio and relative concentration of the two electron species.

A study is made of ion-acoustic double layers in a plasma consisting of any number of cold positive and negative ion (and cold electron) species in addition to one isothermal electron population. The Sagdeev potential is obtained in general, together with limits on both compressive and rarefactive solutions for ion-acoustic double layers and/or solitons. Weak ion-acoustic double layers are described by a modified Korteweg-de Vries equation. Such double layers are not possible in plasmas with only positive ion species and one electron population. When one or more negative ion and/or cold electron species are included above a certain threshold density, rarefactive ion-acoustic double layers occur, but no compressive ones. The double-layer form of the potential is given, together with an application to a plasma with one positive and one negative ion component. It is shown that there is indeed such a threshold density for the negative ion density, depending on the charge-to-mass ratios of both types of ions. The threshold density is determined numerically for a range of such ratios and discussed in view of possible relevance to auroral and experimental plasmas. In the discussion, cold electrons can play the role of the negative ion species.

The (usually neglected) effect of shear on the equilibrium of rippled, magnetically focused beams of relativistic charged particles is investigated analytically in the cold-fluid approximation. Closed expressions for the beam-related parameters and magnetic and electric fields are derived. The results obtained in this work represent the basis for the stability analysis of sheared rippled beams that is required, for example, for beam stabilization and generation of free-electron laser devices.

Simple higher-order approximations for the linear growth rate γ(k) of the electron Weibel instability are obtained by using fractional approximations for the plasma dispersion function. Approximate expressions for γ(k) are found that are valid in the regions T⊥/T‖ < 5 and T⊥/T‖ > 120 (where T⊥ and T‖ are perpendicular and parallel electron temperatures respectively).

We consider the transition scattering of waves on charged dust particles in a plasma. The scattered power is first derived from perturbation theory, for the case of weakly charged grains, where linear screening by the plasma particles can be assumed. In the case of a highly charged grain we first determine the nonlinear screening by the plasma particles, in a model where the grain can be treated as a small spherical probe at floating potential, and then solve the nonlinear transition scattering due to the electron shielding cloud. One of the results of our calculation is that the radiation pressure on the grains can be greatly enhanced with respect to the case of usual Thomson scattering on free particles, and some possible astrophysical consequences are discussed.

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.

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.

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.

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

.