M. A. Hellberg

A dispersion function for plasmas containing superthermal particles

It is now well known that space plasmas frequently contain particle components that exhibit high, or superthermal, energy tails with approximate power law distributions in velocity space. Such nonthermal distributions, with overabundances of fast particles, can be better fitted, for supra‐ and superthermal velocities, by generalized Lorentzian or kappa distributions, than by Maxwellians or one of their variants. Employing the kappa distribution, with real values of the spectral index κ, in place of the Maxwellian we introduce a new plasma dispersion function expected to be of significant importance in kinetic theoretical studies of waves in space plasmas. It is demonstrated that this function is proportional to Gauss’ hypergeometric function 2F1[1,2κ+2;κ+2;z] enabling the well‐established theory of the hypergeometric function to be used to manipulate dispersion relations. The reduction, for integer values of κ, to the less general so‐called modified plasma dispersion function [Phys. Fluids B 3, 1835 (1991...

The Korteweg–de Vries–Zakharov–Kuznetsov equation for electron-acoustic waves

Motivated by a recent paper [Phys. Plasmas 7, 2987 (2000)] highlighting the potential importance of the electron-acoustic wave in interpreting the solitary waves observed by high time resolution measurements of the electric field in the auroral region, the effect of a magnetic field on weakly nonlinear electron-acoustic waves is investigated. A Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation is derived for a plasma comprised of cool and hot electrons and a species of fluid ions. Two models are employed for the ions: magnetized and unmagnetized. When the ions are magnetized the frequency constraints imposed upon the electron-acoustic wave packet prove to be too limiting to be of general use. The second model, which treats the ions as a stationary neutralizing background, overcomes the restrictions imposed by the former and is more fitting for the frequency domain of the electron-acoustic wave. Plane and ellipsoidal soliton solutions are admitted by the KdV-ZK equation, the latter perhaps able to explain some of the two dimensional features of the solitary waves observed in the Earth’s high altitude auroral region. Both models for the ions predict only negative potential solitons. It is discussed how the plasma model might be adapted to produce positive potential solitons.

Arbitrary-amplitude electron-acoustic solitons in a two-electron-component plasma

Motivated by plasma and wave measurements in the cusp auroral region, we have investigated electron-acoustic solitons in a plasma consisting of fluid ions, a cool fluid electron and a hot Boltzmann electron component. A recently described method of integrating the full nonlinear fluid equations as an initial-value problem is used to construct electron-acoustic solitons of arbitrary amplitude. Using the reductive perturbation technique, a Korteweg-de Vries equation, which includes the effects of finite cool-electron and ion temperatures, is derived, and results are compared with the full theory. Both theories admit rarefactive soliton solutions only. The solitons are found to propagate at speeds greater than the electron sound speed (e0c/e0e)½υe, and their profiles are independent of ion parameters. It is found that the KdV theory is not a good approximation for intermediate-strength solitons. Nor does it exhibit the fact that the cool- to hot-electron temperature ratio restricts the parameter range over which electron-acoustic solitons may exist, as found in the arbitrary-amplitude calculations.

The electron-acoustic mode in a plasma with hot suprathermal and cool Maxwellian electrons

The electron-acoustic wave, in a plasma with hot suprathermal, kappa-distributed electrons and cool, Maxwellian electrons, is investigated. This model is a generalization of those that have been investigated previously, and through its parametrization by κ, can be reduced to many previous models of the stable wave. It is found that the hot suprathermal electrons significantly increase the Landau damping of the wave at small wave numbers, i.e., in its acoustic regime. Results from a survey of parameter space, which help to identify parameters for which the stable mode will be only weakly Landau damped, are presented. The dependence of the Landau damping on the fraction of suprathermal electrons, which is related to the index, κ, of the hot electron distribution, is investigated in detail.

Electrostatic solitons in multispecies electron-positron plasmas

Acoustic solitons are investigated in electron-positron plasmas containing equal hot and cool components of both species. The hot components are isothermal Boltzmann distributed, the cool constituents are modelled by adiabatic fluids. The equations are integrated exactly in terms of a Sagdeev potential. Solitons are shown to be possible, but no double layers, due to the symmetry in the model. Bearing in mind the constraints imposed by the Boltzmann assumption, small amplitude solitons only are found. Such findings are relevant for different kinds of astrophysical plasmas, as well as for other types of similar acoustic solitons.

Compressive and rarefactive ion-acoustic solitons in bi-ion plasmas

Nonlinear propagation of ion-acoustic solitary structures in plasmas with an admixture of heavy ions is studied in the wave frame, where they are stationary, using a recently developed gas-dynamic approach, as an alternative to the conventional Sagdeev pseudopotential method. This viewpoint brings out the gas-dynamic aspects, which then allow a characterization of the solitary wave structures in terms of the species’ sonic points, the global charge neutral points, and critical collective Mach numbers. It is shown that the concepts of a critical density in the Korteweg–de Vries (KdV) treatment, and of a changeover from compressive to rarefactive soliton character, correspond to the formation of a second charge neutral point (outside equilibrium) in the rarefactive regime, at which the electric stresses maximize. It is possible therefore that in certain regions of parameter space compressive and rarefactive solitons can co-exist. The compressive solitons are not predicted by a weakly nonlinear KdV treatment...

Generalized Langmuir waves in a magnetized plasma with a Maxwellian–Lorentzian distribution

The generalized Langmuir modes in a magnetized plasma whose electrons have a hybrid kappa-Maxwellian velocity distribution are investigated in both the strongly and weakly magnetized regimes. It is found that the kappa distribution significantly alters both the dispersion relation and the Landau damping of the waves from what is ordinarily accepted based on the Maxwellian distribution. In general, the kappa distribution decreases the damping rate of the generalized Langmuir modes in the short wavelength region, but enhances it at the longest wavelengths. The spectral index of the distribution affects the real part of the dispersion relation also, but usually to a somewhat lesser extent. The modifications to both the real and imaginary parts of the dispersion relation are discussed in detail and the implications for plasma waves in space plasmas are briefly noted.

Alfvén-Jeans and Magnetosonic Modes in Multispecies Self-Gravitating Dusty Plasmas

Perpendicularly propagating electromagnetic waves in magnetized, multispecies, self-gravitating dusty plasmas are investigated in terms of their wave dispersion properties as well as with respect to their susceptibility to gravitational collapse. In particular, waves on the ordinary as well as extraordinary mode branches are considered. Within the one-dimensional propagation model employed, all modes except the ordinary mode produce density perturbations that can be unstable to gravitational collapse. The wavelengths that are unstable are comparable to the well-known Jeans length for a neutral gas/dust, but there are interesting modifications due to the presence of a magnetic field and charged particles. Furthermore, the effects of the gravitational coupling of a multicomponent plasma to a neutral dust are discussed.

Jeans stability of dusty space plasmas.

Abstract The Jeans stability of dusty plasmas is re-considered. In contrast to a gas, a dusty plasma can support a plethora of wave modes each potentially able to impart to the dust particles the randomising energy necessary to avoid Jeans collapse on some length scale. Consequently, the analysis of the stability to Jeans collapse is many-fold more complex in a dusty plasma than it is for a charge-neutral gas. After recalling some of the fundamental ideas related to the ordinary Jeans instability in neutral gases, we extend the discussion to plasmas containing charged dust grains. Besides the usual Jeans criterion based upon thermal agitation, we consider two other ways of countering the gravitational collapse: (i) via the excitation of dust-acoustic modes and (ii) via a novel Alfven-Jeans instability, where perturbations of the dust mass-loaded magnetic field counter the effects of self-gravitation. These two mechanisms yield different minimum threshold length scales for the onset of instability/condensation. It is pointed out that for the study of the Jeans instability produced by density enhancements induced in the plasma by the presence of normal wave modes, even more prohibitive plasma size constraints must necessarily be satisfied.

On the existence of ion-acoustic double layers in negative-ion plasmas

It is well known that ion-acoustic double layers occur in plasmas containing two-temperature electron species and positive ions. In a recent study Verheest suggested that such structures can occur when there is only one electron species but both negative and positive ion species. There a stationary modified Korteweg de Vries equation was derived to support his deduction. This prediction, however, contradicts our own arbitrary-amplitude studies, which also cover the Verheest parameter regime. Here we resolve the discrepancy by examining both approaches in the pseudo-potential formulation in more relevant detail. The implications of this study extend beyond the realm of the present subject.