A recent paper [L.-N. Hau and W.-Z. Fu, Phys. Plasmas 14, 110702 (2007)] deals with certain mathematical and physical properties of the kappa distribution. We comment on the authors’ use of a form of distribution function that is different from the “standard” form of the kappa distribution, and hence their results, inter alia for an expansion of the distribution function and for the associated number density in an electrostatic potential, do not fully reflect the dependence on κ that would be associated with the conventional kappa distribution. We note that their definition of the kappa distribution function is also different from a modified distribution based on the notion of nonextensive entropy.

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)] is demonstrated. An example illustrating the use of the function is presented.

Dust ion acoustic solitons in an unmagnetized dusty plasma comprising cold dust particles, adiabatic fluid ions, and electrons satisfying a distribution are investigated using both small amplitude and arbitrary amplitude techniques. Their existence domain is discussed in the parameter space of Mach number M and electron density fraction f over a wide range of values of. For all Ͼ 3 / 2, including the Maxwellian distribution, negative dust supports solitons of both polarities over a range in f. In that region of parameter space solitary structures of finite amplitude can be obtained even at the lowest Mach number, the acoustic speed, for all. These cannot be found from small amplitude theories. This surprising behavior is investigated, and it is shown that f c , the value of f at which the KdV coefficient A vanishes, plays a critical role. In the presence of positive dust, only positive potential solitons are found.

-Ion acoustic solitary waves in two-temperature electron plasmas have been studied in the past, and negative-potential solitons and double layers found, in addition to positive-potential solitons. Here, further investigations show that positive-potential double layers can form below a critical density ratio, associated with the third derivative of the Sagdeev potential evaluated at the origin for the phase velocity of the linear wave. For density ratios that support positive double layers, solitons are also reported beyond the double layers, depending on the cool-to-hot electron temperature ratio. In addition, when both polarities can be supported, solitary structures can propagate at the acoustic speed, contrary to a KdV prescription. Copyright c EPLA, 2010Introduction. -Ion acoustic solitary waves in a twotemperature plasma have been studied by a number of authors in the past [1][2][3][4]. Using fluid equations, Nishihara and Tajiri [2] considered a plasma with hot and cool Boltzmann electron components and showed that there are two regions of wave propagation, normal and anomalous, where the anomalous propagation is characterized by the steepening of the wave so as to decrease the density. They also found that for a certain parameter region, finite-amplitude rarefactive and compressive ion acoustic solitons can both be supported (loosely, "coexist"), with the small-amplitude rarefactive (or compressive) solitons existing only in the plasma configuration having anomalous (or normal) propagation properties. As we shall show, in terms of Sagdeev potentials [5], the two regions are separated by a curve obtained for parameter values for which both the second and third derivatives of the Sagdeev potential vanish at the origin.As the terminology "compressive" and "rarefactive" is not well defined in a multifluid plasma, we point out that in this model, rarefactive (compressive) solitons have negative (positive) electrostatic potential. In this paper we show that in the region of "coexistence", if the negative solitons have amplitudes that vanish as their velocity approaches the acoustic speed, as for Korteweg-de Vries

A generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys. Plasmas 2, 2098 (1995)]. In many instances plasmas are found to have anisotropic power-law distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a one-dimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed. It is used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field. This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique.

An investigation into both small and large amplitude dust acoustic solitary waves in dusty plasmas with cold negative dust grains and kappa-distributed ions and/or electrons is discussed. Existence conditions for the arbitrary amplitude case are found in an appropriate parameter space, viz., an effective Mach number of the structure speed and the fraction of the charge density that resides with the free electrons, expressed in terms of the ion density. Results indicate that the kappa distribution has only a quantitative, not a qualitative effect on the existence domains and only negative potential solitons exist regardless of whether the electrons or the ions, or both, have a kappa distribution. Despite a wide-ranging search, we have not found double layers in such a plasma. In the case of positive dust, an equivalent set of results holds.

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 (ε0c/ε0ε)½υε, 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.

We discuss critical curves that allow us to predict, qualitatively, the topological behaviour of higher-order modes in a two-electron-temperature plasma as wavenumber and hot electron fraction are varied. The relationship of these higher-order modes to the electron-acoustic wave is elucidated.