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.

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

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.

Using a kinetic theoretical approach, the characteristics of electron acoustic waves (EAWs) are investigated in plasmas whose electron velocity distributions are modeled by a combination of two kappa distributions, with distinct densities, temperatures, and κ values. The model is applied to Saturn's magnetosphere, where the electrons are well fitted by such a double‐kappa distribution. The results of this model suggest that EAWs will be weakly damped in regions where the hot and cool electron densities are approximately equal, the hot to cool temperature ratio is about 100, and the kappa indices are roughly constant, with κc ≃ 2 and κh ≃ 4, as found in Saturn's outer magnetosphere (R ∼ 13–18 RS, where RS is the radius of Saturn). In the inner magnetosphere (R < 9 RS), the model predicts strong damping of EAWs. In the intermediate region (9–13 RS), the EAWs couple to the electron plasma waves and are weakly damped.

Existence domains and characteristics of ion acoustic solitons are studied in a two-temperature electron plasma with both electron components being kappa-distributed, as found in Saturn’s magnetosphere. As is the case for double-Boltzmann electrons, solitons of both polarities can exist over restricted ranges of fractional hot electron density ratio for this plasma model. Low κ values, which indicate increased suprathermal particles in the tail of the distribution, yield a smaller domain in the parameter space of hot density fraction and normalized soliton velocity (f, M), over which both soliton polarities are supported for a given plasma composition (the coexistence region). For some density ratios that support coexistence, solitons occur even at the lowest (critical) Mach number (i.e., at the acoustic speed), as found recently for a number of other plasma models. Like Maxwellians, low-κ distributions also support positive potential double layers over a narrow range of low fractional cool electron density (&lt;10%).

Using the Sagdeev potential approach, arbitrary amplitude modified ion acoustic solitons and double layers have been studied in an electron-positronion (e-p-i) plasma composed of Cairns-distributed electrons, Boltzmann positrons and cold ions. Existence domains are presented in different slices of parameter space, and care is taken to differentiate between behaviour at a fixed soliton speed, and at the Mach number normalized with respect to the true acoustic speed for the three-component plasma. Negative solitons, limited in Mach number by double layers, have been found over small ranges in β, relative positron density and Mach number. These have not previously been reported in an e-p-i plasma. A region of 'coexistence' in parameter space has been identified, in which solitons of both polarities are supported. In this region, one polarity behaves in a 'Korteweg-de Vries (KdV)-like' fashion, vanishing at the acoustic speed, while solitons of the other polarity have finite amplitude at the acoustic speed ('non-KdV-like'), as has been reported recently in a number of other plasma models. This work extends considerably and also corrects some errors in a recent publication (Pakzad 2009 Phys. Lett. A 373 847-50).

Using a kinetic theory approach, dust ion acoustic (DIA) waves are investigated in an unmagnetized collisionless plasma with kappa-distributed electrons and ions, and Maxwellian dust grains of constant charge. Both analytical and numerical results, the latter following from the full solution of the associated dispersion relation, are presented, and a comparison is made. The effects of the ion and electron spectral indices, as well as the species' density (ne/ni) and temperature (Te/Ti) ratios, on the dispersion and damping of the waves are considered. In the long wavelength regime, increases in both the electron spectral index (κe) and the dust density fraction (reduced f=ne/ni) lead to an increase in phase velocity. The range in wavelength over which modes are weakly damped increases with an increase in Te/Ti. However, the ion spectral index, κi, does not have a significant effect on the dispersion or damping of DIA waves.