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.

Velocity distribution functions with an excess of superthermal particles are commonly observed in space plasmas, and are effectively modeled by a kappa distribution. They are also found in some laboratory experiments. In this paper we obtain existence conditions for and some characteristics of ion-acoustic solitary waves in a plasma composed of cold ions and-distributed electrons, where Ͼ 3 / 2 represents the spectral index. As is the case for the usual Maxwell-Boltzmann electrons, only positive potential solitons are found, and, as expected, in the limit of large one recovers the usual range of possible soliton Mach numbers, viz., 1 Ͻ M Ͻ 1.58. For lower values of , modeling the presence of a greater superthermal component, the range of accessible Mach numbers is reduced. It is found that the amplitude of the largest possible solitons that may be generated in a given plasma ͑corresponding to the highest allowed Mach number for the given plasma composition͒ falls off with decreasing , i.e., an increasing superthermal component. On the other hand, at fixed Mach number, both soliton amplitude and profile steepness increase as is decreased. These changes are seen to be important particularly for Ͻ 4, i.e., when the electrons have a "hard" spectrum.

The nonlinear dynamics of electron-acoustic localized structures in a collisionless and unmagnetized plasma consisting of "cool" inertial electrons, "hot" electrons having a kappa distribution, and stationary ions is studied. The inertialess hot electron distribution thus has a long-tailed suprathermal (non-Maxwellian) form. A dispersion relation is derived for linear electron-acoustic waves. They show a strong dependence of the charge screening mechanism on excess suprathermality (through κ). A nonlinear pseudopotential technique is employed to investigate the occurrence of stationaryprofile solitary waves, focusing on how their characteristics depend on the spectral index κ, and the hot-to-cool electron temperature and density ratios. Only negative polarity solitary waves are found to exist, in a parameter region which becomes narrower as deviation from the Maxwellian (suprathermality) increases, while the soliton amplitude at fixed soliton speed increases. However, for a constant value of the true Mach number, the amplitude decreases for decreasing κ.

The nonlinear propagation of ion-acoustic waves is considered in a magnetized plasma, composed of kappa distributed electrons and an inertial ion fluid. The fluid-dynamical system of equations governing the dynamics of ion-acoustic waves is reduced to a pseudoenergy-balance equation. The properties of arbitrary amplitude, obliquely propagating ion-acoustic solitary waves are thus investigated via a mechanical-motion analog ͑Sagdeev potential͒ approach. The presence of excess superthermal electrons is shown to influence the nature of magnetized ion-acoustic solitons. The influence on the soliton characteristics of relevant physical parameters such as obliqueness ͑the angle between soliton propagation direction and magnetic field͒, the electron deviation from a Maxwellian ͑"superthermality"͒ and the soliton speed is investigated.

A study is presented of the nonlinear self-modulation of low-frequency electrostatic (dust acoustic) waves propagating in a dusty plasma, in the presence of a superthermal ion (and Maxwellian electron) background. A kappa-type superthermal distribution is assumed for the ion component, accounting for an arbitrary deviation from Maxwellian equilibrium, parametrized via a real parameter κ. The ordinary Maxwellian-background case is recovered for κ→∞. By employing a multiple scales technique, a nonlinear Schrödinger-type equation (NLSE) is derived for the electric potential wave amplitude. Both dispersion and nonlinearity coefficients of the NLSE are explicit functions of the carrier wavenumber and of relevant physical parameters (background species density and temperature, as well as nonthermality, via κ). The influence of plasma background superthermality on the growth rate of the modulational instability is discussed. The superthermal feature appears to control the occurrence of modulational instability, since the instability window is strongly modified. Localized wavepackets in the form of either bright-or dark-type envelope solitons, modeling envelope pulses or electric potential holes (voids), respectively, may occur. A parametric investigation indicates that the structural characteristics of these envelope excitations (width, amplitude) are affected by superthermality, as well as by relevant plasma parameters (dust concentration, ion temperature).

No abstract

A head-on collision between two dust ion acoustic solitary waves (DIASWs) travelling in the opposite direction in a weakly relativistic plasma composed of four distinct particle populations, namely, weakly relativistic ion fluid, superthermal electrons as well as positrons, and immobile dust, is investigated. By employing extended Poincaré-Lighthill-Kuo method, two Korteweg-de Vries (KdV) equations are derived. The analytical phase shift after a head-on collision of two dust ion acoustic (DIA) solitary waves is also obtained. The combined effects of relativistic factor (β), electron to positron temperature ratio (α), ion to electron temperature ratio (σ), positron to electron density ratio (P), dust density ratio (d), and superthermality of electrons as well as positrons (via κ) on the phase shifts are numerically studied. All these physical parameters have also changed the potential amplitude and the width of colliding solitary waves. It is found that the presence of superthermal electrons as well as positrons and dust grains has emphatic influence on the phase shifts and potential pulse profiles of compressive DIA solitons. Our results are general and may be helpful in understanding a head-on collision between two DIASWs in astrophysical and laboratory plasmas, especially the interaction of pulsar relativistic winds with supernova ejecta that produces the superthermal particles and relativistic ions.