The model of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] is generalized. A physically meaningful nonextensive nonthermal velocity distribution is outlined. As the nonextensive character of the nonthermal electrons increases, the distribution shoulders may become less or more prominent and high-energy states are less or more probable than in the extensive nonthermal case. It is found that our plasma model supports the coexistence of smooth rarefactive and spiky compressive ion-acoustic solitary waves. The rarefactive solitons are more affected by nonextensivity than their compressive counterpart and a slight increase in the nonextensive parameter may destroy this dual nature.
Arbitrary amplitude ion-acoustic solitary waves are addressed in a two-component plasma with a q-nonextensive electron velocity distribution. Our results show that in such a plasma solitary waves, the amplitude and nature of which depend sensitively on the q-nonextensive parameter can exist. Due to the electron nonextensivity, our plasma model can admit compressive as well as rarefactive ion-acoustic solitons. For q>1 (−1<q<1), the lower limit of the allowable Mach numbers is smaller (greater) than its Boltzmannian counterpart, allowing therefore the possibility of the existence of subsonic ion-acoustic solitons. As the nonextensive character of the plasma becomes important, the potential pulse amplitude increases while its width is narrowed. For −1<q<0, our plasma model can admit only rarefactive ion-acoustic solitary waves involving relatively high Mach numbers. Due to the flexibility provided by the nonextensive q-parameter, our results should help in providing a good fit between theoretical and experimental results.
The seminal paper of Mamun et al. [Phys. Plasmas 3, 702 (1996)] is revisited within the theoretical framework of the Tsallis statistical mechanics. The nonextensivity may originate from the correlation or long-range interactions in the dusty plasma. It is found that depending on whether the nonextensive parameter q is positive or negative, the dust-acoustic (DA) soliton exhibits compression for q<0 and rarefaction for q>0. The lower limit of the Mach number for the existence of DA solitary waves is greater (smaller) than its Maxwellian counterpart in the case of superextensivity (subextensivity).
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.
The modulational instability (MI) of ion-acoustic waves (IAWs) in a two-component plasma is investigated in the context of the nonextensive statistics proposed by Tsallis [J. Stat. Phys. 52, 479 (1988)]. Using the reductive perturbation method, the nonlinear Schrödinger equation (NLSE) which governs the MI of the IAWs is obtained. The presence of the nonextensive electron distribution is shown to influence the MI of the waves. Three different ranges of the nonextensive q-parameter are considered and in each case the MI sets in under different conditions. Furthermore, the effects of the q-parameter on the growth rate of MI are discussed in detail.
The phenomenon of Debye Shielding is revisited within the theoretical framework of the Tsallis statistical mechanics. The plasma consists of nonextensive electrons and ions. Both the effective Debye length λDq and the fall-off of the electrostatic potential Φ are considered and a parameter study conducted. Owing to electron nonextensivity, the critical Mach number derived from the modified Bohm sheath criterion may become less than unity allowing therefore ions with speed less than ion-acoustic speed to enter the sheath from the main body of the plasma. Considering the wide relevance of collective processes, our analysis may be viewed as a first step toward a more comprehensive Debye shielding and electrostatic plasma sheath in nonequilibrium plasmas.
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