Nonextensive dust acoustic solitary and shock waves in nonplanar geometry

Abstract

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.

Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution

“…The physical explanation for the parameter q different from unity was represented for the nonequilibrium plasma system with Coulombian long-range interactions 19 . Many of the basic characteristics of electron-ion plasmas and dusty plasmas have been investigated under the condition of the power-law q-distributions, such as electron and ion dust charging process 26 , ion acoustic waves [27][28][29][30][31][32][33] , dust acoustic waves [34][35][36][37] , solitary waves 29,[36][37][38] , electron acoustic waves [39][40][41] , and Jeans' instability in space plasma 42,43 , etc. Nevertheless, according to present knowledge, the usually employed q-distribution function is not factorized for kinetic and potential energies because without considering the nonextensivity of the energy.…”

Assumptions and ambiguities in nonplanar acoustic soliton theory

“…However, one finds in the literature other plasma models, which then either lead to an equation like (23), but with more complicated coefficients, [12][13][14][15][16][17][18][19][20][21]24,25,30,32,33,36,[38][39][40][41][42]44,46,49,54 or to modifications of related evolution equations like the Burgers, 23,31,35 KdV-Burgers, 22,37,45,47,48 Gardner, [26][27][28][29]34,43,44,[50][51][52][53]55,56 or Schamel 23 equations. The standard forms of these equations have been well studied in the literature over many decades.…”

Dust-acoustic solitary waves in a dusty plasma with dust of opposite polarity and vortex-like ion distribution

“…Direct evidence is available for the existence of both positively and negatively charged dust particles in the earth's mesosphere (Klumov et al 2000;Havens et al 2001;Smiley et al 2003), as well as in cometary tails and comae (Horanyi and Mendis 1986). Because of the involvement of the charged dust grains in plasmas, different collective processes exist and very rich wave modes can be excited in dusty plasmas such as dustacoustic (DA) waves (Rao et al 1990), dust ion acoustic waves (Shukla and Silin 1992;Barkan et al 1996;Alinejad 2011) and dust-lattice waves (Melandsø 1996;Homann et al 1997;Sahu and Tribeche 2012a). On the contrary, Schamel et al (2001) reported the existence of a new class of ultra low-frequency nonlinear mode called dust-Coulomb waves in a dense charge-varying dusty plasma with trapped dust particles.…”