Dust-ion-acoustic shock waves due to dust charge fluctuation

Abstract

A dusty plasma system containing Boltzmann electrons, mobile ions and charge fluctuating stationary dust has been considered. The nonlinear propagation of the dust-ion-acoustic waves in such a dusty plasma has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and is responsible for the formation of the dust-ionacoustic shock waves. The basic features of such dust-ion-acoustic shock waves have been identified. The implications of our results in space and laboratory dusty plasmas are discussed.It has been first theoretically [1] shown that, due to the conservation of equilibrium charge density n i0 e − n e0 e = z d0 n d0 e and the strong inequality n e0 n i0 [where n s0 is the equilibrium particle number density of the species s with s = e, i, d for electrons, ions, dust particles, z d0 is the equilibrium number of electrons residing onto the dust grain surface, and e is the magnitude of the electronic charge], a dusty plasma (with negatively charged static dust grains) supports low frequency dust-ion-acoustic (DIA) waves with phase speed much smaller (larger) than electron (ion) thermal speed. The dispersion relation (a relation between the wave frequency ω and the wave number k) of the linear DIA waves is [1] ω 2 = (n i0 /n e0 )k 2 C 2is the ion-acoustic speed (with T e being the electron temperature and m i being the ion mass) and λ De = (k B T e /4πn e0 e 2 ) 1/2 is 0375-9601/$ -see front matter

Dust ion-acoustic solitary and shock waves in a dusty plasma with non-thermal electrons

“…Actually, this view point may not be a realistic situation in space and laboratory devices because the charge on the dust particles varies with time and space. The dusty plasma waves are always concerned with the dust fluctuation (Duha and Mamun 2009;Popel et al 2003;Mamun and Shukla 2002a;Moslem 2006;Shukla 2000), which is one of the unique features of any dusty plasma system. However, it has been demonstrated (Shukla and Mamun 2002) that the dust charge fluctuation effect is important only for those waves whose period is comparable to dust grain charging period.…”

“…Therefore, the effect of the dust charge fluctuation is very important for the investigation of the DIA wave. A number of theoretical investigations (Duha and Mamun 2009;Popel et al 2003;Mamun and Shukla 2002a;Moslem 2006;Shukla 2000;Ghosh et al 2000aGhosh et al , 2000b has been made on the effects of the dust charge fluctuation on the nonlinear propagation of the DIA wave during the last few years. Most of the studies discussed up to now investigated the basic properties of nonlinear waves associated with DIA waves, when electrons are isothermal (non-isothermal) and follow the Boltzmann (vortex-like) distribution function.…”

Charge variation induced nonlinear wave damping in a nonthermal plasma

“…͑27͒ have been derived. [20][21][22][23][24] Except for the damping term a 3 in Eq. ͑27͒ which depends sensitively on the nonthermal parameter ␣, the coefficients a 1 and a 2 are similar to those already derived by Ghosh et al 13 Figure 1 indicates that a 3 decreases with increasing ␦ = n e0 / n i0 ͑n d0 → 0͒ and ultimately disappears in the dust-free plasma case ͑␦ =1͒ revealing therefore that the damping effect is solely due to the dust charge variation.…”

Compressive and rarefactive DIA solitons beyond the KdV limit

“…After the prediction of the novel dust-ion acoustic (DIA) waves [1] by Shukla and Silin, the nonlinear structures associated with these novel DIA waves [1][2][3][4], particularly DIA solitary [5][6][7][8][9][10] and shock [11][12][13][14][15][16][17] waves, have received a great deal of interest in understanding the basic properties of the localized electrostatic perturbations in space [18][19][20][21][22] and labo ratory dusty plasmas [3,4,[10][11][12]. The finite ampli tude DIA solitary (shock) structures in a dusty plasma have been intensively investigated by deriving KdV or Burgers equation in either planar [10,11,15,17] or nonplanar [7,23,24] geometry.…”