Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Abstract

Abstract:We study the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in an unmagnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili Burgers (KPB) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the KPB equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.PACS Numbers: 52.27.Lw, 52.35.Fp, 52.35.Tc IntroductionIn the last few decades, numerous investigations have been made on the study of nonlinear waves and structures in low-temperature dusty plasmas as the presence of extremely massive charged dust particles plays a vital role in understanding the electrostatic disturbances in space plasma environments [1][2][3] as well as laboratory plasma devices [4,5]. It has been pointed out that the static charged dust grains can drastically modify the existing response of electrostatic wave spectra in dusty plasmas [4][5][6][7][8][9][10][11]. On the other hand, depending upon whether the dust grains are static or mobile, there appear new types of electrostatic waves including solitary or shock waves in plasmas. Shukla and Silin first theoretically [12] investigated the existence of low-frequency dust-ion acoustic (DIA) waves (with phase speed much smaller than the electron thermal speed and larger than the ion thermal speed) in a three-component dusty plasma. Later, this DIA wave was experimentally observed by Barkan et al using a dusty plasma device [13].The Korteweg-de Vries (KdV) equation, which governs the evolution of solitary waves, was first derived by Washimi and Tanuiti in a normal two-component plasma [14] using a reductive perturbation technique. It has been reported that multi-component plasmas in presence of sufficient amount of negative ions can support both compressive and rarefactive KdV solitons [15]. Furthermore, the properties of DIA solitary waves and shocks as observed in laboratory dusty plasmas are well explained by the modified KdV and KdV-Burgers (KdVB) equations [5,11,16,17].

Kadomstev-Petviashvilli-Burgers (KPB) Equation in a Five Component Cometary Plasma with Kappa Described Electrons and Ions

“…Here the coefficients A and B represent the nonlinearity and dispersion respectively; while C and D are respectively due to the kinematic viscosities and transverse perturbations. These coefficients are given by ( ) ( ) 3 3 3 2 2 2 2 2 2 1 1 1 1 2 3 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 1 1 1 1 5 5 5 5 3 3 3 3 27 5 5 3 1 3 27 5 5 5 18 3 3 3 1 As a check on our results we note that they reduce to that in Dev et al [31] when the additional ion and electron components are removed.…”

“…We use the reductive perturbation method to derive the KPB equation from (5) to (9) by introducing the transformations [31] ( )…”

Ion-acoustic shock waves in magnetized pair-ion plasma

“…An external magnetic field B 0 has been considered in the system directed along the z-axis defining B 0 = B 0 ẑ, where B 0 and ẑ are the strength of the external magnetic field and unit vector directed along the z-axis, respectively. The dynamics of the magnetized PI plasma system is governed by the following set of equations [36,37,38,39,40,41,42]…”

Propagation of dust-acoustic nonlinear waves in a homogeneous collisional dusty plasma

“…Typical examples are provided by the behavior of long waves in shallow water and waves in plasmas. For wave solutions, of the Kadomtsev-Petviashvili (KP) and modified Kadomtsev-Petviashvili (MKP) equations have been known for some time, but many problems involve not only dispersion but also dissipation, and these are not governed by the (KdV) or KP equation [20][21][22][23][24]. However, many examples of these more complex problems are found in fluid flow when there is a difference between the temperature of the layers, the propagation of waves in collisional plasma and also the propagation of the waves in viscous liquids [25][26][27].…”