A theoretical model is presented to study the characteristics of dust acoustic shock in a viscous, magnetized, rotating dusty plasma at both fast and slow time scales. By employing the reductive perturbation technique, the non-linear Zakharov-Kuznetsov-Burger (ZKB) equation is derived for both cases when the dust is inactive and dynamic (fast and slow time scales). Both electrons and ions are considered to follow the kappa/Cairns distribution. It is observed that in both cases, i.e. when dust is in the background and active, viscosity plays a key role in dissipation for the propagation of acoustic shock. Magnetic field and rotation are responsible for the dispersive term. Superthermality is found to affect significantly the formation of the shock wave along with viscous nature of plasma, whereas the dust charge affects the non-linear coefficient of the ZKB equation. The present investigation may be beneficial to the understanding of the rotating plasma, in particular the experiments being carried out. K E Y W O R D S dusty plasmas, nonlinear waves, shocks, ZK Burger equation 1 INTRODUCTION Despite a history spanning nearly a century, research into complex (dusty) plasmas (consisting of solid particles of nanometres to hundreds of micrometres size in a conventional two-component plasma) has progressed significantly only in last two decades, mainly after the marvellous observation of dusty plasma crystals by Thomas et al. in 1994. [1] Also, for more than 10 years dusty plasmas under minute gravity conditions have been studied on board the International Space Station (ISS) under the joint Russian/German venture of Plasma Kristall (PK), along with PKE-Nefedov, PK-3 Plus, and PK-42014 onwards. [2] Other than novel experimental discoveries of dusty plasma crystals, dust Mach cones, [3] dust acoustic waves, dust voids, [4] etc., the notion of possible existence of 'dust atoms and molecules' was also put forward by Tsintsadze, Murtaza, and Ehsan. [5] The authors later reported the crystallization of dust atoms in the localized region of the electromagnetic wave. [6] The importance of dusty plasma physics has been manifold, because such plasmas are omnipresent in astrophysical environment like comets, interplanetary or interstellar clouds, the rings of giant planets like Saturn, etc., whereas
Linear and nonlinear properties of electrostatic waves on the ion time scale in a collisional rotating magnetoplasma with warm relativistically streaming ions and non-Maxwellian electrons have been investigated here. In the weak nonlinearity limit, we have derived Zakharov-Kuznetsov-Burgers equation to study the shock wave propagation in dissipative magneto-rotating plasmas with non-Maxwellian electrons. It has been found that ion acoustic shock waves with kappa distributed electrons admit only compressive shock structures, however, the ones with Cairns distributed electrons have been shown to allow for the formation of both compressive and rarefactive structures. This change in behavior has been found to be closely linked with the difference in the shapes of both distribution functions. The dependence of the characteristics of ion acoustic shock structures on rotation, obliqueness, relativistic streaming, kinematic viscosity and non-Maxwellian electrons has also been explored in detail. The relevance of the work with regard to planetary magnetospheres and pulsars has also been pointed out.
A study has been presented for the nonlinear features of ion-acoustic (IA) shock waves in a magnetorotating plasma consisting of warm viscous streaming ions along with kappa-distributed electrons having two different temperatures. In this regard, we have employed the reductive perturbation technique to derive the Zakharov-Kuznetsov-Burgers (ZKB) equation that governs the dynamics of IA shock waves. The solution obtained by the hyperbolic tangent method has been shown to depend on various plasma parameters such as spectral index (c), density fraction (f), effective rotation frequency (Ω c), ion kinematic viscosity (o), and temperature ratio (). In the limiting case when dissipative coefficient D → 0, we have also examined the solitary potential distributions, which are the solutions of Zakharov Kuznetsov (ZK) equation. It is found that both rarefactive and compressive structures exist for the system under consideration. The transition in the nature of such profiles is due to the enhancement in the density of cold electrons. The importance of present theoretical investigations has been carried out with regard to Saturn's magnetosphere, where two temperature superthermal electron populations have been observed by various satellite missions. K E Y W O R D S ion acoustic waves, kappa distribution, nonthermal plasma, shocks/solitons, two electron thermal population 1 INTRODUCTION Ion acoustic waves (IAW) are one of the fundamental low-frequency modes in a plasma and are associated with plasma compression during their propagation. [1,2] Various plasmas allow propagation of several types of nonlinear waves, e.g. solitons and shocks. [3,4] The former can trap plasma particles and cause a redistribution of energy and momentum. These structures arise due to the interplay between wave dispersion and nonlinearity as described by the Korteweg de Vries (KdV) equation. The system becomes more interesting in the presence of dissipation and, for weakly nonlinear 1-D systems, is depicted by Korteweg-de Vries-Burgers (KdVB) Equation. [5,6] Such dissipation is mainly caused by interparticle collisions, ion kinematic viscosity, and/or wave-particle interaction. The dissipation term is often recognized as the Burgers term and supports formation of shock waves. [7-12]
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