Dust Acoustic Gravity Vortices in Collisional Dusty Plasma

A. A. Shaikh1,� and J. R. Bhatt2,��

1 C. U. Shah Science College, Ashram Road, Ahmedabad-380 014, Gujarat, India2 Theoretical Physics Division, Physical Research Laboratory, Navrangpura, Gujarat, Ahmedabad-380 009, India

Received December 8, 2002; accepted January 6, 2003

PACS Ref: 52.25.Ya, 52.27.Lw, 52.31.Ex, 52.35.Mw, 52.35.We, 52.65.Kj

Abstract

We study dust acoustic gravity modes in a partially ionized collisional dusty

plasma in linear and non linear limits. In the linear regime unstable collisional

dust acoustic gravity waves are found. In the non linear regime we found that

the presence of frictional force strongly affects various type of vortex

formation. It is shown that the condition for the formation of chains of

vortices is modified due to the frictional force. Possible applications of the

result in context of lower planetary dusty atmosphere and astrophysical dusty

fluid are discussed.

1. Introduction

Dusty or complex plasma is characterized by the presenceof highly charged and massive dust grains, in addition tothe usual electron, ion and neutral species. Charged dustgrains are ubiquitous in industrial, astrophysical and spaceplasma environments. It has been realized, that dustyplasma could have wide ranging application in a variety ofplasma environments, and this has given rise to a rapidgrowth in studies of plasma. It is well known thatbarometric equilibrium supports acoustic-gravity waves.It is also found that these waves may become unstable in astratified medium. In an acoustic wave the pressuregradient is responsible for restoration of the displacedfluid element from its equilibrium position. On the otherhand for a gravity wave, action of the gravitational forceon a displaced fluid element acts as a restoring force. e.g.,ocean waves exist only at the surface of the water, wherethere is a sharp and abrupt change in the density.Generation of vortices is a special feature of stratifiedflow in plasma. Stratified flows and vortex motion havealso been studied in other branches of physics, e.g., Zonalflow and the Great Red Spot in the Jovian atmosphere,astrophysical fluid, etc. A large body of work, dealing withvortex structures, exists in literature of formation of non-linear structures in plasma ([5] and reference cited therein).Large scale atmospheric nonlinear structures, e.g., Rossbywaves are well understood by Charney’s model [2].Hasegawa and Mima [3] substantiated an analogy betweenRossby waves and drift waves in magnetized plasmas. Theynoted that the role of Coriolis force was replaced byLorentz force in the case of drift waves. An equationdescribing MHD vortices stretched along field lines wasobtained by Kadomtsev and Pogutse [4]. Nonlinear studyof acoustic-gravity waves has shown that under certainconditions, acoustic-gravity waves could lead to formationof acoustic solitary vortices [9]. The observed structures in

the lower planetary atmosphere can then be understood asa localized vortex chain solution of the equations describ-ing acoustic gravity waves [10]. Stenflo [12] also showedthat nonlinear low frequency acoustic gravity waves canappear in form of localized dipole type vortices. In short,acoustic gravity vortices are extensively studied in Refs. [9–13] in the context of pristine plasma. Since the existence ofdust grains are indubitable in a planetary atmosphere, theabove discussion regarding acoustic gravity wave andvortex could be interesting also for dusty plasma. Keepingthis in mind, acoustic-gravity waves have been analyzed industy environment by Shukla and Shaikh [8]. The problemof waves in stratified barometric equilibrium was alsoaddressed in the presence of charged dust by Shaikh et al.[6].

It ought to be stated that, systematic studies of collectivebehavior of complex plasma, at linear and non-linearlevels, have revealed that the presence of highly chargedgrains could lead to new time and length scales in theplasma as well as produce several new waves andinstabilities (e.g., in Ref. [7]). One of the most importantaspects of dusty plasma, apart from charged dynamics, isthat of collisional nature of the complex plasma. It is foundthat dissipative charging process is characterized by acharging frequency �ch; Zd times larger than the ion–ioncollision frequency, where Zd ’ 103 is a measure of theelectronic charge on the grain [1]. The rate of the elasticcollisions of the ions with the dust particles differs from thecharging collisions of ions on dust by a factor ln lD=rd,where lD is the dusty Debye length and rd the grain radius.Typically for grains in dusty plasmas lD � rd, thereforecharging and elastic frequencies of the ions could be muchlarger than ion–ion, electron–electron binary collisions.Frequency of acoustic-gravity waves could be comparableto the collision frequencies. In this situation, it isimperative to consider the consequences of collisions onthe non-linear structure in complex plasma. In thismanuscript, we therefore, study dust acoustic gravitymodes in a partially ionized dusty plasma where the effectsof frictional forces between dust grains and neutrals anddust grains with ions are important.

We have derived an appropriate set of equations withnon-Boussinesq approximation. The problem has beenstudied in both linear as well as non-linear regimes. It isfound that the presence of frictional force strongly affectsthe growth of instability leading to vortex formation. Wealso find that for charge dependent decay length, with colddust, the condition for existence of chains of vortices ismodified. Finally, the usefulness of the results in context of� e-mail: acd@prl.ernet.in

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Physica Scripta. Vol. 68, 58–62, 2003

Physica Scripta 68 # Physica Scripta 2003