Electron-magnetohydrodynamic description of a steady-state current flow in a plasma with a three-dimensional localized d
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ElectronMagnetohydrodynamic Description of a SteadyState Current Flow in a Plasma with a ThreeDimensional Localized Density Perturbation D. A. Tolstik Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, Moscow oblast, 141700 Russia Received October 14, 2009; in final form, December 12, 2010
Abstract—The problem of a steadystate current flow through a localized density perturbation is analyzed in the framework of electron magnetohydrodynamics. It is examined how the degree of localization of such a flow depends on the plasma magnetization parameter and the geometric characteristics of the density pertur bation. Corrections to the unperturbed current field are found by the iteration method. It is shown that the firstorder correction to the current can be determined for an arbitrary perturbation. In the case of perfectly conducting plasma, the secondorder correction can be found only for dipole perturbations, for which the integral change in the density is zero. In this case, the firstorder correction to the current is localized, which makes possible the existence of the secondorder correction. The finite plasma conductivity also assists cur rent localization; therefore, for sufficiently small values of the plasma magnetization parameter, both first and secondorder steadystate corrections to the current can be obtained for any moderate plasma density perturbation. DOI: 10.1134/S1063780X11070154
1. INTRODUCTION Studies of the processes affecting the plasma con ductivity are important for many experiments on the physics of hightemperature plasmas. Plasma heating can result in the onset of various instabilities, and the transport of the magnetic field depends substantially on the plasma conductivity. In Zpinches and plasma opening switches (POSs), the plasma resistivity is anomalous, i.e., it is substantially higher than that determined by elementary interactions between plasma electrons and ions. Classically, the mechanism of anomalous resistivity is attributed to the effect of plasma oscillations (phonons) on the momentum transfer from electrons to ions [1]. In [2], it was pointed out that density fluctuations play an important role in the dynamics of the Zpinch current sheath and the transport of the magnetic field in it. In [3], the plasma dynamics in a POS was studied and the impor tant role of the magnetic field transport in the develop ment of shock waves was indicated. In [4], the anom alous resistivity caused by the onset of ionacoustic instability was considered. In [5], the resistivity of the Zpinch neck was analyzed by considering the gener ation of helicons on density perturbations and the electrontoion momentum transfer by means of these helicons. Helicontype instabilities of a lowpressure Zpinch were also considered in [6, 7], where it was assumed that the Ampére force was balanced by ion inertia. According to [6, 7], the presence of the radial plasma density gradient in a Zpinch is sufficient for
the onset of electronmagnetohydrodyn
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