On hydrodynamic stability of a plasmoid moving in a magnetic field

A. P. Likhachev - S. A. Medin

High Energy Density Research Center, Joint Institute for High Temperature, Russian Academy of Sciences, IVTAN, Moscow, Russia

Abstract
The problem of hydrodynamic stability of high-conducting plasmoids moving in a magnetic field under conditions of intense flow past them by a non- or low-conducting compressible fluid is considered. Being an inherent feature of many naturally occurring and applied MHD flows, the flow past the plasmoid leads to several specific aspects of the problem. The present paper is devoted to the theoretical study of these aspects. Particular emphasis has been placed on the consideration of MHD instabilities of Rayleigh - Taylor and Kelvin-Helmholtz types which can develop at the interface of plasmoid and surrounding gas. The former is induced by nonuniformity of the normal (to the interface) component of the ponderomotive force, and the latter is initiated by nonuniformity of the tangential velocity component. Of special interest is the possible interference of these instabilities and its influence on the development of each of them. To investigate these phenomena the layered one-dimensional approximation of undisturbed flow structure has been considered. The flow past the plasmoid has been simulated by assignment of the tangential (to the interface) component of velocity in the region upstream of the high-conducting layer. The instability development has been induced by either of the two types of artificial disturbance of the initial flow state. The study of the RT1 linear stage has been carried out in order to estimate the limits of feasibility of the inviscous computational model used to describe the nonlinear evolution of both instabilities. Besides that, dispersion relations in the framework of inviscid incompressible as well as compressible approximations have been obtained and discussed. The nonlinear analysis of the RT and KH instabilities has been conducted by means of computational modeling. The time-dependent two-dimensional computational model based on Euler gasdynamic equations has been developed. Fundamental differences between the results obtained within the limits of linear and nonlinear approaches have been shown. In particular, the characteristic times of the RT1 development arising from nonlinear analysis are one order of magnitude greater than those predicted from linear theory and rather weakly depend on the disturbances mode. Strong manifestations of the interplay of the RT and KH instabilities have been observed. One of them is the destruction of the surface of the high-conducting lover with separation of its fragments. This feature may be rather important in the problem of plasmoid stability. Figs 5, Refs 10.