Global modes of flute instability of a rotating cylindrical plasma
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Global Modes of Flute Instability of a Rotating Cylindrical Plasma E. A. Sorokina Institute of Nuclear Fusion, Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia Received August 20, 2008; in final form, November 13, 2008
Abstract—The influence of rotation on the flute instability of a cylindrical gravitating plasma in a straight inhomogeneous magnetic field is studied in the framework of onefluid magnetohydrodynamics. The disper sion relation and integral expression for the instability growth rate of eigenmodes are derived. It is shown that, in the framework of the given problem, rotation is a destabilizing factor, and the corresponding theorem is proved for the general case. For a linear radial profile of the rotation frequency, the structure of eigenmodes is calculated. The growth rate of these modes is shown to increase with increasing rotation velocity and azi muthal mode number. It is found that plasma rotation in the eigenmode localization region leads to the dis placement of perturbation from the rotation region, which results in a decrease in the instability growth rate. The absence of eigenmodes (i.e., exponential instability of the system) for certain profiles of the density and rotation frequency is demonstrated. PACS numbers: 52.35.Py DOI: 10.1134/S1063780X09050080
1. INTRODUCTION Flute modes are one of the wellstudied instabilities of a magnetized plasma. The mechanism for their excitation is related to plasma diamagnetism—a fun damental plasma property due to which plasma is expelled from the region of the maximum magnetic field. Flute perturbations, i.e., perturbations extended along magnetic field lines, develop at an arbitrarily low plasma pressure, because these modes do not perturb the magnetic field, but, according to the figurative expression by Kadomtsev [1], lead to the percolation of plasma “tongues” through the ambient magnetic field. Flute instability can be stabilized by arranging a “minimum B” (in the general case, “average mini mum B”) configuration. This was exhaustively dem onstrated in experiments performed in [2]. The “tongue” structure of flute modes can be disrupted by the magnetic shear, which has a stabilizing effect [3]. In recent years, the possible favorable effect of sheared plasma rotation, which is also capable of affecting the structure of developing perturbations, has been actively discussed (see, e.g., [4]), especially in connec tion with the phenomenon of transport barriers [5]. In this case, however, the problem of whether sheared (differential) plasma rotation suppresses the instability or only changes the level and structure of the resulting turbulence is beyond the scope of examination. Note that the stabilizing role of rotation is not obvious, because rotation (i) introduces in the system such a destabilizing factor as the centrifugal force and
(ii) may enhance instability due to the rotational inter action with other hydrodynamic modes, their cou pling, and buildup. In this paper, we consider the pro
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