Approximation of radial structure of unstable ion-sound modes in rotating magnetized plasma column by eikonal equation

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The problem of the correct asymptotic construction of the radial structure of linearly unstable ion-sound electrostatic eigenmodes is studied. The eigenvalue problem with boundary conditions of the first and second kind (electrodynamic and hydrodynamic types) for the oscillations that propagate in a uniform cylindrical column of magnetized plasma along an axial homogeneous magnetic field is formulated. A method for constructing a discrete spectrum of small-scale unstable oscillations of the system based on the basic principles of geometric optics is proposed. The main idea of the method is an explicit idea of the type of boundary conditions - the conductivity and absorbing properties of the wall bounding the plasma cylinder. A dispersion relation for unstable small-scale modes destabilized due to the effects of differential rotation is derived from the Eikonal equation. For the correct construction instability growth rates spectra an universal recipe for the selection of radial wave numbers of small-scale eigenmodes in accordance with any of the types of boundary conditions is proposed.

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1. Introduction It is well known that rotation of the plasmas in magnetic field is a source of various instabilities [1-6]. The most common of them are of a convective nature and occur for non-axisymmetric flute-like perturbations with

About the authors

Nikita A. Marusov

Kurchatov Institute; Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
ORCID iD: 0000-0002-0763-1505

Candidate of Sciences in Physics and Mathematics, Senior Researcher of Department of Plasma Theory of Kurchatov Institute; Senior Lecturer of Institute of Physical Research and Technology of Peoples’ Friendship University of Russia

1, Kurchatov Square, Moscow, 123182, Russian Federation; 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation


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