Dynamic stabilization of magnetohydrodynamic instabilities by means of multipole high-frequency fields

Abstract

This article is devoted to problems of stability in a plasma column which has a hybrid current (constant and variable in time) flowing through it. The variable component of the current is, generally speaking, a helical multipole with zero skin layer. The constant current component exhibits either a skin effect or a uniform distribution over the column cross-section. The perturbations considered here are of the surface-wave type, since it is known that this type of perturbation plays a major role in a current plasma with a free boundary.Analysis of the dispersion equation obtained indicates that the application of high-frequency multipole fields reduces the critical q-value in current systems. From the physical point of view, stabilization is brought about by the presence of a time-averaged magnetic well and by the effect of dynamic shear. It was found that the effectiveness of stabilization increases as the multipolarity of the high-frequency field, a fact which is explained by increased depth (on average) of the magnetic well. This requires an increase in the radio-frequency circuit currents, however, which means that circuits with a high Q-factor must be used.The authors also show to what extent the high-frequency circuit (helical conductors) can assume the role of a stabilizing sheath. In the model adopted here the circuit is taken to be an anisotropically conducting sheath and the helical pattern is reflected; perturbations are found on which the circuit exercises a stabilizing effect. These are perturbations whose helix coincides with that of the high-frequency circuit currents projected on a cylindrical plasma surface of radius “a”. All other perturbations remain unaffected by the circuit: the perturbed currents do not form a circuit because the helices of the perturbation and the circuit are crossed.

Parametric instability in the region of low-frequency hybrid resonances

“…This resonance develops in a sufficiently r a r efied plasma (u^ « u ^ ), when the dispersion equation ( 1) governs the natural frequency u h2 °f plasma oscillations (6) We shall briefly dwell on the derivation of the equation describing non-linear ion oscillations in the region u s ^ insofar as it differs from that used in Refs [11,12]. Differentiating Eq.…”

“…At present, the character of high-frequencyfield interaction with plasma is being widely discussed. This interest is due, first of all, to a partial or total high-frequency stabilization of various dangerous instabilities preventing prolonged plasma confinement in magnetic traps (see Refs [1][2][3][4][5][6] and the references quoted therein). Furthermore, under certain conditions, a strong high-frequency field causes parametric instabilities, when the electron and ion oscillation amplitudes (hence, their kinetic energy) increases appreciably (e.g.…”