Wall stabilization of the rigid ballooning $m=1$ mode in a long-thin mirror trap

Abstract

The prospect of stabilization of the m = 1 "rigid" ballooning regime in an open axially symmetric trap with the help of a conducting lateral wall surrounding a column of isotropic plasma is studied. It is found that for effective wall stabilization, the beta parameter must exceed 70%. The dependence of the critical value of beta on the mirror ratio, the radial pressure profile, and the axial profile of the vacuum magnet has been studied. It is shown that when a conductive lateral wall is combined with conductive ends simulating the attachment of end MHD stabilizers to the central cell of an open trap, there are two critical beta values and two stability zones that can merge, making stable the entire range of allowable beta values 0 < β < 1.

Stabilization of the $m=1$ mode in a long-thin mirror trap with high-beta anisotropic plasmas

“…Following LoDestro and some other authors we use rationalized electromagnetic units (also known as Heaviside-Lorentz units) where the factor [4π] before p ⊥ and p is dropped in Eqs . (1) and (5). This factor occurs in the Gaussian system of units, but we omit it throughout the paper.…”

“…As in our first article [1], the subsequent calculations were performed in the Wolfram Mathematica © for four values of the index k = {1, 2, 4, ∞}. The f 1 function describes the smoothest pressure profile.…”

“…Continuing the study of ballooning instability in isotropic plasma started in our article [1], in this paper we present the results of the study of the so-called wall stabilization of rigid ballooning perturbations with azimuthal mode number m = 1 in a mirror trap (also called open trap) with anisotropic plasma. According to the physics of the case, wall stabilization of plasma with a sufficiently high pressure is achieved by exciting image currents in the conducting lateral walls of the vacuum chamber surrounding the plasma column.…”

“…Unlike many other works on the stability of a rigid balloon mode m = 1 [2][3][4][5][6][7][8][9][10][11][12], which were focused exclusively on the plasma model with a stepwise pressure profile, in our article [1] we recently investigated the stability of the m = 1 mode in a plasma with a diffuse pressure profile, but then limited ourselves to the case of an isotropic plasma. Specifically, we calculated the so-called critical beta β crit , such that a rigid balloon mode m = 1 can be stabilized by an external conducting wall if β > β crit (β is the ratio of plasma pressure to the magnetic pressure field).…”

“…To avoid unnecessary repetitions, we will not analyze the content of the articles cited above, since their detailed review was previously done in our article [1], and we will immediately proceed to the description of the new calculations. In the section II, LoDestro's equation will be written and the necessary notation will be introduced.…”