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

Abstract

Stability of a ``rigid'' ballooning mode $m = 1$ is studied in application to a mirror axisymmetric trap designed to confine anisotropic plasma with a large beta ($\beta$, the ratio of plasma pressure to magnetic field pressure). It was found that for effective stabilization by lateral perfectly conducting wall, the beta parameter must exceed some critical value $\beta_{\text{crit}}$. The dependence of $\beta_{\text{crit}}$ on the plasma anisotropy, mirror ratio and width of vacuum gap between plasma and the wall was studied. Unlike the works of other authors focused on the plasma model with a sharp boundary, we calculated the boundaries of the stability zone for a number of diffuse radial pressure profiles and several axial magnetic field profiles. With a combination of a conducting lateral wall and conducting end plates imitating the attachment of end MHD stabilizers to the central cell of an open trap, there are two critical values of beta and two stability zones, $\beta \beta_{\text{crit}2}$, which can merge, making the entire range of allowable beta values $0<\beta<1$ stable.Comment: 26 pages, 12 figures, 3 tables. arXiv admin note: text overlap with arXiv:2203.0837