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

Abstract: The stabilization of ``rigid'' flute and ballooning modes $m = 1$ in an axisymmetric mirror trap with the help of an ideally conducting lateral both in the presence and in the absence of end MHD anchors is studied. The calculations were performed for an anisotropic plasma in a model that simulates the pressure distribution during the injection of beams of fast neutral atoms into the magnetic field minimum at a right angle to the trap axis. It was assumed that the lateral wall has the shape of a cylinder with a variable radius, so that on an enlarged scale it repeats the shape of the plasma column. It has been found that for the effective stabilization of the listed modes by an ideally conducting lateral wall, the parameter beta ($\beta$, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value $\beta_{\text{crit}}$. When combined with a conducting lateral wall and conducting end plates imitating MHD end stabilizers, there are two critical beta values and two stability zones $0<\beta<\beta_{\text{ crit}1}$ and $\beta_{\text {crit}2}<\beta<1$ that can merge, making the entire range of allowable beta values $0<\beta<1$ stable. The dependence of the critical betas on the degree of plasma anisotropy, the mirror ratio, and the width of the vacuum gap between the plasma and the lateral wall is studied. In contrast to the works of other authors devoted to 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.