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MHD stabilization of a high beta mirror plasma partially enclosed by a conducting wall

An MHD formulation is used in the study of a wall-stabilized high beta mirror plasma with isotropic pressure. The stabilizing wall extends axially only over a part of the distance between the mirror midplane and the throat. In a model of this arrangement, a wall is used which is near the plasma surface in the bad curvature region and distant from the plasma surface in the good curvature region. A variational method is used to solve the equations for both regions. For the connection of the regions of close and distant plasma-wall proximity, a jump condition is used. The variational calculation is performed with a simple trial function (the choice of the trial function is substantiated with an exact numerical solution). The results show that (a) the removal of the conducting wall in the good curvature region does not significantly degrade plasma stability, (b) the acceptable ratio of the radius of the conducting wall to the plasma radius is about 1.1, and (c) for cases with a low mirror ratio, more conducting wall is needed for stability than for cases with a high mirror ratio. This is in agreement with the physical mechanism of wall stabilization.