Pressure anisotropy stabilization of axisymmetric mirror machines

Abstract

The stability of a two species, anisotropic pressure, axisymmetric plasma is studied using the guiding center plasma model. Successively, asymptotic expansions are applied appropriate to a long, thin plasma, and to a plasma with flux surfaces close to cylinders. The resultant stability problem may be cast as an ordinary differential equation eigenvalue problem or as a problem in the calculus of variations. It is shown that low beta plasmas cannot be confined and be stable although plasmas may be stable in which the pressure gradients are nonzero where the pressure tends to zero. Stable profiles are given; these profiles include the possibility of field reversed regions. These stable profiles require the anisotropic species to be cold near the axis. Rather than absolute stability, a weaker condition is also considered which for fixed azimuthal mode number ‖m‖ puts the point of accumulation of the spectrum of modes on the stable side. It is hoped that such a condition may yield systems stable to ‖m‖ small modes although not all values of ‖m‖. This condition is more readily satisfied and allows more reasonable profiles near the axis.