Plasma stability in a dipole magnetic field

Abstract

The MHD and kinetic stability of an axially symmetric plasma, confined by a poloidal magnetic field with closed lines, is considered. In such a system the stabilizing effects of plasma compression and magnetic field compression counteract the unfavorable field line curvature and can stabilize pressure gradient driven magnetohydrodynamic modes provided the pressure gradient is not too steep. Isotropic pressure, ideal MHD stability is studied first and a general interchange stability condition and an integro-differential eigenmode equation for ballooning modes are derived, using the MHD energy principle. The existence of plasma equilibria which are both interchange and ballooning stable for arbitrarily large beta = plasma pressure / magnetic pressure, is demonstrated. The MHD analysis is then generalized to the anisotropic plasma pressure case. Using the Kruskal-Oberman form of the energy principle, and a Schwarz inequality, to bound the complicated kinetic compression term from below by a simpler fluid expression, a general anisotropic pressure interchange stability condition, and a ballooning equation, are derived. These reduce to the usual ideal MHD forms in the isotropic limit. It is typically found that the beta limit for ballooning modes is at or just below that for either the mirror mode or the firehose.

(cont.) Finally, kinetic theory is used to describe drift frequency modes and finite Larmor radius corrections to MHD modes. An intermediate collisionality ordering in which the collision frequency is smaller than the transit or bounce frequency, but larger than the mode, magnetic drift, and diamagnetic frequencies, is used for solving the full electromagnetic problem. An integro-differential eigenmode equation with the finite Larmor radius corrections is derived for ballooning modes. It reduces to the ideal MHD ballooning equation when the mode frequency exceeds the drift frequencies. In addition to the MHD mode, this ballooning equation permits an entropy mode solution whose frequency is of the order of the ion magnetic drift frequency. The entropy mode is an electrostatic flute mode, even in equilibrium of arbitrary beta. Stability boundaries for both modes, and the influence of collisional effects on these boundaries has also been investigated.