Magnetostatic Equilibria of Finite-Pressure Minimum-B Plasma Configurations

Abstract

Magnetostatic equilibria for a broad class of plasma conditions are shown to correspond to solutions of the equations ∇·B = 0, ∇× H =0, where B = μ H. Magnetohydrodynamic stability then corresponds to satisfaction of the criteria H>0 and dH/dB>0, where B = |B | and H =μ−1B. Equilibria are studied for a variety of plasma distributions taken as functions of total energy and magnetic moment and in the most general cases, the coordinates of a line of magnetic flux. A new result is the determination of a relationship between well depth and the maximum pressure for magnetohydrodynamic stability which puts an upper limit on the well depth to achieve given pressure when the value of the maximum field strength is fixed. For so-called collisional distributions, if p is the total pressure at the center and B0 is the maximum magnetic field, β̃ = 8πp/B02<0.2, and the mirror ratio to achieve maximum β̃ may not exceed 1.8. More general equilibria, where the pressures are functions of field lines as well, cannot improve the results and may be even more unstable.