Theory of the Optimal Design of Straight-Axis Minimum-B Mirror Confinement Configurations

摘要

The design of modern straight-axis linked-mirror plasma-confinement configurations involves a balance between many competing requirements. The dipole and quadrupole components of magnetic induction required in one confinement region often do not match onto the fields of an adjacent region without complications that seriously affect particle drifts or confinement stability. Here, the relevant factors are set down together with the techniques for analytical optimization of the design of a general configuration. A general sufficient condition for the stability of an arbitrary guiding-center MHD equilibrium is derived. This condition makes explicit the stabilizing qualities of good normal curvature and diamagnetic axial current. The instability drive depends on two terms: one carries the sign of normal curvature and the other relates to the relative signs of geodeics curvature and geodesic torsion. The theory is applied to low-beta, large-aspect-ratio equilibria for which analytic expressions for the confining magnetic fields are known. Two optimizations are required to specify the arbitrary features of the quadrupole and dipole fields. One optimization is nonlinear and can be performed by the ordinary calculus of variations; the second optimization is linear and subject to the rules of game theory. Appropriate quality factors are obtained, thus giving the designer quantitative measures with which to balance design trade-offs. (ERA citation 07:062495)