Energy Principle With Specific Inductance
US Atomic Energy Commission (AEC), Glenn Bateman, New York Univ. (NYU), NY (United States) · 1971
The determination of stability for a scalar pressure, toroidal plasma has been formulated by means of an energy variational principle in which the geometric problem of variation of the flux surface shapes is separated from the variation of the flux profile. By means of successive minimizations, holding the surface shapes and the flux profiles fixed, the potential energy is written as a one-dimensional integral over a function of pressure, differential flux, and the specific inductance matrix. The latter depends upon only the geometry of the surfaces. Stability conditions are derived by varying the flux profile and the geometry (specific inductance). Also, a nonlinear condition is derived for the special case of finite geometric distortions of the flux surfaces holding the flux profiles fixed. Exact results for the specific inductance are calculated for straight cylinders axisymmetric toruses, and helically symmetric configurations, all with arbitrary cross sections.