Tokamak, reversed field pinch and intermediate structures as minimum-dissipative relaxed states

The principle of minimum energy dissipation rate is utilized to develop a u nified model for relaxation in toroidal discharges. The Euler-Lagrange equa tion for such relaxed states is solved in toroidal coordinates for an axisy mmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain, The C-K eigenfunctions are hyppergeometric functions that are solutions of the sca lar Helmholtz equation in toroidal coordinates in the large-aspect-ratio ap proximation. Equilibria are constructed by assuming the total current J=0 a t the edge. This yields the eigenvalues for a given aspect-ratio. The most novel feature of the present model is that solutions allow for tokamak, low -q as well as reversed field pinch-like behavior with a change in the eigen value characterizing the relaxed state. (C) 2000 American Institute of Phys ics. [S1070-664X(00)01001-1].