Most probable ideal magnetohydrodynamic equilibria. I. Tokamak regime and quasi-force-free states

Given the information on only a few global parameters (e.g., energy E, magnetic helicity H, flux phi, current I, ... - constraints that can be either experimentally imposed or constants of the motion...) the statistical theory of Montgomery, Turner and Vahala, which determines the most probable ideal magneto-hydrodynamic equilibrium compatible with the given information, is investigated in the tokamak regime. It is shown that in this regime of phi >> I one obtains typical experimentally relevant profiles e.g. B/sub theta/ << B/sub z/, slightly diamagnetic toroidal fields with torodial currents peaked on axis. A sequence of most probable equilibria, with decreasing ratio of E/H at fixed phi and I, is investigated showing less diamagnetic states with rapidly decreasing plasma beta. Linearized analytic force-free states can also be constructed for certain regimes of the global parameters together with their nonlinear quasi-force-free counterparts