Finite-beta minimum energy equilibria of RFPs, screw pinches and tokamaks

A recent finite-#betta# theory based on the minimization of the potential energy of a non-ideal MHD plasma has been applied to describe the various pinch and tokamak experiments. The cylindrically symmetric solution of this variational principle is analysed and the corresponding equilibrium states are represented in an F-THETA-#betta#-qsub(ax)/epsilon diagram; F and THETA are the toroidal and poloidal magnetic field at the plasma boundary normalized with respect to the averaged toroidal field, qsub(ax) is the safety factor at the magnetic axis, and epsilon is the inverse aspect ratio. Since in a toroidal expansion these quantities possess no first-order contribution, the diagrams can also represent toroidal discharges with a large aspect ratio. On these diagrams, where F is plotted as F(THETA, qsub(ax)/epsilon) with #betta# as a parameter, equilibrium solutions exist only in limited parameter regions, corresponding to the operating conditions of current types of fusion experiments. For qsub(ax)/epsilon<1, THETA>1 solutions are identified as slow RFPs with a peaked jsub(z)-profile (Zeta, eta-#betta#-II, ETL-TPE-IR). The range qsub(ax)/epsilon>1, THETA>1 shows fast RFPs with a hollow jsub(z)-profile (eta-#betta#-I, HBTX 1). Tokamaks and screw pinches (diamagnetic or paramagnetic, peaked or hollow current profile) are represented in the range qsub(ax)/epsilon>1, THETA>1. The first-order toroidal correction turns out to be important in establishing the agreement between theory and experiment for magnetic field profiles of the eta-#betta#-II RFP and for pressure profiles of the SPICA screw pinch. (orig.)