Analytic magnetohydrodynamic equilibria of a magnetically confined plasma with sheared flows

Analytic solutions of the magnetohydrodynamic equilibrium equations for a s ymmetric magnetically confined plasma with sheared incompressible flows ass ociated with electric fields similar to those observed in the transition fr om the low- to the high-confinement mode in tokamaks are constructed in cyl indrical and toroidal geometries. In particular, an exact toroidal solution is obtained which for vanishing flows reduces to the Solovev equilibrium w hich has been extensively employed in tokamak confinement studies. Owing to the flow, several toroidal configurations having either one or two stagnat ion points are possible in addition to the usual ones with a single magneti c axis. For flows pertaining to tokamak operational regime the extremum of the electric field becomes larger as flow and its shear increase, the locat ion of the extremum being, however, nearly independent of these variations. In addition, the flow affects the safety factor profile and the shape of t he magnetic surfaces and results in an increase of the magnetic shear and a decrease of the toroidal beta. The impact of plasma elongation on the abov e-mentioned confinement figures of merit is also evaluated. (C) 2001 Americ an Institute of Physics.