Tokamak equilibria with arbitrary cross-section

Magnetohydrodynamic equilibria are obtained by semi-analytic means for large-aspect-ratio tokamaks with fixed, non-circular boundaries and slightly non-uniform currents. The method uses the fact that there is a conformal map of any simple closed region onto the unit circle. Solutions are expressed as quadratures which involve the conformal maps. These quadratures are evaluated numerically for specific examples. Results for equilibria with circular, elliptical, dee-shaped and doublet-shaped cross-sections are presented and compared. Toroidal and finite-beta effects are noted and stability against flutes is examined by Mercier's criterion for the various configurations. (author)