MHD equilibrium in non-circular tokamaks with field-shaping coil systems

This paper concerns the determination of axially symmetric MHD equilibria with arbitrary cross section. A numerical solution to the appropriate two-dimensional free-boundary elliptic nonlinear partial differential equation has been used to relate current profile, coil configuration, and plasma geometry for noncircular tokamaks with external field-shaping coil systems. The bifurcation properties of the solution spaces for such tokamaks have been studied, and the parameter regions where bifurcation occurs determined. The structural stability of the resulting equilibrium suggests ways of controlling the shape of different plasmas (in particular doublet plasmas) over a wide range of plasma parameters.