Equilibria is an ellipsoidal co-ordinate system

The Grad-Shafranov equation for axisymmetric plasma equilibria has been solved in the ellipsoidal co-ordinate system (ρ, ζ, φ) with quasi-uniform current density profile up to the sixth order in ζ. Bean shaped and elongated elliptic equilibria and dee shaped equilibria can be described in this co-ordinate system. The basic characteristics of these equilibria are determined by the size, aspect ratio, elongation, poloidal beta, triangularity, and separatrix location. (author)