Exact Solov'ev equilibrium with an arbitrary boundary

Exact Solov'ev equilibria for arbitrary plasma cross sections are calculated using a constrained least squares method. The boundary, with or without X-points, can be specified with an arbitrarily large number of constraints to ensure an accurate representation. Thus, the order of the polynomial basis functions in the homogeneous solution of the Grad-Shafranov equation becomes an independent parameter determined only by the accuracy requirements of the overall solution. Examples of exact, highly shaped equilibria are presented. Published under license by AIP Publishing.