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.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.