Convergent spectral representation for three-dimensional inverse magnetohydrodynamic equilibria

By rearranging terms in a polar representation for the cylindrical spatial coordinates (R,phi,Z), a renormalized Fourier series moment expansion is obtained that possesses superior convergence properties in mode number space. This convergent spectral representation also determines a unique poloidal angle and thus resolves the underdetermined structure of previous moment expansions. A conformal mapping technique is used to demonstrate the existence and uniqueness of the new representation