Optimized Fourier representations for three-dimensional magnetic surfaces

The selection of an optimal parametric angle theta describing a closed magnetic flux surface is considered with regard to accelerating the convergence rate of the Fourier series for the Cartesian coordinates x(theta,phi) identical with R - R0 and y(theta,phi) identical with Z - Z0. Geometric criteria are developed based on the Hamiltonian invariants of Keplerian orbits. These criteria relate the rate of curve traversal (tangential speed) to the curvature (normal acceleration) so as to provide increased angular resolution in regions of largest curvature. They are, however, limited to either convex or starlike domains and do not provide rapid convergence for complex domains with alternating convex and concave regions. A generally applicable constraint criterion, based directly on minimizing the width of the x and y Fourier spectra, is also derived. A variational principle is given for implementing these constraints numerically. Application to the representation of three-dimensional magnetic flux surfaces is discussed