Optimized Fourier representations for three-dimensional magnetic surfaces

The selection of an optimal parametric angle θ describing a closed magnetic flux surface is considered with regard to accelerating the convergence rate of the Fourier series for the Cartesian coordinates x(θ,φ)≡R−R0 and y(θ,φ)≡Z−Z0. A system of algebraic equations, which are quadratic in the Fourier amplitudes of x and y, is derived by minimizing the width of the surface power spectrum. The solution of these nonlinear equations, together with the prescribed surface geometry, determines a unique optimal angle. A variational principle is used to solve these constraint equations numerically. Application to the representation of three-dimensional magnetic flux surfaces is considered.