An integral equation technique for the exterior and interior neumann problem in toroidal regions

Abstract

An integral equation technique for the Neumann problem of finding a function Φ satisfying ΔΦ = 0 with prescribed values of ∂Φ∂n on the boundary is described. Fourier representation of the potential Φ on the boundary with respect to two angle-like variables transforms the integral equation to an infinite set of linear equations for the Fourier coefficients of Φ. The singularity of the Green's function is treated by a regularization method: a function with the same singularity is subtracted and its analytically calculated Fourier-transform is added to the Fourier transformed integral equation. A computer code named NESTOR is developed. Applications include studies of toroidal magnetic vacuum fields and calculation of the vacuum field contribution for the 3D free-boundary equilibrium problem.