A NEW TECHNIQUE FOR CALCULATING TOROIDAL HARMONIC COEFFICIENTS FOR CURL-FREE MAGNETIC-FIELDS IN HELICAL TOROIDAL DEVICES

In a curl-free toroidal magnetic system, the vector magnetic field may be derived from a scalar magnetic potential expressed as a series of toroidal harmonic functions. A new method of computing the coefficient s of the toroidal harmonics of the magnetic scalar potential is presen ted in this paper. The method uses Fourier integrals performed over th e poloidal and toroidal angles on a closed toroidal surface. The integ rand includes the component of the magnetic field normal to the toroid al surface and a multiplying factor chosen to create a set of simple e quations which are linear in the coefficients. This set of equations i s then inverted to obtain the toroidal harmonic coefficients. The magn etic fields calculated using the magnetic scalar potential with these coefficients are found to agree well with the original magnetic field even for a small number of coefficients. For a small number of coeffic ients used in the scalar potential, the time required to calculate the magnetic field is reduced by up to a factor of five from standard Bio t-Savart methods.