Three-Dimensional Magnetic Field Calculation for a Localised Current Distrib ution in Unbounded Space

Algorithm for field Calculation The topic of this work is a new method for the rapid numerical field calculation from a current with arbitrary spatial variation. It is designed for applications in toroidal fusion machines, but extensible to other devices. The displacement current is considered to be negligible. The evaluation of the 6 dimensional Biot-Savart integral can lead to excessive computing time for this type of problem. We instead solve Ampere’s equation for the magnetic vector potential. A cylindrical coordinate system (R, j, Z) aligned with a suitably defined vertical axis is introduced. Since we do not deal with radiation phenomena, the Coulomb gauge N ¢ A = 0 is appropriate and also serves for simplifying the equations. Amperes equation −DA = µ0J is then written in cylindrical coordinates, and decomposed in toroidal Fourier modes along the j coordinates. With the definition Y = RAR, we arrive at