The virtual-casing principle for 3D toroidal systems

The capability to calculate the magnetic field due to the plasma currents in a toroidally confined magnetic fusion equilibrium is of manifest relevance to equilibrium reconstruction and stellarator divertor design. Two methodologies arise for calculating such quantities. The first being a volume integral over the plasma current density for a given equilibrium. Such an integral is computationally expensive. The second is a surface integral over a surface current on the equilibrium boundary. This method is computationally desirable as the calculation does not grow as the radial resolution of the volume integral. This surface integral method has come to be known as the 'virtual-casing principle'. In this paper, a full derivation of this method is presented along with a discussion regarding its optimal application. (brief communication)