Elliptical Toroidal Geometry—A Geometric Transport Correction

The transport and diffusion equations are developed in toroidal geometry, with the torus exhibiting a general elliptical cross section. These equations are presented in two different coordinate systems, each of which has its own advantage. It is shown that the elliptical toroidal diffusion equation can be cast into the standard r - θ cylindrical equation by appropriately redefining the interaction cross sections and external source. This suggests a “geometric transport correction”—a geometric modification to the r - θ cylindrical transport equation which accounts for both the toroidal and elliptical character of the system.