Slab models for classical diffusion in the Belt-Pinch

Classical diffusion is considered as a time-dependent and self-consistent problem for a free-boundary plasma in the plane slab and cylindrical slab geometries. These conditions approximate the Belt-Pinch experiment. It is found that the instantaneous diffusion rate changes rapidly as the plasma spreads and the fields decay. There is a succession of, at least, four physical phenomena which can dominate under different conditions: The poloidal electric field decays rapidly during an initial, finite-β, transient stage. The pinch effect due to the toroidal electric field may impede diffusion for an intermediate time span. After the pinch effects have become negligible. Spitzer diffusion induces a pressure decay which is algebraic with time and a poloidal B-field decay which is exponential with time. Although the pressure decay is initially faster, the rates soon become comparable. The Pfirsch-Schlüter effect enhances this diffusion only late in the discharge after the plasma has spread out and the rotational transform has decayed. A formula is also found for the radial position of the cylindrical slab as the fields decay. For passive field programming, there is a fixed but unstable position.