Neoclassical transport in strong gradient regions of tokamaks

Strong gradient regions in tokamaks, such as the pedestal or internal transport barriers, are regions of reduced turbulence where neoclassical transport can play a dominant role. However, standard neoclassical transport theory assumes that the gradient length scales of density, temperature, and potential are of the order of the system size. In the pedestal, gradient length scales are much shorter and are measured to be of the order of the ion poloidal gyroradius. We present an extension of neoclassical theory that is applicable in regions of strong gradients and find modifications to transport fluxes for ions and electrons and the bootstrap current in both the banana and the plateau regimes. In strong gradient regions, density, electric potential, mean parallel flow and ion temperature are shown to no longer be flux functions. Instead, they have a small but important poloidally varying piece that modifies the transport equations to lowest order. We calculate this poloidal variation, explain physically how it arises in these regions and compare our modifications to neoclassical transport to XGCa simulations.