Neoclassical ion transport through the separatrix in divertor tokamaks

Ion transport through the separatrix in tokamaks with divertors is considered, in an attempt to understand ion confinement in the H-mode. Assuming the ions to be nearly collisionless, their escape from the main plasma occurs by scattering into velocity space loss regions, corresponding to diverted drift surfaces. The drift kinetic equation is averaged over the finite banana width guiding-centre drift orbits and solved variationally with the boundary condition that the ion distribution function is zero on the loss region boundaries. By matching to the neoclassical distribution function far inside the separatrix, the form of the distribution function near the separatrix is determined. The ion temperature gradient length is shown to be roughly an ion banana width, at the separatrix.