Tokamak ripple transport at arbitrary collision frequency

The bounce-averaged Fokker-Planck equation for the distribution function of ripple-trapped particles in a Tokamak has been solved, for arbitrary collision frequencies, in the 'Tokamak' limit in which ripple wells are localized close to the mid-plane. The equation includes the main terms contributing to collisionless (de)trapping. The solution employs power series expansions for the distribution function in the pitch-angle variable k2 and the poloidal angle, θ; the series in k2 and θ both terminate. The boundary conditions applied at the trapping-detrapping boundary, that f and (∂f/∂k2) be continuous, become requirements that in the collisionless limit the derivative with respect to k2 reflects the scale length set by the motion in toroidally blocked orbits. The resulting series solutions reduce to the usual expressions in the high collision frequency limit, but are considerably lower than results of previous calculations (which neglect the collisionless detrapping effects), in the low collision frequency limit. Comparison with Monte-Carlo calculations for INTOR parameters shows that the analytic results lie somewhat below the numerical results, in all cases. Since banana-drift diffusion is also present in the Monte-Carlo calculation, this is a partial confirmation of the validity of our theory. 15 refs