Fast-ion thermalization in non-circular tokamaks with large-banana-width effects

Fusion-product thermalization and heating are calculated on the assumption of collisional slowing-down. The present analytical model describes fast-ion orbits and their distribution function in realistic, high-beta, non-circular tokamak equilibria. The Fokker-Planck equation is bounce-averaged over the large banana-width orbits after the variables have been transformed to the constants-of-motion space. First-orbit losses, trapping effects, and slowing-down drifts are fully treated. By solving a 3-D (+ time) partial differential equation, it is possible to obtain an invariant of the slowing-down process, μ/E=(magnetic moment)/energy = constant, and explicit expressions for the slowing-down drifts. Large banana-width effects give rise to a net cogoing alpha-particle current. The large banana-width orbits smear the energy deposition over large regions of the plasma. This causes the in-situ heating rates to be 20-25% above the flux-surface-averaged rates on axis but enhances the edge heating approximately > 10-fold over in-situ deposition. While this result implies reduced alpha 'ash' accumulation on axis, the reduced heating rate makes start-up and maintenance of ignition more difficult. (author)