A geometric model of ion orbit loss under the influence of a radial electric field

A geometric approach is used to find the threshold energies for ion orbit loss in experimental tokamak geometry, like that of ASDEX Upgrade. The effects of any pre-existing radial electric field are maintained as they nontrivially affect the calculations. The associated velocity-space loss hole is investigated using equilibria and profiles from ASDEX Upgrade discharges 30628, in the L-mode just before the L-H transition and in the resultant H-mode, and 31533, an H-mode shot with a comparably high ion temperature. We use a novel technique to calculate the shift of the passing-trapped boundary and see that the experimental radial electric field allows for upwardly bounded regions (UBRs) of the loss hole, which are now studied in detail. We further develop a new loss-hole-shape sensitive method to treat the steady-state ion orbit losses by considering relaxation processes along the border of the loss cone. Typical characteristic times of the steady-state losses in the pedestal region of an H-mode are found to be between 1 and 10 ms. The UBRs significantly enhance the steady-state losses in two ways: these velocity-space loss regions reach further into thermally accessible regions and the extensions are shaped such that they have the ability to refill under both diffusive and slowing down relaxation processes.