Effects of particle trapping on the slowing-down of fast ions in a toroidal plasma

The effect of toroidal geometry upon the slowing-down of fast ions in a tokamak plasma is considered. An appropriate bounce-averaged Fokker-Planck equation which includes particle trapping in the toroidal field gradient is derived. The equation is solved by expressing the solution in terms of a series of 'finite-geometry' eigenfunctions. This solution is then used to show that the trapping of the fast ions in the toroidal field gradient reduces the fast-ion current by terms of order (r/R)½. The radial transport of the fast ions as they slow down is calculated, and it is found that for counter-injection (co-injection) the ions diffuse outwards (inwards) by approximately a fast-ion banana width. The diffusion is accompanied by a loss of fast-ion toroidal momentum and a consequent reduction in the momentum transferred to the background plasma.