The effect of trapped electrons on beam driven currents in toroidal plasmas

A Fokker-Planck treatment of the effect of trapped electrons on the current induced by a beam of fast ions circulating in a toroidal plasma is presented.The theory applies to the 'banana' regime of small collision frequency and to systems of large aspect ratio.The perturbation of the electron distribution function due to trapping is described by an integro-differential equation in which the driving term depends on the electron distribution function for no trapped electrons.This equation is solved (a) analytically for a large plasma Z,, and (b) numerically for several values of Z , and for the complete range of ue/ub, the ratio of the electron thermal and fast ion velocities.The effect of trapped electrons on the current driven by the toroidal rotation of the thermal ions is also discussed.The net circulating current predicted by the theory is presented for parameters relevant to present and planned Tokamak experiments.