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A kinetic theory of beam-induced plasma currents

A Fokker-Planck treatment of the current induced by a beam of fast ions circulating in a toroidal plasma is developed. The electron Fokker-Planck equation is first reduced to an integro-differential equation which is then solved analytically in the limiting cases of: (a) a large plasma Z and (b) a large ratio of the electron thermal velocity ve to the fast ion velocity vb. In addition, a numerical solution was obtained for the complete range of values of ve/vb and for several values of Z. It is found that the resulting net plasma current has a very different functional dependence upon electron temperature than that given by the conventional theoretical treatment in which the electrons are assumed to be Maxwellian. In particular, for ve > vb and Z = 1, which is the limit appropriate to many present tokamak experiments, the net current is found to be in the opposite direction to the fast-ion current. The theory is compared with recent measurements of this current which were made by using the Culham Levitron, and agreement is found between theory and experiment.