Velocity space diffusion of electrons induced by a beam of electron cyclotron waves of finite size in toroidal geometry

Generalizing earlier results, the quasilinear diffusion tensor D is derived for circulating electrons interacting with an electron cyclotron wave beam of finite size in a Tokamak configuration. Two approaches are considered, the first starting from Vlasov's equation following the lines of standard quasilinear theory, the other using a test particle model. The result is applied to rediscuss the limitations of the quasi-uniform model commonly adopted.