Multispecies transport theory for axisymmetric rotating plasmas

A reduced gyrokinetic equation is derived for a multispecies toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong [Phys. Fluids 28, 3082 (1985)] and by Catto et al. [Phys. Fluids 30, 2784 (1987)], has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ‘‘explicit’’ velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to Spitzer’s inductive terms.