Theory of runaway collisional transport

The purpose of this paper is to formulate the transport problem for a multispecies rotating toroidal magnetoplasma in the so‐called runaway regime, which is defined by an appropriate ordering of relevant characteristic frequencies, in particular, the Larmor frequency, the characteristic acceleration frequency due to the applied electric field and the effective collision frequency, all evaluated at some characteristic speed v₀. A suitable form of the gyrokinetic equation is obtained to describe the time‐dependent, multispecies plasma response to an applied electric field, in toroidal geometry and for a strongly rotating, quiescent, and collisional plasma. Its moment equations are proven to imply the reduction of the energy equation to Joule’s law, as well as consequences on the form of Ohm’s law and of the Grad–Shafranov equation. To construct an approximate solution of the gyrokinetic equation and to evaluate all relevant fluxes, appearing in the moment equations, a general variational solution method is developed.