Self-consistent electron transport in tokamaks.

Electron particle, momentum, and energy fluxes in axisymmetric toroidal devices are derived from a version of the action-angle collision operator that includes both diffusion and drag in action-space [D. A. Hitchcock, R. D. Hazeltine, and S. M. Mahajan, Phys. Fluids 26, 2603 (1983); H. E. Mynick, J. Plasma Phys. 39, 303 (1988)]. A general result of the theory is that any contribution to transport originating directly from the toroidal frequency of the particle motion is constrained to be zero when the electron temperature is equal to the ion temperature. In particular, this constraint applies to those components of the particle and energy fluxes that are proportional to the magnetic shear, independent of the underlying turbulence and of whether the particles are trapped or untrapped. All the total fluxes describing collisionless transport of passing electrons in steady-state magnetic turbulence contain contributions proportional to the conventional thermodynamic drives, which are always outward, and contributions proportional to the magnetic shear, which have both magnitude and sign dependent on the ion-electron temperature ratio. The turbulent generalization of Ohm's law includes a hyper-resistive term, which flattens the current density profile on a fast time scale, and a turbulent electric field, which can have both signs depending on the electron-ion temperature ratio.