KINETIC AND TRANSPORT THEORIES OF TURBULENT, AXISYMMETRICAL, LOW-COLLISIONALITY PLASMAS AND TURBULENCE CONSTRAINTS

The kinetic equations describing the evolution of the macroscopic distribution functions of electrons and ions in turbulent, axisymmetric, low-collisionality plasmas are derived in a systematic fashion. The first irreversible time scales are those of electron and ion classical collisions on which the distributions relax, in their lowest order, to Maxwellians. These results are sufficient to derive the nonlinear equations that describe the evolution of the "low-frequency" microturbulence. This turbulence controls the evolution of the Maxwellians on longer time scales and also influences the higher-order equilibrium distribution functions. By taking moments of the kinetic equations obtained on the diffusion time scale, (i) the equations of evolution of the density and pressures of the lowest-order Maxwellians, (ii) an expression for the macroscopic toroidal current driven from the passing electrons by the autocorrelation of the turbulent electric field parallel to B with the turbulent density, and (iii) a "constraint" equation telling that the anomalous sources and sinks of ion parallel momentum must be balanced by the divergence of the anomalous radial flux of the same momentum are thus obtained. It is noted that the transport is automatically ambipolar, that ion and electron anomalous heat transport are of the same order, that magnetic aspects of the turbulence are considered, although via a low-beta expansion scheme: They contribute to the anomalous bootstrap current which is estimated to be possibly of the order of 15% of the Ohmic current; and that the constraint, a consequence of ion momentum conservation, is automatically satisfied for weak turbulence in the "random phase" approximation if the plasma has up-down symmetry.