Transport processes and entropy production in toroidal plasmas with gyrokinetic electromagnetic turbulence

Transport processes and resultant entropy production in magnetically confined plasmas are studied in detail for toroidal systems with gyrokinetic electromagnetic turbulence. The kinetic equation including the turbulent fluctuations are double averaged over the ensemble and the gyrophase. The entropy balance equation is derived from the double-averaged kinetic equation with the nonlinear gyrokinetic equation for the fluctuating distribution function. The result clarifies the spatial transport and local production of the entropy due to the classical, neoclassical and anomalous transport processes, respectively. For the anomalous transport process due to the electromagnetic turbulence as well as the classical and neoclassical processes, the kinetic form of the entropy production is rewritten as the thermodynamic form, from which the conjugate pairs of the thermodynamic forces and the transport fluxes are identified. The Onsager symmetry for the anomalous transport equations is shown to be valid within the quasilinear framework. The complete energy balance equation, which takes account of the anomalous transport and exchange of energy due to the fluctuations, is derived from the ensemble-averaged kinetic equation. The intrinsic ambipolarity of the anomalous particle fluxes is shown to hold for the self-consistent turbulent electromagnetic fields satisfying Poisson’s equation and Ampère’s law.