Entropy Production and Onsager Symmetry in Neoclassical Transport Processes of Toroidal Plasmas

"Entropy production and Onsager symmetry in neoclassical transport processes of magnetically confined plasmas are studied in detail for general toroidal systems including nonaxisymmetric configurations. We find that the flux surface average of the entropy production defined from the linearized collision operator and the gyroangle-averaged distribution function coincides with the sum of the inner products of the thermodynamic forces and the conjugate fluxes consisting of the Pfirsch-Schluter, banana-plateau, nonaxisymmetric parts of the neoclassical radial fluxes and the parallel current. We prove from the self-adjointness of the linearized collision operator that the Onsager symmetry is robustly valid for the neoclassical transport equations in the cases of general toroidal plasmas consisting of electron and multi-species ions with arbitrary collision frequencies. It is shown that the Onsager symmetry hold whether or not the ambipolarity condition is used to reduce the number of the conjugate pairs of the transport fluxes and the thermodynamic forces. We also derive the full transport coefficients for the banana-plateau and nonaxisymmetric parts, separately, and investigate their symmetry properties. The nonaxisymmetric transport equations are obtained for arbitrary collision frequencies in the Pfirsch-Schluter and plateau regimes, and it is directly confirmed that the total banana-plateau and nonaxisymmetric transport equations satisfy the Onsager symmetry.