Thermodynamics of neoclassical and turbulent transport

Abstract

A variational principle based on the calculation of the entropy production rate is derived, which covers particle, momentum and heat transport. This principle is used to define proper thermodynamical forces and fluxes. When turbulent parallel wavenumbers are small, and fluctuations are ballooned, it is found that the forces are the gradients of density, velocity and temperature normalized to canonical profiles, which are power laws of the magnetic field. The transport matrix is symmetrical for a given background of fluctuations, i.e. if the dependence of the turbulence intensity on gradients is ignored. Minimization of the entropy production rate implies that the profiles tend to relax towards their canonical values, though these values are never reached simultaneously since they are linearly stable. Also it turns out that parallel and perpendicular canonical temperatures are not the same, so that the equilibrium distribution function relaxes towards a two-temperature Maxwellian. When finite turbulence parallel wavenumbers are accounted for, residual fluxes appear. Forces can be redefined to preserve Onsager symmetry but residual heat and momentum sources remain, which correspond to turbulent heating and momentum transfer.