Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations

Abstract

Linearized model collision operators for multiple ion species plasmas are presented that conserve particles, momentum, and energy and satisfy adjointness relations and Boltzmann's H-theorem even for collisions between different particle species with unequal temperatures. The model collision operators are also written in the gyrophase-averaged form that can be applied to the gyrokinetic equation. Balance equations for the turbulent entropy density, the energy of electromagnetic fluctuations, the turbulent transport fluxes of particle and heat, and the collisional dissipation are derived from the gyrokinetic equation including the collision term and Maxwell equations. It is shown that, in the steady turbulence, the entropy produced by the turbulent transport fluxes is dissipated in part by collisions in the nonzonal-mode region and in part by those in the zonal-mode region after the nonlinear entropy transfer from nonzonal to zonal modes.

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

“…For example, the collision operator is normally linearized in the gyrokinetic equation for df where terms of O½ðdf Þ 2 are neglected although the linearized collision operator still retains the properties associated with the conservation laws and the entropy production. Several approximate models are proposed to construct the linearized gyrokinetic collision operators (Madsen 2013;Catto and Tsang 1977;Xu and Rosenbluth 1991;Lin et al 1995;Wang et al 1999;Abel et al 2008;Sugama et al 2009) which can be applied to neoclassical and turbulent transport simulations.…”

Benchmark of Electromagnetic Gyrokinetic Codes in High Performance Fusion Plasma

“…Thus the finite collisional drive is confirmed to be affected by the details of the collision operator. Nevertheless, Sugama's self-adjoint collision operator in GKV [16] and Landau-Boltzmann collision operator in GENE [17] here capture equivalent physics for the destabilization of MTMs.…”

Differential formulation of the gyrokinetic Landau operator

“…This is not to say that significant effort would not have been made in order to develop collision operators for gyrokinetics. In contrast, several papers (see, e.g., Abel et al 2008;Sugama et al 2009;Li & Ernst 2011) provide expressions for both model and full linearized collision operators that are suitable for numerical implementation. These linear operators are typically presented in the form of…”