Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

TL;DR

This paper introduces a Fourier-based method for solving the drift kinetic equation in axisymmetric magnetic fields, deriving fluid closures and transport relations for plasma physics applications.

Contribution

It develops a novel Fourier moment expansion technique to derive plasma closure relations and transport properties in toroidally confined plasmas.

Findings

Derived closure relations linking heat flux and viscosity to gradients.

Reproduced full moment solutions using linearized fluid equations.

Method applicable to multi-ion and electron-ion plasmas.

Abstract

A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments a set of ordinary differential equations are obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the density, temperature, and flow velocity perturbations in terms of radial gradients of equilibrium pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity, are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. The method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.