Relativistic neoclassical radial fluxes in the 1/nu regime

TL;DR

This paper calculates relativistic effects on neoclassical radial fluxes in the 1/nu regime, finding a small reduction at fusion temperatures and providing a formulation compatible with existing non-relativistic solvers.

Contribution

It introduces a relativistic formulation for radial fluxes using the relativistic drift-kinetic equation and Maxwell-Jüttner distribution, extending non-relativistic methods to relativistic regimes.

Findings

Relativistic effects reduce radial fluxes by up to 10% at T_e<100 keV.

The relativistic formulation includes an additional temperature-dependent correction term.

The approach allows use of existing non-relativistic transport solvers for relativistic calculations.

Abstract

The radial neoclassical fluxes of electrons in the 1/nu regime are calculated with relativistic effects taken into account and compared with those in the non-relativistic approach. The treatment is based on the relativistic drift-kinetic equation with the thermodynamic equilibrium given by the relativistic Maxwell-J\"uttner distribution function. It is found that for the range of fusion temperatures, T_e<100 keV, the relativistic effects produce a reduction of the radial fluxes which does not exceed 10%. This rather small effect is a consequence of the non-monotonic temperature dependence of the relativistic correction caused by two counteracting factors: a reduction of the contribution from the bulk and a significant broadening with the temperature growth of the energy range of electrons contributing to transport. The relativistic formulation for the radial fluxes given in this paper is expressed in terms of a set of relativistic thermodynamic forces which is not identical to the canonical set since it contains an additional relativistic correction term dependent on the temperature. At the same time, this formulation allows application of the non-relativistic solvers currently used for calculation of mono-energetic transport coefficients.