Equations and improved coefficients for parallel transport in multicomponent collisional plasmas: Method and application for tokamak modeling

Abstract

New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improved versions of the expressions written in Zhdanov [ Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)], based on Grad's 21N-moment method. Both explicit and approximate approaches for the calculation of transport coefficients are considered. Accurate application of this closure for the Braginskii transport equations is discussed. Viscosity dependence on the heat flux is taken into account. Improved expressions are implemented into the SOLPS-ITER code and tested for deuterium and neon ITER cases. Some typos found in Zhdanov [ Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)] are corrected.

Impact of the improved parallel kinetic coefficients on the helium and neon transport in SOLPS‐ITER for ITER

“…Indeed, a smaller (than for the standard method) fraction of the impurity flow returns upstream and a larger fraction of the impurity flow goes into the pumping system, as was mentioned in our earlier work. [8] It is important to mention that no significant changes in the deuterium transport are observed in ref. [8] and in the present paper.…”

“…Now a complete Grad-Zhdanov module is implemented in the SOLPS-ITER code for kinetic coefficients calculation using the 21 N-moment method. [3] This module operates in two regimes: (a) Improved analytical method (IAM) [8] ; and (b) explicit matrix inversion method (EMIM). [3,8] The new module calculates thermal and friction forces coefficients between all ions, whereas the standard approach considered the thermal force only due to main ion interaction with impurities.…”

“…[3] This module operates in two regimes: (a) Improved analytical method (IAM) [8] ; and (b) explicit matrix inversion method (EMIM). [3,8] The new module calculates thermal and friction forces coefficients between all ions, whereas the standard approach considered the thermal force only due to main ion interaction with impurities. Moreover, the heat flux according to Grad-Zhdanov closure is applied instead of the Braginskii ion heat conductivity.…”

“…[5] It is important to mention that multi-temperature generalization of this method is in progress for the SOLEDGE3X-EIRENE code. [6,7] In the present paper, a new Grad-Zhdanov module based on the improved approach [8] and complete Grad-Zhdanov method [3,8] has been implemented in the SOLPS-ITER code (Section 2). Impact on the helium and neon transport is studied (Section 3).…”

The 21N-moment multi-temperature coefficients for Zhdanov closure

“…This is important for modelling impurity dynamics because impurities may be present as a significant fraction of the background plasma species, or, in case of deuterium-tritium plasmas, tritium, being a main ion species, cannot be modelled as trace over an existing deuterium-electron plasma. The Zhdanov closure is already implemented, though only using single-temperature collision coefficients at the plasma common temperature, in SOL/edge simulators such as Soledge3x-EIRENE [1,6,7], SOLPS [8][9][10], B2-EIRENE [11], and EDGE2D [12].…”