Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications

J P Brodrick,M M Marinak,J T Omotani,R J Kingham,C P Ridgers,A V Chankin,G D Kerbel,J T Parker,M V Patel,M V Umansky,M Sherlock,D Del Sorbo,B Dudson

doi:10.1063/1.5001079

Abstract

Three models for nonlocal electron thermal transport are here compared against Vlasov-Fokker-Planck (VFP) codes to assess their accuracy in situations relevant to both inertial fusion hohlraums and tokamak scrape-off layers. The models tested are (i) a moment-based approach using an eigenvector integral closure (EIC) originally developed by Ji, Held, and Sovinec [Phys. Plasmas 16, 022312 (2009)]; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph, and Umansky [Phys. Plasmas 21, 055907 (2014)]; and (iii) Schurtz, Nicolaï, and Busquet’s [Phys. Plasmas 7, 4238 (2000)] multigroup diffusion model (SNB). We find that while the EIC and NFLF models accurately predict the damping rate of a small-amplitude temperature perturbation (within 10% at moderate collisionalities), they overestimate the peak heat flow by as much as 35% and do not predict preheat in the more relevant case where there is a large temperature difference. The SNB model, however, agrees better with VFP results for the latter problem if care is taken with the definition of the mean free path. Additionally, we present for the first time a comparison of the SNB model against a VFP code for a hohlraum-relevant problem with inhomogeneous ionisation and show that the model overestimates the heat flow in the helium gas-fill by a factor of ∼2 despite predicting the peak heat flux to within 16%.

Highlights

Performing full integrated simulations of large-scale fusion devices, such as the National Ignition Facility (NIF) or the ITER tokamak, is very challenging due to the wide range of scales over which the important physical processes occur
We compare three different models for kinetic effects on electron thermal conduction against Vlasov-Fokker-Planck (VFP) simulations: (i) the eigenvector integral closure (EIC)3–5 and (ii) the non-Fourier Landau-fluid (NFLF)6,7 models, which have recently been suggested for application in the tokamak edge and scrape-off layer (SOL); and (iii) the Schurtz, Nicola€ı, and Busquet’s multigroup diffusion (SNB) model,8–12 which is currently the most widely used in inertial fusion and laser-plasma applications
We investigate the accuracy of the EIC, NFLF, and SNB models in calculating the heat flow in the case where we have a large relative temperature variation

Summary

Introduction

Performing full integrated simulations of large-scale fusion devices, such as the National Ignition Facility (NIF) or the ITER tokamak, is very challenging due to the wide range of scales over which the important physical processes occur. Codes, such as HYDRA1 and BOUTþþ, used to perform integrated simulations of inertial and magnetic confinement fusion (ICF/MCF), respectively, often include reduced models to capture the complex aspects of the physics. Note that Epperlein and Haines have calculated jðBÞ to an increased accuracy and Epperlein and Short later suggested that this can be approximated well by jðBÞ % nðZÞ128=3p, where nðZÞ 1⁄4 ðZ þ 0:24Þ=ðZ þ 4:2Þ

Results

Discussion

Conclusion