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

## TL;DR

This paper compares three nonlocal electron thermal conduction models against Vlasov-Fokker-Planck simulations to evaluate their accuracy in fusion-related plasma conditions, revealing strengths and limitations of each model.

## Contribution

It provides the first detailed comparison of the SNB model with VFP results for inhomogeneous ionization in fusion-relevant scenarios.

## Key findings

- EIC and NFLF models predict damping rates within 10% but overestimate peak heat flow by up to 35%.
- SNB model aligns better with VFP for large temperature differences when properly defining mean free path.
- SNB overestimates heat flow in helium gas-fill by a factor of ~2 but accurately predicts peak heat flux.

## 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; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph and Umansky; and (iii) Schurtz, Nicola\"i and Busquet's 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%.