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

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%

Designing radiation transport tests: Simulation-driven uncertainty-quantification of the COAX temperature diagnostic

“…The Euler equations for momentum, mass and energy conservation implicitly assume matter is in thermal equilibrium. In the low-density conditions of the hohlraum, not only are the ions, electrons and photons decoupled with respect to each other, but these particles tend not to be in equilibrium in parts of the hohlraum [20,3,23].…”

“…It is because of these limita-tions that we have a rather large uncertainty in our drive. The Euler equations used in codes like Hydra [15], RAGE [8] or FLAG [12] do not capture this out-ofequlibrium physics to model the hohlraum and, although they can be used to make a first order estimate of the emission, simulations using these codes can lead to incorrect estimates of averaged terms like heating [3].…”

“…Historically, through analysis of experimental results, interial confinement fusion (ICF) designers very quickly realized this problem of overestatimation of the heat flux, and decided to use flux limiter models (which cannot be predictive, and need to be calibrated against experiments), and later nonlocal convolu- tion kernel to represent the nonequilibrium effects [13,22,14]. Recent studies, however, have suggested that for problems relevant to ICF hohlraum conditions, the nonlocal models depart strongly from Vlasov-Fokker-Planck simulations [3,23]. These observations indicate the need to go beyond equilibrium and near-equilibrium models and adopt kinetic approaches (Boltzmann, Vlasov-Fokker-Planck) to describing electrons dynamics for the near-vacuum hohlraum experiments.…”

Non‐local heat flux application for scrape‐off layer plasma

“…Departure between Braginskii fluid description and kinetic modelling has been highlighted, particularly an underestimation of temperature gradient by the fluid approach . Several kinetic corrections have been proposed to improve the plasma description at intermediate collisionality . In this contribution, we investigate kinetic corrections to the local Spitzer‐Härm (Braginskii) closure for the heat flux; more precisely, we focus on applying the non‐local expression for the heat flux proposed by Luciani‐Mora‐Virmont to scrape‐off layer physics.…”

“…[1] Several kinetic corrections have been proposed to improve the plasma description at intermediate collisionality. [2][3][4][5] In this contribution, we investigate kinetic corrections to the local Spitzer-Härm (Braginskii) closure for the heat flux; more precisely, we focus on applying the non-local expression for the heat flux proposed by Luciani-Mora-Virmont [6] to scrape-off layer physics. In particular, we adapt boundary conditions and implement the non-local expression into a 1D hydrodynamic model for the scrape-off layer.…”