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%

We compare the reduced non-local electron transport model developed by Schurtz et al. (Phys. Plasmas 7, 4238 (2000)) to Vlasov-Fokker-Planck simulations. Two new test cases are considered: the propagation of a heat wave through a high density region into a lower density gas, and a 1-dimensional hohlraum ablation problem. We nd the reduced model reproduces the peak heat ux well in the ablation region but signi cantly over-predicts the coronal preheat. The suitability of the reduced model for computing non-local transport e ects other than thermal conductivity is considered by comparing the computed distribution function to the Vlasov-Fokker-Planck distribution function. It is shown that even when the reduced model reproduces the correct heat ux, the distribution function is signi cantly di erent to the Vlasov-Fokker-Planck prediction. Two simple modi cations are considered which improve agreement between models in the coronal region.

Accurate modelling of the thermal transport in the 'scrape-off-layer' (SOL) is of great importance for assessing the divertor exhaust power handling in future high-power tokamak devices. In conditions of low collisionality and/or steep temperature gradients that will be characteristic of such devices, classical local diffusive transport theory breaks down, and the thermal transport becomes nonlocal, depending on conditions in distant regions of the plasma. An advanced nonlocal thermal transport model is implemented into a 1D SOL code 'SD1D' to create 'SD1D-nonlocal', for the study of nonlocal transport in tokamak SOL plasmas. The code is applied to study typical ITER steady-state conditions, to assess the relevance of nonlocality for ITER operating scenarios. Results suggest that nonlocal effects will be present in the ITER SOL, with strong sensitivity in simulation outputs observed for small changes in upstream density conditions, and drastically different temperature profiles predicted using local/nonlocal transport models in some cases. Global flux limiters are shown to be inadequate to capture the spatially and temporally changing SOL conditions. Introducing impurity seeding, under conditions where detached divertor operation is achieved using the flux-limited Spitzer-Härm models used in standard SOL codes, simulations using the nonlocal thermal transport model under equivalent conditions were found to not reach detachment. An analysis of the connection between SOL collisionality and nonlocality suggests that nonlocal effects will be significant for future devices such as DEMO as well. The results motivate further work using nonlocal transport models to study disruption events and low collisionality regimes for ITER, to further improve accuracy of the nonlocal models employed in comparison to kinetic codes, and to identify more appropriate boundary conditions for a nonlocal SOL model.

We present a simple method to incorporate nonlocal effects on the Nernst advection of magnetic fields down steep temperature gradients, and demonstrate its effectiveness in a number of inertial fusion scenarios. This is based on assuming that the relationship between the Nernst velocity and the heat flow velocity is unaffected by nonlocality. The validity of this assumption is confirmed over a wide range of plasma conditions by comparing Vlasov-Fokker-Planck and flux-limited classical transport simulations. Additionally, we observe that the Righi-Leduc heat flow is more severely affected by nonlocality due to its dependence on high velocity moments of the electron distribution function, but are unable to suggest a reliable method of accounting for this in fluid simulations.

Nonlocal models are widely used for approximating kinetic effects on electron heat flow in fusion-relevant plasmas. Almost universally, such models have no explicit time dependence and are designed to make heat flow predictions based directly on instantaneous profiles of macroscopic plasma parameters. While this is usually justified by the claim that transient effects fade before temperature profiles evolve appreciably, a more rigorous justification of the stationarity assumption in terms of kinetic theory is desirable. In this Letter, such a justification is provided by demonstrating that nonstationary effects related to the time dependence of the isotropic part of the electron distribution function vanish up to third order in Chapman–Enskog theory (irrespective of ion charge state or presence of magnetic fields). However, it is found that the electron inertia term (whose appearance in Ohm's law stems from the time derivative of the anisotropic part of the electron distribution function) does have a small but finite third order effect that is most prominent for plasmas with low average ion charges. This Letter additionally provides a convenient analytic inverse for the isotropic part of the Landau electron–electron collision operator.