# Heat loads to the wall: the thermal conduction approach

## TL;DR

This paper introduces a thermal conduction model for plasma heat flux to fusion machine walls, accounting for anisotropic heat transfer and complex geometries, revealing significant deviations from traditional models.

## Contribution

The study develops a physically relevant anisotropic heat conduction model that captures cross-field transport and geometric effects, improving upon conventional field-line based approaches.

## Key findings

- Power flux on parallel walls is significant, contrary to traditional assumptions.
- Heat flux profiles deviate from exponential near the separatrix, showing steeper gradients.
- Inclined surfaces receive several times more power than predicted by simple models.

## Abstract

Calculations of the heat flux carried by plasma to the wall of a magnetic fusion machine often assume that power flows only along the field lines, but this cannot be true in general. Instead, we treat the plasma as an anisotropic non-linear thermally conducting medium. The model is physically relevant if parallel and cross-field transport are driven at least in part by temperature gradients, which means they are affected by the proximity of material surfaces. The model generates a familiar asymmetrical power distribution on the divertor target, and divergent heat flux on sharp edges, as described previously. The power landing on a wall that is parallel to the field (identically zero in the conventional model) is a substantial fraction of that landing on the target. The flux profile across the scrape-off layer (SOL) deviates strongly from an exponential, because the parallel heat conduction is very large near the separatrix, giving a much steeper fall-off in that region. When a portion of the wall protrudes into the SOL at a grazing angle, the power striking the inclined surface is several times the value derived by integrating the parallel heat flux calculated in the absence of the inclined surface. We have also calculated the degree to which the shadowing effect of a first wall component on other parts of the wall falls off with distance - something that cannot even be estimated using the field-line following technique.

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Source: https://tomesphere.com/paper/1702.01613