On thermal axisymmetric liquid-metal divertors

Abstract

Abstract Motivated by liquid-metal divertor concepts, we consider a detailed model of a thin liquid-metal film flowing down a toroidally-symmetric solid substrate, driven by gravity as well as thermal and mechanical interaction with the SOL. In the relevant physical limit where the film is thin relative to the divertor extent, and the induced magnetic field is weaker than the applied field, the governing equations may be approximated asymptotically to yield tractable reduced-order dynamics. The analysis incorporates gravitational, thermocapillary and thermoelectric forces, and reveals several nontrivial findings. Firstly, we find that the influence on the liquid metal flow of the toroidal component of the applied field is negligible compared to that of the poloidal component. This has important ramifications for the behaviour of the liquid metal. Secondly, we identify a “spiral-type flow” due to a flow component in the toroidal direction. This flow has been previously reported in the literature in the isothermal case when using extreme parameters. Our analysis explains why these extreme parameter choices were required to observe the isothermal flow, and reveals that, for typical parameters in the thermal case, the flow becomes significant due to thermoelectric forces. Thirdly, we deduce full dimensional velocity scalings. Finally, we present a case study that employs the reduced-order model to explore the effects of sweeping the plasma strike point up and down the divertor. We simulate fully transient dynamics within the divertor and demonstrate how, in some regions of parameter space, the sweeping might promote dry-out or droplet ejection of the liquid metal. We discuss how the case study can inform both divertor material choice as well as tokamak operating parameters.