A simple model for evaporation-driven migration of liquid metal between plasma pulses in a fusion reactor with liquid metal plasma-facing components

Liquid metal plasma-facing components are being considered for a variety of fusion power plant designs, and careful control of the liquid metal inventory will be essential in these systems to mitigate challenges with liquid metal corrosion and hydrogen fuel retention. Since many power plant designs and existing test facilities rely on pulsed plasma sources, it is critical to understand how liquid metal evaporation leads to material migration within a reactor over the periods of time when no plasma is present. This work addresses this question by developing a simple particle balance model to efficiently calculate liquid metal vapor transport patterns over indefinitely long time periods, using a particle redistribution matrix to capture the vapor transport details. After developing the mathematical model, characteristics of a future Liquid Metal Core-Edge (LMCE) research facility with liquid lithium divertors are used as a reference to demonstrate how the particle balance model can be used. Examples of lithium migration during the cooldown period between plasma pulses show that the pattern of lithium deposition depends primarily on the system geometry. An important secondary effect in these scenarios is the relative cooldown rate of the lithium divertor with respect to other PFCs in the device. Examples are also provided to demonstrate how the particle balance model can be used to optimize the design of a cold finger to collect liquid metal condensation for extraction and reprocessing, with the results showing that a future LMCE facility may be capable of collecting all of the lithium evaporated between plasma pulses if the main chamber walls can be maintained above 350 C during operation.