Advanced vertical control for tokamak reactors with double-null divertors

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The double-null divertor is an attractive exhaust solution for compact tokamak reactors, but its success is contingent on achieving vertical plasma position control which is both robust and precise, and uses some non-magnetic state estimation. A natural choice for this would be sensing the heat flux imbalance between the two divertors, since this quantity is exactly what we wish to minimise to ensure equal power sharing. The time delay between plasma moving vertically and the heat flux being detected - a part of which is accounted for by transience in the scrape-off layer (SOL) - is an important parameter in this control concept. If the information advects along the SOL quickly, then heat flux becomes a good estimator of the plasma displacement, but if it is slow (compared to the vertical oscillation timescale) then closed-loop control becomes much more challenging. It is unknown what this characteristic SOL time will be in a reactor, but it seems prudent to mitigate against the possibility it is 'slow' by devising an advanced vertical control scheme of the kind which would be required in this scenario. We propose to create a model predictive control algorithm which makes use of a fast reduced/surrogate model for the time-dependent SOL behaviour to predict, based on recent measurements, the future evolution of the system in real time and actuate on the vertical control coils accordingly. This model should be validated against MAST-U data and simulations, and the algorithm tested in-silico to demonstrate that real-time control of MAST-U and/or a reactor divertor power balance could be achieved by this method.