Iterative learning optimization and control of MAST-U breakdown and early ramp-up scenarios

Plasma start-up is a crucial phase for tokamak operations and its design and optimization is getting more and more attention in view of the operation of future large tokamaks like ITER, where costs, risks and operational limits require more design tools. Magnetic controllers during this phase must guarantee a high electric field to ionize the neutral particles with a low stray magnetic field in a sufficiently large region inside the plasma chamber, to avoid that the ionized particles escape towards the tokamak vacuum chamber walls, and then to sustain the plasma current rise whilst maintaining the force balance. Preliminarily to feedback control design, a proper design of the breakdown and early plasma current ramp-up nominal current and voltage waveforms must be done. This paper describes a design procedure based on quadratic programming and iterative learning control methodologies to achieve an optimal design of these waveforms. In fact, after a first model-based design, the scenario is corrected step by step using, as additional information, the results of previous experiments rapidly converging to an optimal solution. After a first application to the Tokamak a Configuration Variable where a quite reliable, though simple, magnetic model was available, the proposed methodology is applied to the MAST-U medium size spherical tokamak for which an approximate model is built using Green functions.