A numerical tool to optimize voltage waveforms for plasma breakdown and early ramp-up in the presence of constraints

Plasma initiation is an important phase in a tokamak discharge. The main objective of magnetic control in this phase is to first obtain sufficiently high electric field and connection length (implying a low poloidal magnetic field) in the breakdown region, and then, once plasma is formed, to force the plasma current to increase, guaranteeing force balance equilibrium. The problem is dominated by the presence of significant eddy currents induced in the passive structures and by the many constraints due to the coil system and power supplies. The present paper shows how, with minor simplifying hypotheses, the magnetic control design problem can be converted into a Quadratic Programming problem with both linear and quadratic constraints that can be solved with an ad hoc iterative algorithm. On the other hand, the full design problem, including the choice of possible Switching Network resistors, becomes nonlinear and an evolutionary Genetic Algorithm solver is proposed. The algorithms are tested on DEMO breakdown and early ramp-up design which is a quite challenging problem because of the large distance between active coils and vacuum chamber, the presence of shielding passive structures with large time constants, and the active constraints on the CS/PF coil system.