Optimal control of a Vlasov-Poisson plasma by fixed magnetic field coils

Abstract

We consider the Vlasov-Poisson system that is equipped with an external magnetic field to describe the time evolution of the distribution function of a plasma. An optimal control problem where the external magnetic field is the control itself has already been investigated in [arXiv:1708.02464] and [arXiv:1708.02753]. However, in real technical applications it will not be possible to choose the control field in such a general fashion as it will be induced by fixed field coils. In this paper we will use the fundamentals that were established in [arXiv:1708.02464] and [arXiv:1708.02753] to analyze an optimal control problem where the magnetic field is a superposition of the fields that are generated by N fixed magnetic field coils. Thereby, the aim is to control the plasma in such a way that its distribution function matches a desired distribution function at some certain final time T as closely as possible.