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

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