  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.
