Title data
Weber, Jörg:
Optimal Control of the TwoDimensional VlasovMaxwellSystem.
Bayreuth
,
2018
.  89 P.
(Master's,
2016
, University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)


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Abstract
The time evolution of a collisionless plasma is modeled by the VlasovMaxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'twodimensional' version of the problem since existence of global, classical solutions of the full threedimensional problem is not known. We add external currents to the system, in applications generated by inductors, to control the plasma in a proper way. After considering global existence of solutions to this system, differentiability of the controltostate operator is proved. In applications, on the one hand, we want the shape of the plasma to be close to some desired shape. On the other hand, a cost term penalizing the external currents shall be as small as possible. These two aims lead to minimizing some objective function. We prove existence of a minimizer and deduce first order optimality conditions and the adjoint equation.