*URN to cite this document:*urn:nbn:de:bvb:703-epub-3860-2

## Title data

Weber, Jörg:

**Optimal Control of the Two-Dimensional Vlasov-Maxwell-System.**

Bayreuth
,
2018
. - 89 P.

(Master's,
2016
, University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

PDF
MA.pdf - Published Version Available under License Creative Commons BY 4.0: Attribution . Download (619kB) |

## Abstract

The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of the problem since existence of global, classical solutions of the full three-dimensional 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 control-to-state 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.