2014/11/26 by C. Meyer, Meyer, C., S. M. Schnepp +3
Mathematics · Physics and Astronomy · #35Q61 #49J15 #49J20 #49K15 #49K20 #Accelerator Physics (physics.acc-ph) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Optimization and Control (math.OC) #math.OC #msc:35Q61 #msc:49J15 #msc:49J20 #msc:49K15 #msc:49K20 #physics.acc-ph #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.1411.7265
32 pages, 8 figures
arxiv created 2014/11/26 · arxiv updated 2014/11/27
This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic potential which leads to an additional state equation in form of a very weak elliptic PDE. Existence and uniqueness for the state equation is shown and the existence of a global optimal control is established. Moreover, first-order necessary optimality conditions in form of Karush-Kuhn-Tucker conditions are derived. A numerical test illustrates the theoretical findings.