Minimization Problems for the Witness Beam in Relativistic Plasma Cavities

This thesis deals with an optimization problem from the field of theoretical plasma physics. Specifically, it deals with the question of how the accelerated electrons are spatially arranged in a plasma wave generated by a laser pulse. An internal structure of this so-called witness beam is of interest for the radiation characteristics of such electron beams, in particular with regard to the coherence of the generated radiation. The resulting internal structure of the electron beam is a result of the interaction of the electrons with each other and the electric fields of the wakefield, therefore it is determined by solving a minimization problem. The thesis builds on previous results in this field and aims to find suggestions for improved algorithms to determine the minimum sought. About the Author Melinda Hagedorn is a PhD student in Mathematical Optimization, research associate and teaching assistant at Heinrich Heine University in Düsseldorf. She holds master's degrees in mathematics and physics. In her research, she focuses in particular on variants of the stochastic gradient method applied to convex optimization problems.