Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method

In this thesis, we present methods for integrating Maxwell's equations in Frenet-Serret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines to the study of coherent synchrotron radiation, an important topic in accelerator physics. We build upon the published computational work of T. Agoh and D. Zhou in solving Maxwell's equations in the frequency-domain using a paraxial approximation which reduces Maxwell's equations to a Schrödinger-like system. We also evolve Maxwell's equations in the time-domain using a Fourier series decomposition with 2D DG motivated by an experiment performed at the Canadian Light Source. A comparison between theory and experiment has been published (Phys. Rev. Lett. 114, 204801 (2015)). Lastly, we devise a novel approach to integrating Maxwell's equations with 3D DG using a Galilean transformation and demonstrate proof-of-concept. In the above studies, we examine the accuracy, efficiency, and convergence of DG.This material is based upon work primarily supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Number DE-FG02-99ER41104 and supported in part by the National Science Foundation under Grant No. NSF PHY 0855678.Applied MathematicsDoctoralUniversity of New Mexico. Dept. of Mathematics and StatisticsLau, StephenEllison, JamesAppelö, DanielWarnock, RobertHeinemann, Klau