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.

Name thesis:degree_name

Mathematics

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics & Statistics

Year

2016

Author dc:creator

• Bizzozero, David

Contributors dc:contributor

• Lau, Stephen
• Stephen Lau
• James Auby Ellison
• Daniel Appelö
• Robert Warnock

• Maxwell
• discontinuous Galerkin
• coherent synchrotron radiation
• electromagnetic

Language dc:language

English

Identifier

https://digitalrepository.unm.edu/math_etds/4

OAI identifier oai:identifier

oai:digitalrepository.unm.edu:math_etds-1003