Modeling the Synchrotron: An Exploration of Delay-Coupled Nonlinear Mathieu Equations
A synchrotron is a circular particle accelerator where beams of electrons are maintained at high velocity. Each beam contains clusters of electrons called ``bunches,'' and we model the vertical displacement of each bunch as simple harmonic motion with parametric excitation, i.e. the Mathieu equation. Different types of coupling are accounted for, including one that only takes effect after one orbit, which we model using delay terms; the resulting model is a system of delay-differential equations. Nonlinear and damping terms are also included to make the model more realistic and the dynamics more rich. Variations of this core model are examined using perturbation methods and checked against numerical integration.
Applied mathematics; Accelerator; Delay; Mathieu; Perturbation; Stability; Particle physics; Nonlinear
Rand, Richard Herbert
Guckenheimer, John Mark; Strogatz, Steven H.
PHD of Applied Mathematics
Doctor of Philosophy
Attribution 4.0 International
dissertation or thesis
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