Publication Date

2026

Document Type

Dissertation/Thesis

First Advisor

Erdelyi, Bela

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Physics

Abstract

Particle accelerators consist of some of the most prolific machines for achieving a long-standing history of successful experiments that have progressed fields such as particle physics, nuclear physics, solid state physics, and medical physics. In recent years, multiple studies have been conducted on how further progress in these fields can be made and the beams physics community has concluded that developing new accelerators to minimize the loss of particles, induce high intensity beams, and remain stable under perturbations is essential to the continued success of physics research. Each of these qualities correspond to finding methods to increase the so-called dynamic aperture of the lattice. We conduct a two-fold search to find suitable methods to maximize the dynamic aperture of an accelerator.

First, we conduct a search for a nonlinear integrable Hamiltonian system that may be used as a blueprint for novel accelerators. Fermilab’s Integrable Optics Test Accelerator exemplifies the promise of this method, having established a promising solution in the four-dimensional transverse phase space under certain approximations. We expand the region of interest to include longitudinal dynamics in order to incorporate acceleration, thereby considering a six-dimensional phase space for which an integrable Hamiltonian system must be constructed. It is shown that once this longitudinal motion is included into the Hamiltonian, the system is no longer completely integrable, as any invariant associated with the purely transverse system is lost. However, we show that the system remains at least partially integrable and establish a new family of invariants associated with the longitudinal dynamics.

Our second method of maximizing the dynamic aperture for an accelerator begins by composing the one-turn map for a particular lattice from each element along the beam line with the goal of constructing a stable symplectic map closely related to the original. Since maps consist of multiple components, we instead modify the original map’s associated scalar generating function by introducing a “stabilization function” that modifies the generating function through the use of an invariant surface. We test the suitability of multiple generating types and establish that the largest domain of definition applies to the Extended Poincaré generating type. We then track both electrons and protons through the original and stabilized lattice to examine the efficacy of this stabilization process by analyzing the total number of stable particles for the system. While we show that this method is not completely robust to small perturbations, we find that there is some merit to this method of increasing the dynamic aperture.

Extent

346 pages

Language

en

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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