Anthony Gee

Publication Date


Document Type


First Advisor

Erdelyi, Bela

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Physics


Particle accelerators are ubiquitous in science and society and their use is still growing globally. Beam physics, the physics underlying accelerator science, is focusing in part on studies and applications where intense charged particle beams become essential. The high-intensity may cause new collective instabilities and phenomena which are difficult to be modeled by conventional means. New numerical methods must be developed to efficiently and reliably model, simulate and optimize such high currents. The University of Maryland Electron Ring (UMER) and the Fermilab Integrable Optics Test Accelerator (IOTA) are dedicated test rings to study the high intensity regimes. A 3-D symplectic tracking code, PHAD, was recently developed, which implements the adaptive Fast Multipole Method (FMM) in the differential algebraic (DA) framework to compute accurately and efficiently the self-induced Coulomb forces, and the beam dynamics under the combined external and internal forces. However, beam-environment interactions are missing. To add the beam-wall interactions, a new theory and numerical methods are needed. Previously, the beam-wall interactions were approximated using simplistic geometries that often gave unrealistic results. To this end, we develop the Poisson Integral Solver with Curved Surfaces (PISCS) method and implement it in the general purpose nonlinear dynamics code COSY Infinity. PISCS uses the fast multipole accelerated boundary element method in the differential algebraic framework. PISCS efficiently represents the beam-wall interaction in arbitrary structures. We implement a strategy that can include the beam-wall interaction in other space charge tracking codes too. This work presents and benchmarks PISCS with complicated geometries and includes analyses of space charge and the beam-wall interactions using the extracted transfer maps.


Includes tables, figures, and algorithms.


192 pages




Northern Illinois University

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