Publication Date

2012

Document Type

Dissertation/Thesis

First Advisor

Erdelyi, Bela

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Physics

LCSH

Electric charge and distribution--Measurement--Mathematical models

Abstract

A beam's charge density, treated as a smooth and continuous function, can be approximated using polynomial orthogonal series. This will allow a solution of Poisson's equation to be found. Obtaining the most accurate solution to the space-charge potential requires the best approximated charge density. Several beam distributions are approximated using the classic Jacobi polynomials generated by the traditional recursion relations and the moment method. Varying the particle number and the order of the approximation allows to compare the performance of the different polynomials and to determine if a particular combination of both works best. Although the three polynomials studied give similar results, with Legendre being slightly better, the approximation coefficients should be allowed to converge and taken to high orders for best results.

Comments

Adviser: Bela Erdelyi.

Extent

184 pages

Language

eng

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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