Numerical Solutions of Selected Problems Which Arise in the Theory of Particle Beams.

Abstract : A previous study led to the development of a closed form solution to the dynamic behavior of a charged particle beam. This solution was found for a simple, but nontrivial, single degree of freedom model (the electrostatic approximation model). This thesis investigates the characteristics of this closed form solution using three different types of inputs. The closed form solution is then verified by using finite difference to generate compatible results. Also investigated are the characteristics of the dynamic model prior to the implementation of the electrostatic approximation. Keywords: Closed form solution; Discrete solution; Varying inputs.