This thesis entailed development of a molecular dynamics simulation with which to investigate the behavior of charged particles in electromagnetic traps. The primary objectives of the molecular dynamics simulation--- beyond the obvious goals of accuracy, stability, and speed--- were: (1) to develop an interactive, user-friendly simulation capable of modeling and exploring behaviors of electromagnetically trapped particles; (2) to keep the simulation as general as possible so that many phenomena could be explored and so that the dimensionality of the simulation was not altered through simplifying assumptions which might distort, for example, the nature of phase transitions; (3) to enable investigation of interesting physics, some of which is relatively unexplored or subject to dispute among different research groups.

The following points of interest were investigated using the simulation:

- demonstration of bound behaviors in the lowest-order Paul trap stability region, where most trapping experiments are conducted;
- search for bounded behaviors and Wigner crystallization in a ``higher-order'' Paul trap stability region whose existence is predicted by solution of the Mathieu differential equation;
- stability of few-ion crystals--- studied extensively by Blümel--- and many ion-crystals near the Mathieu instability in stability region A (the lowest-order stability region);
- stability of ordered structures observed in higher-order Mathieu regime B;
- demonstration of behaviors exhibited by Penning-trapped ions;
- exploration of the four dynamical regimes of multiple-ion configurations in the Paul trap;

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Fri May 12 10:36:01 EDT 1995