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A Map of the Thesis

Now that you are familiar with TrapApp, you may use it in conjunction with this thesis to explore trapped particle dynamics. Reading the thesis straight through, one proceeds from Paul traps to Penning traps to methods of the computer simulation, with a final chapter providing a guide to running program TrapApp.

Chapter gif motivates ion-trapping experiments and provides a mathematical basis in terms of the Mathieu equation for single-particle confinement within the Paul trap. Stability conditions and approximate behaviors of a single Paul-trapped particle are analyzed.

In Chapter gif, we explore behaviors observed among a collection of Paul-trapped particles interacting via the Coulomb potential. Four distinct dynamical regimes are investigated: (1) the virtually uncoupled Mathieu regime; (2) the chaotic heating regime in which nonlinear Coulomb effects enable particles to absorb energy from the oscillating electric field; (3) the nonheating ``quasiperiodic'' regime;gif and (4) the crystalline phase.

Chapter gif explains the mechanisms for confining particles in Penning traps with a static quadrupole potential and a static magnetic field. The motivation for Penning traps and the dynamics of a single particle in a Penning trap are briefly discussed.

The final two chapters treat TrapApp not as a tool, but as a focus in itself. Chapter gif concerns the structure of the program and the mathematical methods used in the simulation. Chapter gif provides a detailed guide for using the program.

In lieu of reading this thesis straight through, the curious user may wish to first explore the files listed on previous pages. The reader who wants to examine the program more thoroughly before reading about the dynamics of trapped particles may skip straight to Chapter gif (Methods and Theory of the Computer Simulation) or Chapter gif (A Guide to Using Program TrapApp).

It is my sincere wish that you will enjoy your time with this thesis/program duo and that perhaps you may even learn something.

If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis ... that all things are made of atoms, little particles that move around in perpetual motion...
--- R.P. Feynman[13]



next up previous contents
Next: Theory and Simulation Up: Preface Previous: A Quick Tour



Wolfgang Christian
Fri May 12 10:36:01 EDT 1995