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Webster's dictionary defines an epilogue as ``a short poem or speech to the audience at the end of a play,'' but this addendum is merely intended to fulfill the roles of conclusion, speculation on where one might (armed with TrapApp) go from here, and acknowledgement.

To bring this thesis to a close (and firmly imprint its salient points in your memory), let us briefly survey what we have seen:

  1. Beginning with a mathematical description of the Paul trap's electric field, we have illustrated, in terms of stability regions of the Mathieu equation, conditions under which particle confinement can be achieved in a Paul trap.
  2. An approximation for particle motion in stability region A has been described mathematically and demonstrated via simulation.
  3. Higher-order stability region B was graphed, and particle confinement was achieved for simulations in this parameter region.
  4. The four dynamical regimes (enumerated by Blümel[4]) relevant to Paul-trapping were explored in region A.
  5. In stability region B, we observed dynamics corresponding to the Mathieu regime, the chaotic heating regime, and the ordered phase. However, crystals in region B were not stable in the absence of damping, and no non-heating, quasiperiodic regime was observed. Rather, undamped crystals heated into the Mathieu regime, in accordance with Blümel's speculation that crystals in region B require extensive cooling.
  6. TrapApp demonstrated the validity of Penning trap stability conditions and illustrated that trajectories described by Penning-trapped particles consist of axial harmonic oscillation and, in the radial dimension, small-amplitude cyclotron motion superposed on a slow magnetron motion.

This thesis has not exhausted the resources of TrapApp. In light of this untapped potential, I would like to suggest a few issues one might wish to pursue:

Finally, I'd like to thank everyone who has made this work possible and profitable. Many thanks are due to my advisor, Dr. Wolfgang Christian, for valuable insights, for good and numerous sources, for help with everything from pointers to mean free paths, and for composing the graph objects which enabled me to finally (after a summer of blind work on Fortran 90) see my ions. The Davidson College Physics Faculty provided valuable feedback on the program and drafts of the thesis; in particular, I am grateful to Dr. Laurence S. Cain and Dr. Robert Cline for thouroughly proofreading (and correcting) the thesis. I'd also like to thank Dr. Ken Hawick, a researcher at the Northeast Parallel Architectures Center, who advised my summer (1994) work on TrapApp's ancestor and introduced me to the wonders of Numerical Recipes. Finally, I acknowledge my debt to the many scientists whose works on ion trapping and molecular dynamics I have relied upon.

next up previous contents
Next: References Up: Ions in Electromagnetic Traps Previous: Mouse Clicks on

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