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Previous Studies and Proposed Work

Laboratory experiments with ion traps require expensive equipment and highly sophisticated detection techniques [12]. An accurate, fast numerical simulation would provide a useful supplement to laboratory observation of ion trapping. Prior research on ion trapping simulations includes a comparison of order/chaos transitions in computer simulation of two trapped ions with experimental results [8], a simulation of 100-1000 ions in a Penning trap [5], and an exploration of parameters for which an ion's motion can be modeled by the first approximation of the Mathieu differential equation [3]. The general form of the Mathieu differential equation is

The Mathieu equation has both stable and unstable solutions as a function of and , corresponding to trapping and escaping ions [3]. When the parameters and are sufficiently small, the stable periodic motion can be represented by the first approximation of the solution to the Mathieu differential equation [11]. However, in the stable domain for which and are not sufficiently small, perturbative solutions are no longer valid [3].

The proposed work will explore the computational power of High Performance Fortran (HPF) on a parallel machine to model behavior of a large number of ions and to explore parameter realms for which perturbative mathematical solutions are not valid.

Wed Jul 27 11:57:58 EDT 1994