Data and Significance

In conclusion, the simulation should illustrate the various behaviors exhibited by trapped ions and provide insight into such considerations as:

• order-chaos transitions: at what parameter values do such transitions occur? is hysteresis evident?
• the effects of damping on stability;
• the role of Mathieu instabilities in determining whether ions will escape or remain within the trap;
• ion behavior in the parameter domain of Mathieu stability for which a first approximation is not valid;
• the degree of Coulomb coupling required for the formation of ordered structures, where the Coulomb coupling parameter, , is the ratio of energy due to Coulomb interactions to thermal energy:

  

• the geometry and energy associated with ordered structures, i.e., with the ``crystals" that form under appropriate conditions.

Consideration of these topics will require various forms of numerical analysis and a graphical user interface. The proposed numerical analysis includes Fast Fourier transforms, spatial probability distributions, and energy calculations. A graphical user interface, developed on Application Visualization System (AVS), will allow the user to specify simulation parameters, view a representation of the physical system, and look at graphs of the data.