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Behaviors Simulated for Paul-Trapping in Region B

Stability region B, which corresponds approximatelygif to the a,q parameters indicated in Fig. gif, is an interesting region for simulation since: (a) the literature explicitly states that as of 1989, no Paul-trapping experiment had been conducted in region B,[4] and a literature search revealed only two articles concerning Paul-trapping in region B since 1989;gif (b) the mathematical model (Sec. gif) which approximates the trajectory of an independent ion in region A is not valid in region B.[4]

Comparing a plot of x-position versus axial-position in region B (Fig. gif) to a plot in region A (Fig. gif), one sees that the radial motion in region B is ``pinched''--- that is, the amplitude of radial oscillations is significantly less than that of axial oscillations and is concentrated in the small r region of the plot. This radial ``squeezing'' is intuitively understandable since for stability region B, indicating that the static component of the ring electrode's potential is higher than that of the endcaps. Fourier transforms of axial position and x-position of a single ion in region B (Figs. gif,gif) reveal a larger number of non-negligible high-frequency components than does a transform of axial position in region A (Fig. gif). Plots of axial and radial position versus time (Figs. gif,gif) in region B illustrate the complexity of motion in region B relative to motion in region A (Fig. gif).

Despite the apparent differences between single-ion trajectories in regions A and B, simulations of ions in region B exhibit behaviors corresponding to three of the four dynamical regimes discussed for region A: TrapApp demonstrates a Mathieu regime, a chaotic heating phase, and an ordered phase.




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