next up previous contents
Next: Methods and Theory Up: Theory and Simulation Previous: Stability Conditions for

Behaviors Observed in Penning Trap Simulations

TrapApp was kept as general as possible: it models systems explicitly from their equations of motion, rather than according to special-case simplifications. Even though no time-saving approximations were introduced, TrapApp enables inspection of stability conditions and observation of the trajectories characteristic of Penning-trapped particles.

  
Figure: Axial, radial, and x-positions of a single Penning-trapped Be ion. Note that the cyclotron motion (represented by fluctuations in the radial position) has the largest frequency and smallest amplitude, while the magnetron motion (represented by the x-oscillations) has the smallest frequency and largest amplitude. The axial oscillations have a frequency between those of the magnetron and cyclotron motions. source file: introPen.trp.

Fig. gif shows the large discrepancy in the frequencies and magnitudes of cyclotron, magnetron, axial motions. A three-dimensional representation of the Be ion's position would show fast, small-amplitude radial cyclotron rotation superposed on axial harmonic oscillation superposed on the ion's slowly oscillating magnetron orbit. As depicted in Fig. gif, the single-Penning trapped ion occupies a cylindrical region of space.

  
Figure: x-positions vs. axial position of a single Penning-trapped Be ion. source file: introPen.trp.



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