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Ordered Phase

With sufficient damping, the simulation demonstrates that ``crystals'' can be formed in stability region B. These ordered structures are quantitatively and qualitatively different from the crystals of region A. To begin with, coupling parameters for structures in region B are significantly lower (by a factor of 20-25) than for analogous structures in region A (Tab. gif). Another difference with regard to the coupling is that, whereas coupling parameters for simulations in region A tended to increase (Tab. gif) with an increase in ion number, the parameters for region B simulations tend to decrease with increasing ion number (Tab. gif). This trend suggests that, in region B, the effects of micromotion outweigh potential energy gains due to increased charge when ion number is increased.

  
Table: Coulomb coupling, , for ordered structures in stability region B. Note that in contrast with simulations performed in region A, region B simulations show decreasing with increasing N.

The geometry of two- and four-ion crystals simulated in region B (at , ) is reminiscent of the two- and four-ion crystals of 2CrA.trp and 4CrA.trp (). In both regions the two- and four-ion crystals were virtually confined to the z=0 plane. Damped two- and four- ion crystals in region B demonstrated significantly larger micromotion oscillations than their region A counterparts: for example, the four-ion crystal of 4crB.trp has radial oscillations of m peak-to-peak compared to m peak-to-peak for 4CrA.trp.

The eight-ion crystal of region B (file 8crB.trp) differed from that of region A (file 8CrA.trp) in that (a): it was not planar; and (b): ions' relative axial positions were not fixed--- rather, ions were periodically reflected across the z=0 plane (Fig. gif). Similarly, the axial positions of the 32-ion crystal in region B (file 32crB.trp) oscillated periodically and predictably.

  
Figure: Geometry of a damped 8-Mg ion crystal in stability region B. left: XZ projection shows that the crystal is not planar--- it measures about m in the radial direction, m is the axial direction; center: XY projection shows radial order; right: x-position vs. axial position, showing periodic variation in axial placement. source file: 8CrB.trp.

  
Figure: Large micromotion oscillations (m peak-to-peak) for a 32-ion ordered structure in stability region B. These figures have the same scale and represent the same ordered configuration at different phases of the micromotion. source file: 32CrB.trp.



next up previous contents
Next: Investigation of Crystal Up: Behaviors Simulated for Previous: Chaotic Regime



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