List of Tables

• Experimental parameters for the 1959 work of Weurker, Shelton, and Langmuir.
• Coulomb coupling parameters for damped and undamped crystal simulations in stability region A.
• Simulated two-ion equilibrium spacings for a crystal on the z=0 plane ( left) and a crystal on the z-axis ( right). Mathieu parameters--- left: , , right: , . Theoretical equilibrium spacings--- left: m, right: m. source files: intrCrys.trp, axialCr.trp.
• Test of stability of undamped crystals in stability region A. source files: 2CrA.trp, 4CrA.trp, 5CrA.trp, 8CrA.trp, 15CrA.trp, 32CrA.trp, 64CrA.trp, 65CrA.trp, 128CrA.trp.
• Structural response of 2-ion crystal to instantaneous changes in magnitude of applied oscillating voltage, . Note the increase in micromotion amplitude with increasing magnitude of the oscillating potential, . source file: 2CrA.trp.
• Change in coupling parameter () of a 4-ion crystal in response to instantaneous changes in magnitude of applied oscillating voltage, . source file: 4CrA.trp.
• Behavior of planar crystals in response to linear increase in magnitude of applied oscillating voltage, . The Mathieu instability for occurs at and corresponds to unbounded axial oscillation.
• Frequency analysis of x-motion and axial motion of 1 and 10 Paul-trapped ions in stability region B. The agreement in frequencies illustrates that the 10 ions are in the Mathieu (non-interacting) regime. source files: paul10B.trp, paul1B.trp
• 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.