Control of the conformations of ion Coulomb crystals in a Penning trap

Ion Coulomb crystals containing small numbers of ions have been created and manipulated in a wide range of configurations in a Penning trap, from a linear string, through various three-dimensional conformations, to a planar crystal. We show that the dynamics of the system simplifies enormously in a frame which rotates at half the cyclotron frequency and we discuss the effect of the radial cooling laser beam in this frame. Simulations show that the crystal conformations can be reproduced by finding the minimum energy configuration in a frame whose radial potential is modified by the rotation of the ion crystal. The rotation frequency of the crystal deduced from the simulations is consistent with the known laser parameters. We also show that even though the number of ions in our system is small (typically less than 20), the system still behaves like a plasma and its static properties can be calculated using the standard model for a single-component plasma in a tra