  We present the design of a new type of compact toroidal, or "halo", ion trap.
Such traps may be useful for mass spectrometry, studying small Coulomb cluster
rings, quantum information applications, or other quantum simulations where a
ring topology is of interest. We present results from a Monte Carlo
optimization of the trap design parameters using finite-element analysis
simulations that minimizes higher-order anharmonic terms in the trapping
pseudopotential, while maintaining complete control over ion placement at the
pseudopotential node in 3D using static bias fields. These simulations are
based on a practical electrode design using readily-available parts, yet can be
easily scaled to any size trap with similar electrode spacings. We also derive
the conditions for a crystal phase transition for two ions in the compact halo
trap, the first non-trivial phase transition for Coulomb crystals in this
geometry.
