  We simulate the dynamics, including laser cooling, of 3D ion crystals
confined in a Penning trap using a newly developed molecular dynamics-like
code. The numerical integration of the ions' equations of motion is accelerated
using the fast multipole method to calculate the Coulomb interaction between
ions, which allows us to efficiently study large ion crystals with thousands of
ions. In particular, we show that the simulation time scales linearly with ion
number, rather than with the square of the ion number. By treating the ions'
absorption of photons as a Poisson process, we simulate individual photon
scattering events to study laser cooling of 3D ellipsoidal ion crystals.
Initial simulations suggest that these crystals can be efficiently cooled to
ultracold temperatures, aided by the mixing of the easily cooled axial motional
modes with the low frequency planar modes. In our simulations of a spherical
crystal of 1,000 ions, the planar kinetic energy is cooled to several
millikelvin in a few milliseconds while the axial kinetic energy and total
potential energy are cooled even further. This suggests that 3D ion crystals
could be well-suited as platforms for future quantum science experiments.
