“…Laser-cooled ions in radio-frequency (rf) and Penning traps form Coulomb crystals, spatially ordered structures that arise due to a balance between trapping fields and Coulomb repulsion. Decades-long advancements in the preparation and control of cold ion crystals allow for precise manipulation of internal and external degrees of freedom [1], giving rise to applications spanning plasma physics [2,3], high-precision spectroscopy [4,5], cold molecules [6][7][8], and quantum computation [9][10][11] and simulation [12][13][14][15]. In these experiments, achieving the desired level of control has typically required an initial characterization of the ion positions, structural phases, normal mode frequencies, and sources of crystal heating.…”