Numerical Studies of Heating and Resonant Relaxation Dynamics in Trapped Ions for Precision Measurements

Linear Paul traps are central to modern precision ion experiments including measurements of the electron electric dipole moment (eEDM). In an interacting thermal ion cloud the Coulomb interactions, trap harmonicity, and micromotion can result in nontrivial RF-induced heating and relaxation behaviors. Molecular-dynamics simulations of Coulomb-interacting ion clouds are performed in a linear Paul trap using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to study these effects. For heating, we report heating rate scaling laws different from those found in the literature. For relaxation, we observe two distinct mechanisms: a collision-mediated redistribution of energy among the motional degrees of freedom of each ion, and a faster resonance-like coupling to collective mean field dynamics that is sensitive to trap harmonicity. These thermalization timescales provide important guidance for preparing more ergodic ion ensembles, which can provide time-averaging of field inhomogeneities and reduce sensitivity to systematics that depend on initial conditions in precision measurements.