Investigations on Dynamical Stability in 3D Quadrupole Ion Traps

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. The system dynamics is characterized using a well established model that relies on two control parameters: the axial angular moment and the ratio between the radial and axial trap pseudo-oscillator characteristic frequencies. We augment this model and employ the Hessian matrix of the potential function in an attempt to better describe dynamical stability and the critical points. Our approach is then used to explore quantum stability in case of strongly coupled Coulomb many-body systems and establish a technique aimed at determining the critical points. Finally, we apply the model in case of a 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. A different approach is used to better characterize many-body dynamics in combined (Paul and Penning) traps, with applications such as stable trapping of antimatter or fundamental tests of the Standard Model. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a cohesive method.