Number dependency in the compensated Penning trap

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Abstract
Due to the increasing role that highly charged ions play in high-precision mass-ratio measurements within a compensated Penning trap, it is imperative that we investigate the dependency of the normal-mode frequencies on the total number of trapped charges. The experimental number dependency has been measured for four different ion species with various states of ionization. The absolute shift in both the observable cyclotron and magnetron frequencies is 0.018(3) Hz per equivalent electronic charge for a trap with characteristic dimension of 0.114 cm (in a 5-T field). The source of this systematic dependency has been traced to image charges induced on the surface of the trapping electrodes, whose electric field at the ion’s position near trap center is approximately linear in the displacement of the trapped ions. A simple spherical model has been developed that is useful as a guide in minimizing this systematic effect.