Cyclotron motion in a Penning-trap microwave cavity

The cavity shifts in the cyclotron motion of a charged particle in a hyperbolic Penning trap are described using a numerical evaluation of the cavity-mode structure. The frequency shifts are about half as large in the hyperbolic cavity as in a cylindrical cavity of equivalent size. However, this still implies an error in the g-2 experiment that is easily five times the present statistical uncertainty. To account for slit electrodes and imperfect tolerances in existing traps, experimental measurements of the mode structure are still needed. The resonant frequencies of a microwave cavity can be measured very precisely. We show here that an accuracy of 10% in the measurements of certain coupling constants is sufficient to compute the shifts for the g-2 experiment at the level of one part in ${10}^9$.