Cyclotron motion in a microwave cavity: Lifetime and frequency shifts

The interaction of a bound electron with the radiation field produced by the image charges that represent a surrounding cavity produces a shift in its orbital frequency and in its radiative decay time. We calculate the frequency shift and the change in the damping constant for a cyclotron motion at the midpoint of a lossy, cylindrical cavity. A change in the cyclotron damping constant has, in fact, been observed in the University of Washington g-2 experiments. These experiments employ electrodes with a hyperbolic shape, but our calculable model should give a useful indication of the size of the effects for them. The frequency shift can easily be so large as to have important consequences for the g-2 measurements, and this systematic effect warrants a thorough experimental investigation. As an intermediate step in this calculation, we also compute the corresponding alterations for a charged particle in the midplane between two infinite parallel conductors.