Cyclotron motion in a microwave cavity: Possible shifts of the measured electron g factor.

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. The frequency shift can easily be so large as to have important consequences for the University of Washington g-2 measurements.