Cyclotron motion in a spherical microwave cavity

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Abstract
We calculate the shifts in the orbital frequency and damping constant for a charged particle in a cyclotron motion that is highly localized near the center of a lossy spherical cavity. In consequence of the spherical geometry, a simple closed form for the frequency shift and damping time is obtained, and the dissipation of a cavity with finite conductivity can be treated exactly. The spherical cavity has a simple mode structure that correlates frequency shift and damping-constant minima. This correlation provides a simple prescription for minimizing the shifts. However, because the modes are more sparsely spaced than are those of the cylindrical cavity treated earlier which models present Penning traps, the overall effects are larger for the sphere.