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We present an analysis of electromagnetic oscillations in a sphericalconducting cavity filled concentrically with either dielectric or vacuumlayers. The fields are given analytically, and the resonant frequency isdetermined numerically. An important special case of a spherical conductingcavity with a smaller dielectric sphere at its center is treated in moredetail. By numerically integrating the equations of motion we demonstrate thatthe transverse electric oscillations in such cavity can be used to acceleratestrongly relativistic electrons. The electron's trajectory is assumed to benearly tangential to the dielectric sphere. We demonstrate that the interactionof such electrons with the oscillating magnetic field deflects their trajectoryfrom a straight line only slightly. The Q factor of such a resonator onlydepends on losses in the dielectric. For existing ultra low loss dielectrics, Qcan be three orders of magnitude better than obtained in existing cylindricalcavities.

Electromagnetic Oscillations in a Spherical Conducting Cavity with Dielectric Layers. Application to Linear Accelerators