A composite accelerating cavity utilizing a resonant, periodic structure with a dielectric sphere located at a spherical conducting cavity center is presented. The resonator design is of the whispering gallery type to take advantage of the excellent electromagnetic field confinement offered by this geometry. The maximum electromagnetic fields of this structure exceed by several orders of magnitude the values reached in resonant cavities of typical linear accelerators. And the skin current losses are reduced without engaging superconductivity and cryogenic systems for this new construction. Especially because all field components at the metallic wall are either zero or very small in this proposed spherical cavity, one can expect the cavity to be less prone to electrical breakdowns than the traditional cavity. In this paper, the new type of accelerating structure was analyzed and calculated. The results are in very well agreement with the corresponding values simulated by CST. And for the existing ultra-low loss dielectrics, Q can be three orders of magnitude better than obtained in existing cylindrical cavities.
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