  Maximum amplitudes of accelerating fields are restricted by electron
breakdown and Joule heating losses in conducting walls in traditional
accelerating structures. In this paper, we presented a resonant composite
accelerating cavity, which utilizes a periodic structure with a dielectric
sphere located at a spherical conducting cavity center. The presence of the
dielectric sphere in the central part of the resonance cavity shifts the
magnetic fields maximum from regions close to the metallic wall to the
dielectric surface, which strongly lowers the skin effect losses in the wall.
By using the existing ultra-low loss Sapphire dielectrics, we made theoretical
analyze and numerical calculations by MATLAB, and further make simulated
calculation by CST for comparison. The results show that all field components
at the metallic wall are either zero or very small, and therefore one can
expect the cavity to be less prone to electrical breakdowns than the
traditional cavity. Furthermore, the quality factor Q can be three orders of
magnitude higher than that obtained in existing cylindrical cavities.
