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

We present an analysis of
electromagnetic oscillations in a spherical conducting cavity filled
concentrically with either dielectric or vacuum layers. The fields are given
analytically, and the resonant frequency is determined numerically. An
important special case of a spherical conducting cavity with a smaller
dielectric sphere at its center is treated in more detail. By numerically
integrating the equations of motion we demonstrate that the transverse electric
oscillations in such cavity can be used to accelerate strongly relativistic
electrons. The electron’s trajectory is assumed to be nearly tangential to the dielectric sphere.
We demonstrate that the interaction of such electrons with the oscillating
magnetic field deflects their trajectory from a straight line only slightly.
The *Q* factor of such a resonator only
depends on losses in the dielectric. For existing ultra low loss dielectrics, *Q* can be three orders of magnitude
better than obtained in existing cylindrical cavities.

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