Electromagnetic fields of relativistic bunches in cavity resonators

A method for calculating the induction electric field of a relativistic particle bunch flying through a cavity resonator is given. It is demonstrated that the described method allows the following assertions to be substantiated: with the increase of particle energy the bunch intrinsic field contracts himself in strict conformity with the Lorentz transformations to become such as if the resonator had been moving together with the bunch; if only the leading, or rear, front of the beam moves over the resonator the intrinsic field contains two components, one of which contracts himself with increase in energy in accordance with the Lorentz transformations, while the second one does not depend on the particle energy at all; if the resonator is filled with a medium having permittivity epsilon and magnetic permeability μ the Lorentz contraction at the sub-Cherenkov velocities proceeds in the same manner as in an empty resonator if the Lorentz factor is equal to 1/√1-epsilonμβ2; after the Cherenkov threshold (epsilonμβ2>1) the intrinsic field has a line spectrum in which every frequency corresponds to a syncrhonism between the beam and the corresponding waveguide type of the wave