Measurements of accelerator beam spectrum through dependence of Cherenkov radiation intensity on phase velocity of electromagnetic waves in optical and microwave ranges

The use of Cherenkov radiation in the optical and microwave ranges for measuring the accelerator beam energy and the energy spectrum is described. Suggested methods are based on a dependence of the radiation intensity on the phase velocity of electromagnetic waves in the Cherenkov radiator medium. Mathematical procedure of extraction of the energy spectrum from the measured intensity is given in detail.