Using anisotropic dispersive materials for high-precision determination of the energy of charged particles

Vavilov-Cherenkov radiation (VCR) generated by a charged particle moving in a waveguide filled with an anisotropic dispersive material is considered. It is shown that, for a certain character of dispersion and anisotropy, which can be realized using artificial metamaterials, it is possible to obtain a pronounced dependence of the frequencies of excited modes on the Lorentz factor in a narrow interval of this parameter. This circumstance can be used for determining the energies of particles and beams with an error that is smaller than the error of measurement of the VCR frequencies. It is also possible to create a "subthreshold" Cherenkov detector, which detects all particles moving with velocities below a certain preset value.