Cherenkov radiation threshold in random inhomogeneous media

Cherenkov radiation in media with random inhomogeneities like aerogel or Earth atmosphere is discussed. The spectral-angular distribution of Cherenkov photons emitted by relativistic charged particle and averaged over the dielectric permittivity fluctuations shows angular broadening similarly to the case of media with the photon absorption. The broadening results in the smoothing of Cherenkov threshold, and therefore media with strong photon scattering have more extended dependence of Cherenkov light output on the particle speed. It can be potentially used for the particle identification