Proposal for experimental observation of the twisted photons in transition and Vavilov-Cherenkov radiations

We propose to use Vavilov-Cherenkov (VC) and transition radiations as a source of twisted photons in a wide range of energies. The experimental setup to observe the orbital angular momentum of photons constituting those radiations is described. The radiation produced by relativistic electrons and ions in passing dielectric plates is considered. The experimental verification of the addition rule for the total angular momentum in the radiation of twisted photons by helically microbunched beams is proposed for VC and transition radiations. The parameters of the experiments are presented.