  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.

Accelerator Physics;Instrumentation and Detectors;Optics