Transition radiation of electrons with orbital angular momentum

Several experimental groups have recently obtained the so-called vortex electrons (electrons with orbital angular momentum (OAM) of $\ell \leq 100\,\hbar$) with energies of $\sim 300$ keV. The angular momentum of such electrons becomes proportional to the OAM value, which leads to the corresponding increase of the electron magnetic moment. In this paper, we investigate the transition radiation from the "charge $+$ magnetic moment" system by means of the classical electrodynamics theory. The circular polarization of optical transition radiation reaches its maximum level to $\sim 70\,\%$, which allows to use this effect for the independent measurement of the electron orbital momentum value.