Angular momentum of radiation from a charge in circular and spiral motion

Abstract

We study theoretically the vortex radiation of a relativistic charged particle. General expressions for the spectral and angular distributions of angular momentum of radiation are derived for an arbitrary moving charge. Special attention is given to calculation of the angular momentum of synchrotron radiation. We obtain the spectrum and the angular distribution of angular momentum carried by synchrotron radiation. Similar expressions for the angular momentum of radiation of a charge moving on a spiral trajectory are derived by use of Lorentz transformations. It is shown that the main part of angular momentum in this case is emitted at a small angle to the vortex axis. Relativistic charged particles at spiral motion are effective source of the vortex photon beams at wave lengths ranging from radio waves to gamma rays. The obtained equations can be used for calculations of the angular momentum emitted by charged particles in the helical undulators and at axial channeling in solid crystal.