Coherent photons with angular momentum in a helical afterburner

Abstract

We analytically examine several important characteristics of coherent radiation emitted from a relativistic electron beam in a helical undulator. The goal is to highlight specific attributes relevant to the production of bright x-rays with angular momentum in a free-electron laser (FEL) afterburner. The far-field complex electric field distribution is derived, and for small forward emission angles, it is confirmed that the spin and orbital components of angular momentum in the radiation are separable, additive, and aligned with the handedness of the electron motion. The coherent energy radiated at harmonics $h$ from a bunched electron beam is then calculated, and used to evaluate the emission energy from a FEL afterburner configuration. Results show that an afterburner undulator with ${N}_{u}\ensuremath{\gg}1$ periods and of sufficient strength will produce harmonic pulses with energy $\ensuremath{\sim}1/{N}_{u}^{h\ensuremath{-}1}$ times that of the fundamental, depending on the Fresnel number $N=k{\ensuremath{\sigma}}_{x}^{2}/{L}_{u}$ of the radiating electron beam.