Radiation of twisted photons in elliptical undulators

TL;DR

This paper derives explicit formulas for the radiation of twisted photons by charged particles in elliptical undulators, revealing a general selection rule for angular momentum and harmonic number, applicable in classical and quantum regimes.

Contribution

It introduces a generalized selection rule for twisted photon radiation in elliptical undulators and describes the class of particle trajectories that produce such radiation.

Findings

Radiation obeys the selection rule: m + n is even.

Formulas are provided for both classical and quantum recoil cases.

The class of particle trajectories producing twisted photons is characterized.

Abstract

The explicit expressions for the average number of twisted photons radiated by a charged particle in an elliptical undulator in the classical approximation as well as in the approach accounting for the quantum recoil are obtained. It is shown that radiation emitted by a particle moving along an elliptical helix which evolves around the axis specifying the angular momentum of twisted photons obeys the selection rule: $m+n$ is an even number, where $m$ is a projection of the total angular momentum of a twisted photon and $n$ is the harmonic number of the undulator radiation. This selection rule is a generalization of the previously known selection rules for radiation of twisted photons by circular and planar undulators and it holds for both classical and quantum approaches. The class of trajectories of charged particles that produce the twisted photon radiation obeying the aforementioned selection rule is described.