# Probability of radiation of twisted photons by cold relativistic particle bunches

## TL;DR

This paper derives the probability of twisted photon radiation from cold relativistic particle bunches, analyzing both incoherent and coherent emissions in various electromagnetic environments, and introduces rules for describing their properties.

## Contribution

It introduces the addition rule for coherent radiation of twisted photons and provides explicit formulas for different bunch profiles, advancing understanding of twisted photon emission mechanisms.

## Key findings

- Incoherent radiation is independent of azimuthal particle distribution.
- Universal properties of forward incoherent radiation at high energies.
- Addition rule for coherent radiation enables superradiant twisted photon sources.

## Abstract

The probability to record a twisted photon produced by a cold relativistic particle bunch of charged particles is derived. The radiation of twisted photons by such particle bunches in stationary electromagnetic fields and in propagating electromagnetic waves is investigated. It is shown that the incoherent radiation by bunches of particles traversing normally an isotropic dispersive medium (the edge, transition, and Vavilov-Cherenkov radiations) and by bunches moving in a helical undulator does not depend on the azimuthal distribution of particles in the bunch and is the same as for round bunches. As for planar undulators, the incoherent radiation by particle bunches is the same as for the bunches symmetric under reflection with respect to the axis of a twisted photon detector. At high energies of recorded twisted photons, this property is universal and holds for the forward incoherent radiation by any cold relativistic particle bunch. The coherent radiation of twisted photons by such particle bunches obeys the property that we call the addition rule. This rule provides a simple means to describe the properties of coherent radiation of twisted photons. Furthermore, the strong addition rule is established for the coherent radiation by sufficiently long helical bunches. The use of this rule allows one to elaborate superradiant pure sources of twisted photons. The coherent radiation by helical bunches is considered for the edge, transition, and Vavilov-Cherenkov processes and for particles moving in undulators and plane laser waves with circular polarization. In these cases, the sum rules are deduced for the total probability to record a twisted photon and for the projection of the total angular momentum per photon. The explicit expressions for both incoherent and coherent interference factors are derived for several simple bunch profiles.