# Semiclassical probability of radiation of twisted photons in the ultrarelativistic limit

## TL;DR

This paper derives a semiclassical formula for the probability of ultrarelativistic particles radiating twisted photons in various electromagnetic fields, accounting for quantum recoil and spin effects, and applies it to different experimental setups.

## Contribution

It introduces a general semiclassical formula for twisted photon radiation that includes quantum recoil and spin, extending classical undulator and nonlinear Compton theories.

## Key findings

- Quantum recoil and spin increase twisted photon radiation probability.
- Selection rules from classical theory remain valid with quantum effects.
- Manifestation of the blossoming out rose effect in nonlinear Compton and wiggler radiation.

## Abstract

The semiclassical general formula for the probability of radiation of twisted photons by ultrarelativistic scalar and Dirac particles moving in the electromagnetic field of a general form is derived. This formula is the analog of the Baier-Katkov formula for the probability of radiation of one plane wave photon with the quantum recoil taken into account. The derived formula is used to describe the radiation of twisted photons by charged particles in undulators and laser waves. Thus, the general theory of undulator radiation of twisted photons and radiation of twisted photons in the nonlinear Compton process is developed with account for the quantum recoil. The explicit formulas for the probability to record a twisted photon are obtained in these cases. In particular, we found that the quantum recoil and spin degrees of freedom increase the radiation probability of twisted photons in comparison with the formula for scalar particles without recoil. In the range of applicability of the semiclassical formula, the selection rules for undulator radiation established in the purely classical framework are not violated. The manifestation of the blossoming out rose effect in the nonlinear Compton process in a strong laser wave with circular polarization and in the wiggler radiation is revealed. Several examples are studied: the radiation of MeV twisted photons by $180$ GeV electrons in the wiggler; the radiation of twisted photons by $256$ MeV electrons in strong electromagnetic waves produced by the CO$_2$ and Ti:Sa lasers; and the radiation of MeV twisted photons by $51.1$ MeV electrons in the electromagnetic wave generated by the FEL with photon energy $1$ keV.