Quantum effects in spontaneous emission by a relativistic, undulating electron beam

TL;DR

This paper introduces a one-dimensional model for spontaneous emission effects on relativistic, undulating electron beams, highlighting differences between classical and quantum regimes, with implications for coherent radiation generation.

Contribution

It presents a novel model that accounts for electron recoil discreteness, bridging classical and quantum descriptions of electron beam dynamics in undulators.

Findings

Classical regime shows continuous energy decrease and diffusion.

Quantum regime exhibits discrete momentum groups following a Poisson distribution.

Narrow momentum features in the quantum regime could enhance coherent radiation applications.

Abstract

Current models of the effect of spontaneous emission on the electron beam dynamics neglect the discreteness of electron recoil associated with photon emission. We present a novel, one-dimensional model of the effect of spontaneous emission on the electron beam dynamics in an undulator both in the classical regime where discrete electron recoil is negligible, and the quantum regime where it is significant. It is shown that in the classical regime, continuous decrease of the average electron energy and diffusive growth of the electron energy spread occurs, in agreement with previous classical models. In the quantum regime, it is shown that the evolution of the electron momentum distribution occurs as discrete momentum groups according to a Poisson distribution. The narrow momentum features of the quantum regime may be useful for generation of coherent radiation, which relies on electron beams having sufficiently narrow momentum/energy distributions.