Instantaneous and Retarded Interactions in Coherent Radiation

TL;DR

This paper introduces a new theoretical framework for electromagnetic interactions in coherent radiation, separating instantaneous and retarded effects, to better understand radiation losses and collective electron behavior.

Contribution

It proposes decomposing electromagnetic interactions into instantaneous and retarded parts, addressing divergences in classical models and improving understanding of coherent radiation phenomena.

Findings

Retarded interactions account for irreversible radiation loss.

Instantaneous interactions relate to space charge effects.

Application to coherent synchrotron radiation wake enhances understanding.

Abstract

In coherent radiation of an ensemble of electrons, radiation field from electrons resonantly drives the other electrons inside to produce stimulated emission. The radiation reaction force on the electrons accounting for this stimulated radiation loss is classically described by the Lienard-Wiechert potential. Despite its being the foundation of beam physics for decades, we show that using the "acceleration field'' in Lienard-Wiechert potential to describe radiative interactions leads to divergences due to its implicit dependence on instantaneous interactions. Here, we propose an alternative theory for electromagnetic radiation by decomposing the interactions into instantaneous part and retarded part. It is shown that only the retarded part contributes to the irreversible radiation loss and the instantaneous part describes the space charge related effects. We further apply this theory to study the coherent synchrotron radiation wake, which hopefully will reshape our understanding of coherent radiation and collective interactions.