Instantaneous and Retarded Interactions in Coherent Radiation

In coherent radiation of an ensemble of electrons, the 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 Liénard-Wiechert potential. Despite its being the foundation of beam physics for decades, we show that using the "acceleration field" in Liénard-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 an 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 energy loss, which hopefully will reshape our understanding of coherent radiation and collective interactions.