  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.
