Models for the radiation damping force of a charged particle in a magnetic or electric field by means of a flux-proportional Lentz force has been shown to be an elegant solution for the inward spiraling trajectories under magnetic fields, and the speed limited trajectories under electric fields. Our phenomenological formulation of the damping force in a magnetic field requires a new attenuation coefficient, α, that has only been evaluated using experimental data, but whose pure theoretical evaluation may lead to improved understanding of the mechanism of electron damping in electromagnetic fields. We believe that the synchrotron radiation and its observed coherence is already sufficient experimental evidence for our modeling of radiation damping. It is hoped that our model could be applied to improve the designs of free electron lasers as well as the design of particle accelerators.