When a charged particle is subject to an applied electromagnetic field it experiences the Lorentz force due to the applied field and a self force due to its interaction with its own electromagnetic field. This self force is negligible in all but the strongest fields and so to date has been of little interest to experiment. However, with the arrival of ultra high intensity laser facilities such as the Extreme Light Infrastructure (ELI), the self force may not only become comparable to the Lorentz force but could possibly even exceed it.

Although of theoretical interest, single-particle radiation reaction is of limited importance since it is unlikely ever to be observed. Modern accelerators accelerate bunches of order 10^8 particles or more and so a kinetic theory of radiation reaction seems prudent. Here we present such a theory and go on to use it to derive a dispersion relation for an electromagnetic wave propagating through a radiating plasma.