Self-force approach to synchrotron radiation

We analyze radiation reaction for synchrotron radiation by computing, via a multipole expansion, the near field and derive from it the Lorentz four-force, which we evaluate on the world-line of the charge. We find that the temporal component of the self four-force agrees with the radiated power, which one calculates in the radiation zone. This is the case for each mode in the multipole decomposition. We also find agreement with the Abraham–Lorentz–Dirac equation.