Classical Electrodynamical Derivation of the Radiation Damping Force

Abstract

A covariant expression for the instantaneous radiation damping force acting on an accelerated charged particle is derived within the frame of classical electrodynamics. The radiation pressure of the wave emitted by the charge is averaged on a sphere of radius $R$ to obtain the net force due to the photon momentum recoil, and the limit is taken when $R$ tends to zero, assuming no internal structure of the particle. The relativistic Doppler effects break the symmetry of the instantaneous rest frame dipole radiation pattern, and the Abraham-Becker damping force is obtained.