Enlarged Lorentz-Dirac equations

Dirac's approach to incorporate the radiation into the equation of motion for a point charge in classical electrodynamics is based on three structural components: the point model for the electron, the Maxwell equations and the principle of relativity. These fundamental components lead to an equation of motion that involves an undetermined 4-vector B-mu. The Lorentz-Dirac equation corresponds to the case in which B-mu = 0, but in general there is a large family of 4-vectors B-mu consistent with the above three basic components. This paper deals with the study of these equations of motion in the case of the three simplest permissible choices for B-mu. We show that these equations admit as exact solutions the motion of an arbitrary number of identical charges that are equally spaced in a circumference and that rotate at constant angular velocity. These solutions show that the rate of radiation emitted by the system of charges is completely independent of the 4-vector B-mu. We also study the restrictions over the dimensionless parameters that appear in the four-vectors B-mu, in order that the trajectories of the corresponding equations cannot be discriminated from the trajectory determined by the Lorentz-Dirac equation in a practical case, as for instance the design and operation of a synchrotron.