Preacceleration without radiation: the non-existence of preradiation phenomenon

An unexpected prediction of classical electrodynamics is that a charge can accelerate before a force is applied. We would expect that a preaccelerated charge would radiate so that there would be spontaneous preradiation, an acausal phenomenon. We reexamine the subtle relation between the Larmor formula for the power radiated by a point charge and the Abraham-Lorentz equation and find that for well-behaved external forces acting for finite times, the charge does not radiate in time intervals where there is preacceleration. That is, for these forces preradiation does not exist even though the charge is preaccelerated. The radiative energy is emitted only in time intervals when the external force acts on the charge.