Bremsstrahlung by a rapidly accelerating point charge

The classical problem of radiation emitted by an accelerated charge in the relativistic case is considered. Only accelerations which occur in a short time interval are taken into account. We first discuss the one dimensional trajectories, for later extending the analysis to the two-dimensional case by means of a first-order approximation. We find an expression for the allowed radiated frequencies and we discuss the inconvenience of the concept of formation time of radiation. The results allow us to treat the case of successive collisions, in order to study the behavior of the interference terms.