Theory of synchrotron radiation: I. Coherent emission from ensembles of particles

Synchrotron emission of relativistic particles in magnetic fields is a process of paramount importance in astrophysics. Although known for over 30 years, there are still aspects of this radiative process that have received little attention, mainly because they appear only in extreme conditions. In the present paper, we first provide a general introduction to synchrotron emission, using a formalism that represents a generalization of the standard calculations. The use of this formalism allows us to discuss situations in which charged particles can radiate coherently, with special attention for the cases in which the production occurs in the form of a bunch of particles created in a pulse of very short duration. We calculate the spectra of the radiation for both monoenergetic particles and distributions of particles with different Lorentz factors. For both cases we study the conditions for the coherent effects to appear, and demonstrate that in the limit of incoherent emission we reobtain the well known results.