  Synchrotron emission of relativistic particles in magnetic fields is a
process of paramount importance in astrophysics. Although known for over thirty
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.
