  A sufficient condition for maser instability in a weakly magnetized
relativistic plasma with an isotropic particle distribution function is given.
The maser growth rates and polarizations are computed starting from the exact
dielectric permittivity tensor of a magnetized plasma. For very weak magnetic
fields, our results confirm the approximate validity of the 'standard maser
theory', which is based on the Einstein coefficients method, with one
significant exception. For inclined propagation and realistic (small but
finite) field, the growth rates of the two (nearly circular) polarizations
differ significantly, while the standard theory predicts two (nearly circular)
polarizations with similar growth rates. We show that this deviation is due to
circularly polarized synchrotron emission, which is neglected in the standard
theory.
  The maser is shown to grow slower than Langmuir waves. Nevertheless,
significant generation of EM waves is seen in (highly simplified) direct
numerical simulations. We study the nonlinear saturation of the maser
instability and find that it offers a mechanism for the conversion of a
significant fraction of the plasma energy into radio waves. We briefly discuss
the conditions under which the maser instability may operate in astrophysical
sources, and provide rough estimates that may be used as a guidance when
studying particular astrophysical sources/phenomena.
