On the theory of astronomical maser. I. Statistics of maser radiation
  In this paper we re-analyse the amplification process of broadband continuum
radiation by astronomical masers in one-dimensional case. The basic equations
appropriate for the scalar maser and the random nature of the maser radiation
field are derived from basic physical principles. Comparision with the standard
radiation transfer equation allows us to examine the underlying assumptions
involved in the current theory of astronomical masers. Simulations are carried
out to follow the amplification of different realisations of the broadband
background radiation by the maser. The observable quantities such as intensity,
spectral line profile are obtained by averaging over an ensemble of the
emerging radiation corresponding to the amplified background radiation field.
Our simulations show that the fluctuations of the radiation field inside the
astronomical maser deviates significantly from Gaussian statistics even when
the maser is only partially saturated. Coupling between different frequency
modes and the population pulsing are shown to have increasing importance in the
transport of maser radiation as the maser approaches saturation. Our results
suggest that the standard formulation of radiation transfer provides a
satisfactory description of the intensity and the line narrowing effect in the
unsaturated and partially saturated masers within the framework of
one-dimensional model. Howerver, the application of the same formulation to the
strong saturation regime should be considered with caution.
