Saturation and beaming in astrophysical masers

A 'four-stream' model system of equations that are closely analogous to the equations of radiative transfer in a maser spectral line and are amenable to numerical solution are constructed. This model is used to investigate radiative transfer in asymmetric maser clouds. Competition between different beams of radiation for available pump photons is important in both unsaturated and saturated masers. Consequently, the radiation from a typical cloud will be highly beamed, even if the maser is saturated, because the shape of a typical cloud is not symmetric. In addition, it is shown that analysis of maser emission lines formed in expanding envelopes does not reveal the degree of saturation of the maser.