The amplification of celestial maser radiation in the general many-level case

A theoretical framework has been developed which can in principle be used for the interpretation of observational data for cosmic masers of all types (e.g. OH, H2O, SiO, CH3OH, megamasers). Our main concern is with the description of the transport of maser radiation and we present a semi-classical formulation of maser saturation in many-level systems in which many masers may propagate simultaneously. Building upon results obtained in earlier semiclassical theories for two-and four-level systems, we include the full coupling between the kinetic model for the maser inversion pump and the saturating effects of maser radiation. We explicitly solve the generalized Bloch equations in the steady state to yield a formula for level populations which depend on the intensities of all masers present in the medium as well as upon the details of the kinetic model. These populations are then coupled to a set of exponential gain equations whose solution yields a set of maser intensities as a function of gain length. (author)