PROBLEMS WITH THE STANDARD THEORY OF 3-DIMENSIONAL MASERS

The standard theory of three-dimensional masers is based upon inadequate approximations. In particular, the standard treatment adopts equations for the steady state molecular level populations and for the transfer of maser radiation which apply strictly only to one-dimensional masers. I consider here the specific case of a partially saturated spherical maser in which the rate of cross-relaxation between molecules of different velocities is small. For that case the standard approach leads to a relationship between the maser intensity and the molecular level populations which differs significantly from that obtained using the exact equations for the transfer of maser radiation. The correct solution to the problem of the partially saturated spherical maser can be obtained numerically by an iterative method and will be considered in a subsequent paper.