Small Signal Analysis of Molecular Beam Masers

A perturbation calculation gives the resonance polarization of a molecule in an electric field as a function of time. An analysis is then made of maser operation with a divergent, univelocity beam. Equations are derived which give the relative beam intensity required to start oscillation and the molecular Q as a function of cavity length. An optimum cavity length is predicted. This theory is compared with a similar theory of K. Shimoda which assumes a Maxwell velocity distribution, and reasonable agreement is obtained. On the basis of this agreement it is possible to define an equivalent divergence of the velocity distributed beam.