The Maser Rate Equations and Spiking

The most fruitful approach for the discussion of maser and laser1 behavior has been through rate equations describing the time rates of change of the atomic populations and the photon numbers of the electromagnetic field. Bloembergen 2 introduced rate equations for the populations in a paramagnetic maser and based his discussion on the steadystate solutions without explicitly considering the photon field. On the other hand, Shimoda, Takahasi, and Townes 3 have considered the photon rate equations and on this basis have given a theory of maser amplification without explicitly considering the atomic populations. Statz and De Mars 4 have shown that the transient behavior of masers depends upon coupled rate equations for both the populations and the photons. A number of authors have rederived these equations and discussed their applications to various maser systems. Considerable attention has been given to the question of whether these equations have periodic (undamped) solutions. It has been shown by Makhov 5 and by Sinnett 6 that the small-signal solutions are always damped, and it has been pre1505