On Maser Rate Equations and Transient Oscillations

Masers exhibit interesting transient behavior that cannot be completely understood on the basis of the rate equations. The use of the rate equations in most transient analyses is usually justified on a more or less intuitive basis and the implied assumptions are not always clear. In this paper, the macroscopic maser rate equations are derived systematically from the Boltzmann equation for the density matrix of the atomic systems and Maxwell's equations for the radiation fields. When the coherence linewidth (T2−1) of the atomic systems is much larger than the cavity linewidth and the natural linewidth (T1−1) of the atomic emission, and with a WKB approximation, in the lowest order of approximation one obtains the two widely used, coupled first-order nonlinear rate equations of Statz and deMars. On the other hand, if the cavity linewidth is much larger than the atomic linewidths (T1−1 and T2−1), one can use the so-called ``reaction-field principle'' of Anderson and obtain, again, two coupled first-order rate equations; however, only one of the equations is nonlinear. The ranges of validity of both approaches are discussed in some detail.