Further Aspects of the Theory of the Maser

The theory of the molecular transitions which are induced by the microwave field in a maser and the effects of various design parameters are examined in detail. It is shown that the theoretical minimum detectable beam intensity when the maser is used as a spectrometer for the 3-3 line of ammonia is about ${10}^9$ molecules/sec under typical experimental conditions. Various systematic frequency shifts and random frequency fluctuations of the maser oscillator are discussed and evaluated. The most prominent of the former are the "frequency-pulling" effect, which arises from detuning of the cavity, and the Doppler shift due to the asymmetrical coupling of the beam with the two traveling wave components of the standing waves which are set up in the cavity. These two effects may produce fractional shifts as large as one part in ${10}^9$. If adequate precautions are taken, however, they can be reduced to one part in ${10}^{10}$ or possibly less. The random fluctuations are shown to be of the order of one part in ${10}^{13}$ under typical operating conditions. For molecular beams in which the electric-dipole transition is used, the $T{M}_{010}$ mode is usually the most suitable for the maser; while in atomic beams in which magnetic transitions are utilized, the $T{E}_{011}$ mode is to be preferred.