Dimensional Sensitivity of End-to-End Phase Difference in Ring Terminated Ramsey Cavities

A transmission line analysis is reported of a long Ramsey cavity for a primary Cesium beam frequency standard, terminated at the extremities with two waveguide rings for distributed phase shift minimization. The purpose of this effort is to understand the effect of the rings on end-to-end phase shift. Contributions to the latter from asymmetries in the Ramsey cavity long arms, in the similarity of the rings, and in the two coupling junctions between rings and Ramsey cavity, are separately analyzed as a function of frequency. It is shown that this third asymmetry source may be a cause of phase shift instability because of its linear dependence on frequency. The slope of this sensitivity to operating frequency is reduced by almost an order of magnitude if the rings are designed to be antiresonant instead of resonant.