Microwave cavity design for an optically-pumped rubidium atomic beam clock

We design a microwave cavity for our developing compact optically-pumped rubidium beam frequency standard. For clock transition of ⁸⁷Rb (F=2, m_F=0 to F=1, m_F=0), the central frequency is 6.8347GHz. The cavity made of WR90 waveguide in previous cesium beam clocks no longer works. In our design, we follow the method of Ramsey-type cavity in cesium beam clocks but change the cross section of waveguide. Some related modifications have to be made such as the lengths of waveguide. Unfortunately one is not likely to obtain analytical results on these values. Finite element analysis software helps to numerically solve the electromagnetic field based on arbitrary boundary conditions. Therefore, the resonant frequency and other characters of a cavity are computable when its dimensions are given. As a result, suitable dimensions can be determined to get a resonant frequency of 6.8347GHz. Considering other effects, e.g. end-to-end phase difference, more optimizations and requirements are proposed.