Improved accuracy of the NPL-CsF2 primary frequency standard: Evaluation of distributed cavity phase and microwave lensing frequency shifts

We evaluate the distributed cavity phase (DCP) and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 caesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the DCP uncertainty to 1.1 × 10^-16. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of 6.2 × 10^-17. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to 2.3 × 10^-16, nearly a factor of two lower than its most recent complete evaluation.