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

Abstract

We evaluate the distributed cavity phase and microwave lensing frequency\nshifts, which were the two largest sources of uncertainty for the NPL-CsF2\ncesium fountain clock. We report measurements that confirm a detailed\ntheoretical model of the microwave cavity fields and the frequency shifts of\nthe clock that they produce. The model and measurements significantly reduce\nthe distributed cavity phase uncertainty to $1.1 \\times 10^{-16}$. We derive\nthe microwave lensing frequency shift for a cylindrical cavity with circular\napertures. An analytic result with reasonable approximations is given, in\naddition to a full calculation that indicates a shift of $6.2 \\times 10^{-17}$.\nThe measurements and theoretical models we report, along with improved\nevaluations of collisional and microwave leakage induced frequency shifts,\nreduce the frequency uncertainty of the NPL-CsF2 standard to $2.3 \\times\n10^{-16}$, nearly a factor of two lower than its most recent complete\nevaluation.\n