  We evaluate the distributed cavity phase and microwave lensing frequency
shifts, which were the two largest sources of uncertainty for the NPL-CsF2
cesium 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 distributed cavity phase uncertainty to $1.1 \times 10^{-16}$. 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 $6.2 \times 10^{-17}$.
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 $2.3 \times
10^{-16}$, nearly a factor of two lower than its most recent complete
evaluation.
