Power dependence of distributed cavity phase-induced frequency biases in atomic fountain frequency standards

We discuss the implications of using high-power microwave tests in a fountain frequency standard to measure the frequency bias resulting from distributed cavity-phase shifts. We develop a theory which shows that the frequency bias from distributed cavity phase depends on the amplitude of the microwave field within the cavity. The dependence leads to the conclusion that the frequency bias associated with the distributed cavity phase is typically both misestimated and counted twice within the error budget of fountain frequency standards.