Characterization of atomic clock anomalies in the dynamic Allan variance domain

The stability of an atomic clock changes with time due to several factors, such as mechanical vibrations, temperature, and radiations. To represent this time variation, we introduced the dynamic Allan variance (DAVAR). The DAVAR is a surface function of time and the observation interval. This surface is stationary with time when the clock follows the specifications, whereas it changes with time when an anomaly occurs. We derive the exact analytic DAVAR for a series of common anomalies, namely, a sinusoid, a phase jump, and a frequency jump. These anomalies are of fundamental interest in space clocks. Our results establish a clear connection between the nature and properties of the anomalies and the corresponding shape of the DAVAR.