A Rubidium Clock Model

Abstract : This report develops a signal model for the rubidium (Rb) clock. This model combines feedback anlaysis of the clock's servo-control circuitry with the atomic physics required to describe the processes occurring within the Rb absorption cell. The model permits clock performance, in terms of Allan variance, to be predicted from a number of electronic and physical parameters. While building on prior studies of Rb standards, the model incorporates a number of features which make it distinctive. All previous models of the Rb clock were limited to an analysis of the clock's short term performance, Allan variance averaging times of less than 10,000 sec. However, by explicitly including the effects of discharge lamp intensity fluctuations, which are transformed into output frequency variations via the light shift effect, clock performance can be predicted for averaging times greater than 10,000 sec. Furthermore, the model is the first which incorporates the influence of an optically thick Rb vapor along with the diffusion of optically pumped atoms to the walls of the absorption cell into the calculation of clock performance. In addition, the model has been developed in sufficient generality to permit its application to diode laser pumped clocks using other alkali metals.