Corrections for Second-Order Doppler Shift and Cavity Phase Error in Cesium Atomic Beam Frequency Standards

From the measured static resonance curve of a cesium beam tube, corrections can be derived for second-order Doppler shift and cavity phase error. For the calculation Fourier transforms are used, which also produce the velocity distribution of the atoms. Data are given for the distortion of the resonance curve from which the corrections can be derived applicable in the case of very slow square wave frequency modulation. A method is also given for calculating corrections for faster modulation rates where the time-of-flight effects are no longer negligible. However, quadrature components will now occur in the beam signal, and their effect on the clock servo is discussed.