Effect of Random Fluctuations on Synchrotron Phase Motion

Previous treatment of this subject has been given by Hereward and Johnsen. In this note a unified presentation is made of the growth of longitudinal phase area occupied by the beam due to random fluctuations of the magnetic field, radio frequency, and cavity voltage. The description is characterized by a linear treatment of the synchrotron motion, introduction of an envelope function similar to that used in betatron motion, and the use of Nyquist´s theorem to obtain power spectra. Application is made to the NAL booster.