Calculation of Impedance from Multibunch Synchronous Phases: Theory and Experimental Results

A novel beam-based method for measuring the longitudi-nal impedance spectrum is demonstrated using experimen-tal data from the PEP-II High Energy Ring (HER). The method uses a digital longitudinal feedback system from which the charge and synchronous phase are measured for every bucket. Calculation of the transfer function from fill shape to synchronous phase yields the impedance seen by the beam at revolution harmonics. The experimentally-derived longitudinal impedance function and lab measure-ments of the impedance of parked RF cavities are com-pared to suggest a mechanism for the occasional instability of low-order coupled bunch modes observed in the HER during commissioning in October 1997.