Frequency Resolved Measurement of Longitudinal Impedances Using Transient Beam Diagnostics

In this paper we present several techniques for characterizing longitudinal impedances based on transient measurements of the growth rates and tune shifts of unstable coupled-bunch modes. These techniques are applicable to measurement of both fundamental and higher-order mode impedances and allow characterization of shunt impedances and quality factors of the HOMs. Methods presented here are complementary to lab bench measurements of RF cavities, in that the beam based measurements directly sense the physical impedance in the installed configuration. In contrast to a single-bunch integrated impedance measurement these techniques resolve the impedances in the frequency domain. These methods allow determination of the impedance's unaliased frequency by analyzing synchronous phase transients. Experimental results from ALS and BESSY-II are presented showing the use of these techniques to measure complex impedances.