Incoherent and coherent tune shifts

The longitudinal and transverse microwave instabilities are the two important limiting factors for the performance of an accelerator. Comparing with the fairly unified approach for the longitudinal microwave instabilities, different approaches have been used to define the transverse microwave instabilities. One reason of this is related to the role played by the space charge incoherent and coherent tune shifts. In this article, the transverse microwave instabilities will be discussed by defining separately the roles of the space charge incoherent and coherent tunes, which are represented by the space charge transverse impedances. Preliminary results for the AGS as proton driver are presented by using this approach