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Description
Reserving certain chromaticity in a storage ring have a damping mechanism to suppress the transverse coupled bunch instability. The suppression comes from the head-tail effect that makes the betatron oscillation motion of particles relates with the longitudinal state. Therefore, the longitudinal impedance intuitively have a significant impact on the chromaticity effect. We start with the exiting theories for computing the transverse coupled-bunch instability
(TCBI) growth rates with chromaticity, taking the longitudinal broadband impedance into the consideration, and further extend the theory to systematically investigate the impact of longitudinal impedance on the stabilizing effect from the chromaticity. In particular, we investigate the underlying mechanism of the longitudinal impedance’s effect through a series of calculations and simulations.
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