Synchrotron Sidebands of a Linear Differential Coupling Resonance

Sidebands of a linear differential coupling resonance are observed in the tune survey of the SPring-8 storage ring. The vertical beam size and the Touschek beam lifetime blow up at a distance by synchrotron tune from the linear differential resonance. The synchrotron sidebands of a linear betatron coupling resonance are excited by the vertical dispersion at sextupole magnets. Although the vertical dispersion of the SPring-8 storage ring is well reduced to a small value, it still generates the sidebands of the coupling resonance in virtue of the strong sextupole magnets. By means of the tracking simulation based on the ring model obtained by the response matrix measurement, we confirm the existence of the synchrotron sidebands of a linear differential coupling resonance. In order to incorporate synchrotron motion, the full six-dimensional code is essential in the simulation.