Longitudinal mode-coupling instabilities of proton bunches in the CERN Super Proton Synchrotron

In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In particular, we see that the uncontrolled longitudinal emittance blowup of single bunches observed before the recent impedance reduction campaign (2018-2021) is due to the radial mode-coupling instability. Unexpectedly, this instability is as strong as the azimuthal mode-coupling instability, which is possible in the SPS for other combinations of bunch length and intensity. We also demonstrate the significant role of rf nonlinearity and potential-well distortion in determining these instability thresholds. Finally, we discuss the effect of the recent impedance reduction campaign on beam stability in single-and double-rf configurations.

Automated summary

In this paper, the authors investigate the single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). The study demonstrates the existence of both radial and azimuthal mode-coupling instabilities in the SPS using the Oide-Yokoya approach and realistic longitudinal impedance model. The results align with macroparticle simulations and beam measurements, revealing the significant contribution of rf nonlinearity and potential-well distortion to these instability thresholds. The effect of the recent impedance reduction campaign on the stability of single- and double-rf configurations is also discussed.