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

TL;DR

This study investigates longitudinal mode-coupling instabilities in CERN's SPS, identifying mechanisms, validating models with simulations and measurements, and assessing the impact of impedance reduction on beam stability.

Contribution

It demonstrates the existence of both radial and azimuthal mode-coupling instabilities in the SPS using the Oide-Yokoya approach and realistic impedance models, and evaluates effects of impedance reduction campaigns.

Findings

Radial mode-coupling instability caused emittance blow-up before impedance reduction.

Both instabilities are as strong as each other under certain conditions.

Impedance reduction improved beam stability in specific configurations.

Abstract

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 blow-up 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.