Controlled Longitudinal Emittance Blow-Up for High Intensity Beams in the CERN SPS
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D. Quartullo, H. Damerau, I. Karpov, G. Papotti, E.N. Shaposhnikova, C. Zisou
CERN, Geneva 23, Switzerland
D. Quartullo
Sapienza University of Rome, Rome, Italy
Controlled longitudinal emittance blow-up will be required to longitudinally stabilize the beams for the High-Luminosity LHC in the SPS. Bandwidth-limited noise is injected at synchrotron frequency sidebands of the RF voltage of the main accelerating system through the beam phase loop. The setup of the blow-up parameters is complicated by bunch-by-bunch differences in their phase, shape, and intensity, as well as by the interplay with the fourth harmonic Landau RF system and transient beam loading in the main RF system. During previous runs, an optimization of the blow-up had to be repeated manually at every intensity step up, requiring hours of precious machine time. With the higher beam intensity, the difficulties will be exacerbated, with bunch-by-bunch differences becoming even more important. We look at the extent of the impact of intensity effects on the controlled longitudinal blow-up by means of macro-particle tracking, as well as analytical calculations, and we derive criteria for quantifying its effectiveness. These studies are relevant to identify the parameters and observables which become key to the operational setup and exploitation of the blow-up.
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New Analytical Criteria for Loss of Landau Damping in Longitudinal Plane
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I. Karpov, T. Argyropoulos, E.N. Shaposhnikova
CERN, Geneva, Switzerland
S. Nese
University of Bergen, Bergen, Norway
Landau damping is a very important stabilization mechanism of beams in circular hadron accelerators. In the longitudinal plane, Landau damping is lost when the coherent mode is outside of the incoherent synchrotron frequency spread. In this paper, the threshold for loss of Landau damping (LLD) for constant inductive impedance ImZ/k is derived using the Lebedev matrix equation (1968). The results are confirmed by direct numerical solutions of the Lebedev equation and using the Oide-Yokoya method (1990). For more realistic impedance models of the ring, new definitions of an effective impedance and the corresponding cutoff frequency are introduced which allow using the same analytic expression for the LLD threshold. We also demonstrate that this threshold is significantly overestimated by the Sacherer formalism based on the previous definition of an effective impedance using the eigenfunctions of the coherent modes.
