The effect of moderate space charge on the transverse Schottky spectrum of a coasting beam is studied using measurements and simulations together with an analytic model. The measurements of transverse Schottky bands from heavy ion beams were performed in the SIS-18 synchrotron at GSI. In addition, we analyze the noise spectrum from a particle tracking code with self-consistent space charge. Both results are compared to an analytic model that is based on the dispersion relation for linear space charge forces and chromatic betatron tune spreads. The analytic model reproduces the characteristic deformation of Schottky bands with increasing space charge, observed in both measurement and simulation.
Transverse Schottky spectra and beam transfer functions (BTFs) of coasting ion beams were measured in the heavy ion synchrotron SIS-18 in order to study the impact of space charge on the transverse beam dynamics. The particle number in the beam was varied to investigate the intensity dependence of the space-charge effect. No cooling was applied to the beams throughout the experiment. The expected deformation of the Schottky spectra and BTFs is observed. An analytic model with linear space charge is employed to describe the deformed Schottky and BTF signals. In this model, the incoherent space-charge force and the coherent forces due to impedances are treated separately. Using the model, the space-charge induced tune shift is evaluated both from the position and the form of the signals. The data are well described by the model, only in the high-intensity BTFs deviations are observed. The stability diagrams are shifted according to the space-charge parameter obtained from the BTFs. In addition, the tune shift is estimated by virtue of measured beam profiles and particle numbers. The estimated tune shift is of the same order of magnitude but smaller than the measured one. Possible explanations for deviations between the measurements, the model, and the estimation are discussed.
The crab cavities are a critical component in the high luminosity LHC upgrade project to compensate the luminosity loss from large crossing angle collision. However, these crab cavities will not be perfect in the real accelerator. In this paper, we studied the effects of crab cavity imperfections on colliding beam luminosity lifetime degradation for the LHC upgrade through detailed numerical simulations. Our simulation results suggest that the white noise jitter in the crab cavity RF phase and voltage rms amplitudes should be kept below a few 10 −5 for a good luminosity lifetime, while with frequency-dependent jitter, the amplitudes should be kept below a few 10 −4 for a good lifetime. The RF multipole errors in the current crab cavity designs are small enough and would not cause extra luminosity degradation.
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