Closed Form Formulas of the Indirect Space Charge Wake Function for Axisymmetric Structures
65
N. Mounet, E. Dadiani, E. Métral, C. Zannini
CERN, Geneva, Switzerland
A. Rahemtulla
EPFL, Lausanne, Switzerland
Indirect space charge contributes significantly to the impedance of non ultrarelativistic machines such as the LEIR, PSB and PS, at CERN. While general expressions exist in frequency domain for the beam coupling impedance, the time domain wake function is typically obtained numerically, thanks to an inverse Fourier transform. An analytical expression for the indirect space charge wake function, including the time dependence as a function of particle velocity, is nevertheless highly desirable to improve the accuracy of time domain beam dynamics simulations of coherent instabilities. In this work, a general formula for the indirect space charge wake function is derived from the residue theorem. Moreover, simple approximated expressions reproducing the time and velocity dependence are also provided, which can even be corrected to recover an exact formula, thanks to a numerical factor computed once for all. The expressions obtained are successfully benchmarked with a purely numerical approach based on the Fourier transform.
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Understanding of the CERN-SPS Horizontal Instability with Multiple Bunches
77
C. Zannini, H. Bartosik, M. Carlà, K.S.B. Li, E. Métral, G. Rumolo, B. Salvant
CERN, Geneva, Switzerland
L.R. Carver
ESRF, Grenoble, France
M. Schenk
EPFL, Lausanne, Switzerland
At the end of 2018, an instability with multiple bunches has been consistently observed during high intensity studies at the CERN-SPS. This instability could be a significant limitation to achieve the bunch intensity expected after the LHC Injector Upgrade (LIU). Therefore, a deep understanding of the phenomena is essential to identify the best mitigation strategy. Extensive simulation studies have been performed to explore the consistency of the current SPS model, give a possible interpretation of the instability mechanism and outline some possible cures.
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