Abstract
© 2018 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. We introduce a perturbation-theory, mode-analysis method for longitudinal multibunch instabilities driven by the higher harmonic cavity (HHC) fundamental mode. The method, based on the exact solution of the unperturbed particle motion in the rf bucket and suitable for modeling the effect of cavities with general settings, is applied to study the feasibility of reutilizing the existing Advanced Light Source (ALS) HHCs in the ALS Upgrade (ALS-U). We find that with ALS cavities the ALS-U would be susceptible to a fast =1 mode instability. Interestingly, the instability is driven by the imaginary rather than the real part of the cavity fundamental-mode impedance.
Highlights
The ALS Upgrade (ALS-U) is the Advanced Light Source (ALS) upgrade to a multibend achromat lattice, diffraction-limited light source [1]
While the upgrade entails the replacement of most components, for obvious reasons it is desirable to recycle as much as possible of the existing infrastructure, including the rf systems and in particular the passive normalconducting higher-harmonic cavities (HHCs)
A larger shunt impedance is accommodated by tuning the HHCs further away from the 3rd-harmonic of the rf generator frequency, and while this comes with some advantages it has the potential to drive the longitudinal l 1⁄4 1 coupled-bunch instability mode
Summary
The ALS-U is the Advanced Light Source (ALS) upgrade to a multibend achromat lattice, diffraction-limited light source [1]. As a result of a lower main-cavity voltage requirement, in the ALS-U the optimum HHC shunt impedance is only 1.35 MΩ. A larger shunt impedance is accommodated by tuning the HHCs further away from the 3rd-harmonic of the rf generator frequency, and while this comes with some advantages (lower dissipated power and Robinson instability growth rate) it has the potential to drive the longitudinal l 1⁄4 1 coupled-bunch instability mode. The study of this mode is the main topic of the paper. The Appendices report formulas for beam loading (A), bunch equilibrium and optimum HHC settings (B), details on the numerical method (C), effective impedance for the modes of interest (D), and useful formulas for motion in a purely quartic potential (E)
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