Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials

Lindberg, Ryan R.

doi:10.1103/PhysRevAccelBeams.21.124402

Title: Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials

Journal Article · 13 December 2018 · Physical Review Accelerators and Beams

DOI: https://doi.org/10.1103/PhysRevAccelBeams.21.124402 · OSTI ID:1485742

Lindberg, Ryan R. ^[1]

Argonne National Lab. (ANL), Argonne, IL (United States)

Here, we present a theory of coupled-bunch longitudinal instabilities that is based on the coupled set of Vlasov equations governing the particle distribution function, and can be applied to arbitrary longitudinal potentials. We find that the coupled-bunch growth rate is given by a dispersion relation that is parametrized by the eigenvalues of the linear (harmonic) coupled-bunch matrix problem. Our theory therefore treats the wakefield-driven source of the instability and the effect of Landau damping together and on equal footing, and also indicates that the stabilizing effects of Landau damping can approximately be compared to the instability growth rates in a harmonic potential that has the same bunch length. We then apply the theory to a weakly nonlinear oscillator and to a quartic potential that is relevant for ultra-low emittance storage rings that employ bunch-lengthening systems. In the latter case we find that the theory compares quite favorably with particle tracking simulations for the parameters of the planned upgrade of the Advanced Photon Source.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1485742

Alternate ID(s):: OSTI ID: 1491846

Journal Information:: Physical Review Accelerators and Beams, Vol. 21, Issue 12; ISSN 2469-9888

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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