Theories derived from Haissinski equation and their applications to electron storage rings

Journal Article · 11 March 2024 · Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment

DOI: https://doi.org/10.1016/j.nima.2024.169243 · OSTI ID:2405142

Zhou, Demin  ^[1]; Ishibashi, Takuya ^[2]; Mitsuka, Gaku ^[2]; Tobiyama, Makoto ^[2]; Bane, Karl ^[3]; Zhang, Linhao  ^[4]

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1. Accelerator Laboratory, KEK, Tsukuba (Japan); The Graduate University for Advanced Studies, SOKENDAI, Hayama (Japan); SLAC
2. Accelerator Laboratory, KEK, Tsukuba (Japan); The Graduate University for Advanced Studies, SOKENDAI, Hayama (Japan)
3. SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
4. University of Science and Technology of China, Hefei (China)

As a stationary solution of the Vlasov–Fokker–Planck equation, the Haissinski equation predicts the equilibrium line density of a bunch that circulates in a storage ring for a given wake function. The research in this paper shows that some equations regarding the centroid shift of the bunch, the peak position of the bunch profile, bunch length, and the impedance from the bunch profile can be derived from the Haissinski equation in a self-consistent manner. Specifically, a generalized quadratic equation for potential-well bunch lengthening is derived to accommodate any arbitrary impedance model (that is, the impedance spectrum under consideration can take any form). This expands upon Zotter's cubic equation, which is primarily applicable to inductive impedance. The equations derived in this paper are tested using computed impedance models for some electron storage rings, showing machine-dependent properties of impedance effects. We conclude that these equations can be employed in electron storage rings to effectively bridge the gap between impedance computations and beam-based measurements.

• Research Organization: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
• Sponsoring Organization: USDOE Offfice of Science (SC)
• Grant/Contract Number: AC02-76SF00515
• OSTI ID: 2405142
• Journal Information: Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, Journal Name: Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment Vol. 1063; ISSN 0168-9002
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English