Analytic studies of the long range beam-beam tune shifts and chromaticities
A formula is derived, which allows efficient analytical evaluation of the long range beam-beam tune shifts and chromaticities with amplitude. It assumes that the beams are infinitely short, oppositely charged, and with Gaussian transversal profile. The formula employs an infinite sum with favorable convergence rates, making it well suited especially for the long range case. For a deeper understanding of the beam-beam effects, the structure of the formula was analyzed. It is shown that the tune shifts and chromaticities change sign at certain values of the separation and/or amplitude, and folds in the footprints are predicted. Some special cases were studied in more detail. Applications to the Tevatron are presented, including some proposed compensation schemes.
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research (ER) (US)
- DOE Contract Number:
- AC-2-76CH03000
- OSTI ID:
- 794463
- Report Number(s):
- FERMILAB-TM-2171; TRN: US0203354
- Resource Relation:
- Other Information: PBD: 29 May 2002
- Country of Publication:
- United States
- Language:
- English
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