Theory of the beta function shift due to linear coupling

Technical Report · Mon Jul 01 00:00:00 EDT 1991

DOI:https://doi.org/10.2172/5561980· OSTI ID:5561980

Parzen, G

This paper presents analytical perturbation theory results for {beta}{sub 1}, {beta}{sub 2}, the beta functions in the presence of linear coupling. It is a continuation of a previous paper that gave analytical perturbation theory results for the tune {nu}{sub 1}, {nu}{sub 2} in the presence of linear coupling. The results for {beta}{sub 1}{beta}{sub 2} hold when {nu}{sub x}, {nu}{sub y} are close to the resonance line {nu}{sub x} {minus} {nu}{sub y} = p. The shift in beta functions is then linear in the skew quadrupole field given by a{sub 1} (s). When {nu}{sub x}{nu}{sub y} are far enough from the {nu}{sub x} {minus} {nu}{sub y} = p resonance, then the shift in the beta function becomes quadratic in the skew quadrupole field. The analytical results show that the important harmonics in the skew quadrupole fields for producing large beta functions shifts are the harmonics near {nu}{sub x} + {nu}{sub y}. The harmonics near {nu}{sub x} + {nu}{sub y} are also the important harmonics for the higher order tune. It is also shown that the beta function shift and the higher order tune shift have the same driving terms, thus, one may except that an a{sub 1} correction system that corrects the higher order tune shift will also correct the beta function shift. 5 refs.

• Research Organization: Brookhaven National Lab., Upton, NY (United States)
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5561980
• Report Number(s): BNL-46459; AD/RHIC--102; ON: DE91016395
• Country of Publication: United States
• Language: English

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