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Title: Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture

Abstract

A tracking study was done of the effects of a tune modulation, due to synchrotron oscillations and the tune dependence on momentum (chromaticity), on the dynamic aperture. The studies were done using several RHIC lattices and tracking runs of about 1 {times} 10{sup 6} turns. The dynamic aperture was found to decrease roughly linearly with the amplitude of the tune modulation and may be represented by A = A{sub o}(l--10 {Delta}{nu}) where A{sub o} is the dynamic aperture for {Delta}{nu} = 0, and {Delta}{nu} is the tune modulation amplitude. In Eq. (1), the range of {Delta}{nu} is such that lower order non-linear resonances, like the 1/3 and 1/4 resonance axe not crossed because of the tune modulation. Three different cases were studied, corresponding to RHIC lattices with different {beta}*, and with different synchrotron oscillation amplitudes. In each case, the tune modulation amplitude was varied by changing the chromaticity. In each case, roughly the same result, Eq. (1), was found. The result found here for the effect of a tune modulation due to chromaticity may be compared with the result found for the effect of a tune modulation due to a gradient ripple in the quadrupoles, which was A = A{submore » o}(l--42 {Delta}{nu}). The effect of a {Delta}{nu} due to a gradient ripple appears to be about 4 times stronger than the effect of a {Delta}{nu} due to chromaticity and synchrotron oscillations.« less

Authors:
Publication Date:
Research Org.:
Brookhaven National Lab., Upton, NY (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10142134
Report Number(s):
BNL-60214; AD/RHIC-128
ON: DE94009935; TRN: 94:007603
DOE Contract Number:  
AC02-76CH00016
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 1 Mar 1994
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BEAM OPTICS; TUNING; BROOKHAVEN RHIC; SYNCHROTRON OSCILLATIONS; BEAM DYNAMICS; APERTURES; CHROMATIC ABERRATIONS; RF SYSTEMS; 430200; BEAM DYNAMICS, FIELD CALCULATIONS, AND ION OPTICS

Citation Formats

Parzen, G. Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture. United States: N. p., 1994. Web. doi:10.2172/10142134.
Parzen, G. Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture. United States. doi:10.2172/10142134.
Parzen, G. Tue . "Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture". United States. doi:10.2172/10142134. https://www.osti.gov/servlets/purl/10142134.
@article{osti_10142134,
title = {Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture},
author = {Parzen, G.},
abstractNote = {A tracking study was done of the effects of a tune modulation, due to synchrotron oscillations and the tune dependence on momentum (chromaticity), on the dynamic aperture. The studies were done using several RHIC lattices and tracking runs of about 1 {times} 10{sup 6} turns. The dynamic aperture was found to decrease roughly linearly with the amplitude of the tune modulation and may be represented by A = A{sub o}(l--10 {Delta}{nu}) where A{sub o} is the dynamic aperture for {Delta}{nu} = 0, and {Delta}{nu} is the tune modulation amplitude. In Eq. (1), the range of {Delta}{nu} is such that lower order non-linear resonances, like the 1/3 and 1/4 resonance axe not crossed because of the tune modulation. Three different cases were studied, corresponding to RHIC lattices with different {beta}*, and with different synchrotron oscillation amplitudes. In each case, the tune modulation amplitude was varied by changing the chromaticity. In each case, roughly the same result, Eq. (1), was found. The result found here for the effect of a tune modulation due to chromaticity may be compared with the result found for the effect of a tune modulation due to a gradient ripple in the quadrupoles, which was A = A{sub o}(l--42 {Delta}{nu}). The effect of a {Delta}{nu} due to a gradient ripple appears to be about 4 times stronger than the effect of a {Delta}{nu} due to chromaticity and synchrotron oscillations.},
doi = {10.2172/10142134},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1994},
month = {3}
}