Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture
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.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 10142134
- Report Number(s):
- BNL-60214; AD/RHIC-128; ON: DE94009935; TRN: 94:007603
- Resource Relation:
- Other Information: PBD: 1 Mar 1994
- Country of Publication:
- United States
- Language:
- English
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Tune modulation due to synchrotron oscillations and chromaticity, and the dynamic aperture
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