Tune Modulation Due to Synchrotron Oscillations and Chromaticity, and the Dynamic Aperture

Technical Report · Tue Mar 01 00:00:00 EST 1994

DOI:https://doi.org/10.2172/1119382· OSTI ID:1119382

Parzen, George ^[1]

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1. Brookhaven National Lab. (BNL), Upton, NY (United States)

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 aper­ ture. The studies were done using several RHIC lattices and tracking runs of about 1 x 10⁶ turns. The dynamic aperture was found to decrease roughly linearly with the amplitude of the tune modulation and may be represented by A = A₀ (1-10 Δv) where A₀ is the dynamic aperture for Δv = 0, and Δv is the tune modulation amplitude. In Eq. (1), the range of Δv is such that lower order non-linear resonances, like the 1/3 and 1/4 resonance are not crossed because of the tune modulation. Three different cases were studied, corresponding to RHIC lattices with different β*, 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 A₀ (1-42 Δv). The effect of a Δv due to a gradient ripple appears to be about 4 times stronger than the effect of a Δv due to chromaticity and synchrotron oscillations.

• Research Organization: Brookhaven National Lab. (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-98CH10886
• OSTI ID: 1119382
• Report Number(s): BNL-102040-2013-IR
• Country of Publication: United States
• Language: English

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