The Effects of Phase Advances between Interaction Points Page: 4 of 10
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chromaticities change in the scan because of the betatron phase changes between IRs. The phase shifting
matrices themselves have no contributions to chromaticities.
2.3 Lattice and beam parameters
Table 1-3 list the tunes, chromaticities, ) at IPs, and phase advances betwen IPs for all the lattices without
phase advance adjustment between IPs.
DAs are calculated in 106 turn trackings. The tunes of zero-amplitude particles are set to (28.675, 29.68)
for proton run and (31.23 , 32.22) for Au-Au run . These tunes are with beam-beam interaction at IP6
and IP8. The first order chromaticities are set to (1,1). The initial relative momentum deviation is 0.0005
for protons and 0.0017 for Au ions. The DA for Au-Au run is after RF re-bucketing. The proton bunch
intensities for the 2011 p-p run lattices is 1.5 x 1011. The Au ion bunch intensities for the 2010 Au-Au run
lattices is 1.0 x 109. The proton bunch intensity for the head-on beam-beam compensation test is 2.5 x 1011.
Half beam-beam compensation is included in this lattice.
3 Results
3.1 2011 p-p run lattices
Figures 1-3 and Figure 4-6 show the calculated horizontal half integer resonance term h20001 and vertical
half integer resonance term h00201 from the triplets in IR6 and IR, second chromaticities and DAs for the
BLue ring and Yellow ring lattices. The axis A4,,y are the phase advances between IP6 and IP8.
For Blue ring, the minimum of h20001 is around At4 = 10.67 and the minimum of h20001 is around
O4)y =8.77. The minimum of horizontal second order chromaticity occurs around At4 = 10.47 and At,
10.87. The minimum of vertical second order chromaticity occurs around At4 = 8.5r and At4 = 9.07.
For Yellow ring, the minimum of h20001 is around At = 8.77 and the minimum of h20001 is around
AOry 10.67. The minimum of horizontal second order chromaticity occurs around A)= 8.5r. The
minimum of vertical second order chromaticity occurs around Ay 11.07 and 11.57.
Figure 3 and Figure 6 show the DAs for the Blue and Yellow rings in the phase advance scan. For the
Blue ring, the maximum DA is around (At = 10.657, Ay 8.57). For the Yellow ring, the maximum
DA is around (At= 8.87, Ay 10.97).
The phase advances without phase adjustment between IP6 and IP8 are (10.657, 8.647) for the Blue
ring and (8.327, 11.037) for the Yellow ring. Therefore, the phase advances between IP6 and IP8 without
phase adjustment are in the good DA region for Blue ring. For the Yellow ring, the default phase advances
between IP6 and IP8 are not in the good DA region.
3.2 2010 Au-Au run lattices
Figures 7-9 and Figures 10-12 plot the half integer resonance terms, second order chromaticities and DAs
for the Blue and Yellow ring lattices for 2010 Au-Au run lattices.
For the Blue ring, the minimum of horizontal and vertical half integer resonance driving terms occur at
A0)= 10.6 and Ay 9.75. The minimum of horizontal and vertical second order chromaticities happen
at A)= 11.55 and Ay 9.5. In this scan, the DA is mostly sensitive to the horizontal phase advance
between IP6 and IP8. The good region of DA is around (A04 = 10.67 or 11.07x, Ay (9.4 -9.8)x).
The Yellow ring, the minimum of horizontal and vertical half integer resonance driving terms happen
at A)= 8.8 and A% =z 11.65. The minimum of horizontal and vertical second order chromaticities
happen at At = 9.15 and Ay 11.45. The good DA region is around (At)= (9.2 - 9.5)r and
O4)y =(11.5 -11.7) 7).
The phase advances without phase adjustment between IP6 and IP8 are (11.41x, 9.44x) for the Blue ring
and (9.047, 11.777) for the Yellow ring. The phase advances between IP6 and IP8 without phase adjustment
are not in good DA region for both rings.
3.3 Beam-beam compensation lattice
Figures 13 and 14 plot second order chromaticities and DA for the proposed head-on beam-beam compen-
sation Blue ring lattice versus the phase advances between IP8 and the center of e-lens. In these plots, the
phase advances At, and Ay are between IP8 and the center of the e-lens.3
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Y., Luo; Tepikian, S.; Fischer, W.; Gu, X. & Trbojevic, D. The Effects of Phase Advances between Interaction Points, report, October 1, 2011; United States. (https://digital.library.unt.edu/ark:/67531/metadc844587/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.