Wide range tune scan simulations for RHIC Page: 3 of 8
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Table 1: Optics and beam parameters of the three base lattices
quantity
Energy
Lorentz factor
nominal working point
j* at IP6 and IP8
j* at other IPs
first order chromaticities
second order chromaticities
third order chromaticities
rms normalized transverse emittance
rms bunch length
RF bucket height
particle's initial (dp/pg) in simulation
beam-beam included in tracking
bunch intensity
beam-beam parameter (total, 2 IPs)proton run lattice
2011 p-p lattice
255 GeV
271
(28.695, 29.685)
0.65 m
7.5 m
( 1,1 )
(2500, 4650)
(0.71e6, 0.55e6)
2.5 pm
2.5 ns
1.1 x 10-3
0.5 x 10-s
Yes
1.6 x 1011
-0.016ion run lattices
IBS-suppression lattice standard lattice100 GeV
107
(31.23, 32.22)
0.7 m
5m
(1,1)
(-4100,-1700)
(-0.7e6, -0.2e6)
2.5 pm
0.8 ns
1.9 x 10-s
1.5 x 10-s
No100 GeV
107
(28.23, 29.22)
0.7 m
5m
(1,1)
(2600, 177)
(-0.5e6, -0.2e6)
2.5 pm
0.8 ns
1.9 x 10-s
1.5 x 10-s
NoThe linear motion is unstable when the fractional tunes approach 0.0, 1.0, and 0.5, which is due to
the large -beat introduced by the tune matching using the arc main quadrupoles only. To investigate the
dynamic apertures in those regions, dedicated lattices would be required instead of this simplified approach.
Including beam-beam interactions, the tunes of the zero amplitude particles are shifted down by the
beam-beam parameter [3]. If the tunes without beam-beam are above a resonance line and the distance with
respect to this resonance is less than the beam-beam parameter, the beam-beam tune shift will push some
particles across this resonance line leading to a possible reduction of the dynamic aperture. On the other
hand, if the tune without beam-beam is below a resonance line, particles will be pushed away from this
resonance by the beam-beam tune shift and the dynamic aperture may not be affected by this resonance.
From Fig. 2, the current nominal working point (28.695, 29.685) is in a good tune area where the dynamic
apertures are above 7 a. Other regions with large dynamic apertures are can be seen around 0.63, 0.73,
0.77, 0.82, and so on. For the near integer tunes (less than 0.1 away from the integers) , Fig. 2 shows that
the dynamic aperture is larger for tunes above integer with respect to the ones below. The same feature is
observed near half-integer. However, several studies have shown that operating above integer or half integer
resonances could lead to instabilities due to coherent beam-beam effects [5]. These effects are not taken in
the weak-strong model used for dynamic aperture calculations. The dynamic apertures around the RHIC
original design tunes (0.19,0.18) are below 6 a [4]. For the p-p run lattice, polarization preservation [6] also
has to be taken into account when chosing the appropriate working point.
2.2 100 GeV ion run lattices
Fig. 3 and 4 show the dynamic aperture's dependence on the fractional vertical tune with the IBS-suppression
and standard ion lattices. The structures or envelopes of the dynamic aperture w.r.t. the fractional tune are
similar for both lattices and driven by the the resonance structure shown in Fig. 1.
However, comparing Fig. 3 and 4, the standard lattice gives larger off-momentum dynamic aperture than
the IBS-suppression lattice in most of the tune regions. For example, for the nominal fractional tunes (0.23,
0.22), the off-momentum aperture for the IBS-suppression lattice is 3.5a, while for the standard lattice, it is
4.5a. In the 2012 RHIC ion runs, we adopted the standard lattices resulting in a improved lifetime due to
the larger off-momentum dynamic aperture [7].
From Fig. 4, for the standard lattice, the tunes above 1/2 give larger off-momentum aperture than the
tunes below 1/2. The good tune areas with off-momentum dynamic aperture larger than 5 a are located
around 0.63, 0.68, 0.72, 0.77, and so on. For the ion run lattices, besides the off-momentum aperture, we
also need to provide (2k + 1)r/2 phase advances between the pickups and kickers of transverse stochastic
cooling [8].2
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Luo, Y.; Bai, M.; Fischer, W. & White, S. Wide range tune scan simulations for RHIC, report, October 15, 2012; United States. (https://digital.library.unt.edu/ark:/67531/metadc843295/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.