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Q = 2/3. We observed a large beam loss when the co-
herent mode was at 0.669. The beam loss was due to an in-
coherent effect instead of coherent beam-beam mode since
the beam loss only took place in one ring. [3].
TRANSVERSE BEAM EMITTANCE
Fig. 6 shows the dynamic aperture versus the proton
beam's transverse emittance. The horizontal axis is 95 %
normalized emittance which is 6 times the rms normal-
ized emittance. In this study, the initial relative momen-
tum deviation is 0.0005. From Fig. 6, the dynamic aperture
drops when the transverse emittance increases. The dy-
namic aperture is measured in units of rms transverse beam
size o- which varies with the transverse emittance. With a
larger transverse emittance, the particles will sample larger
IR nonlinear f elds.
SECOND ORDER CHROMATICITY
Here we focus on the second order chromaticity correc-
tion in the Yellow ring. Based on the off-line lattice model,
the uncorrected second order chromaticities are (-4500, -
2600). With the sorted sextupole families [4], we were able
to correct the second order chromaticities down to (-320, -
130). However, due to the tight machine schedule, these
correction strengths were not applied on line. The actual
measured second order chromaticities were (-3900, -2300).
Fig. 7 shows the off-momentum dynamic aperture with-
out and with second order chromaticity in the Yellow ring.
With the correction, the off-momentum dynamic aperture
is slightly bigger than that without correction. The off-
momentum dynamic aperture is improved to above 2 o-
when dp/po > 0.0021.
197 MHZ RF CAVITY VOLTAGE
In the 2012 RHIC 100 GeV run, we used 200 KV
197 MHz Landau cavity to overcome the observed longi-
tudinal instability. However, during the proton polarization
measurement with a carbon polarimeter, we had to reduce
the Landau cavity's voltage to below 100 KV to achieve
a better signal-to-noise ratio in the polarization measure-
ment.
Fig. 8 shows the dynamic aperture of the Yellow ring
with three sets of 197 MHz RF cavities. In this study,
the initial off-momentum deviation is 0.0005. From it,
there is not clear difference in the dynamic aperture up to
dp/po 0.0015. Above that, higher 197 MHz RF cavity
voltage gave less off-momentum aperture. However, too
low 197 MHz RF cavity voltage will cause loss of Landau
damping to cure the longitudinal instability.
SUMMARY
In the article, based on the 6-D weak-strong beam-beam
simulation, we carried out numerical simulations to investi-
gate the dependence of dynamic aperture in the 2012 RHIC
7
6
a
0
5
4
3
2
1
0
0 0.5 1 1.5 2 2.5I
dp/po [ 10 1
3
Figure 7: Calculated off-momentum dynamic aperture
without and with second order chromaticity correction in
the Yellow ring.
7'
6
a
0
5
4
3
2
1
0
0 0.5 1 1.5 2
dp/po [ 10 1
2.5 3
Figure 8: Calculated off-momentum dynamic apertures
with different 197 MHz Landau cavity voltage.
100 GeV p-p run on the 3*s at the interaction points, on
the proton bunch intensity and the proton transverse beam
emittance. Simulation shows that the off-momentum dy-
namic aperture is smaller in the Yellow ring than that in
the Blue ring and it can be slightly improved through the
second order chromaticity correction.
REFERENCES
[1] Y Luo, et al., BNL C-AD AP Note 349, 2009.
[2] Y Luo, in Proceedings of 2010 IPAC, Kyoto, Japan (2010).
[3] S. White, in Proceedings of 2012 IPAC, New Orlens, USA
(2012).
[4] Y Luo, et al., in Proceedings of 2010 IPAC, Kyoto, Japan
(2010).
No correction
KWith Correction
200 kV i
300 kV
100 kV*-...
-*
