Simulations of beam-wire experiments at RHIC Page: 2 of 3
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02 4 6 8 10 12 14Figure 1: (Color) Tune shift dependence on the wire sep-
aration distance at zero amplitudes: (left) horizontal and
(right) vertical tune shifts.0.25
0.24 d =3.S_ 17
..2 . d,++ =5.50 13 ..} -
d =7 _
,0.221
0.20 -
s os o.20 0.21 0.22 o.23 o.24 0.25
srFigure 2: (Color) Tune footprints dependence on
separation distance for initial amplitudes up to 3o
shift between simulation and theory is less than
measured tune shifts in the recent experiments [1
in good agreement with analytical results.
Figure 2 presents tune footprints obtained by
single particles over 4096 turns and applying the
a Hanning filter into the particle coordinates.
spreads are computed with start vertical and horiz
plitudes up to 3u and initial slopes set to zero.
dots correspond to particles with no wire kicks so*
is the beam base tune. The different colors corr
different beam-wire distances. As the beam-wir
tion decreases, the tune shifts get larger and the sp
broader. For example at a separation of 3.8u, the b
spread spans 5th 9th 13th, and 14th order reson
the larger separations shown here, the beam does
the 5th order resonances.
The results of dynamic aperture calculation are
Fig. 3. The particles are launched with equal ve
horizontal emittances and with a distribution that
ing particles differ in amplitude by half of RMS bis
14
12
10
s
s
4
2
0-dy = 3.8o0
-d = 5.5a0
..*d =7.30
trd =9.1 o
2 4 6 8 10 12 14 16
x (a)Figure 3: (Color) Dynamic aperture for I21
several different wire separations.the wire
1%. The
]are also
tracking
FFT with
The tune
ontal am-
The red
their tune
respond to
e separa-00
05-
10-
-15-
20- bi
4 6 8 10 12 14reads get Figure 4 shows the contour plots of dynamic apertures
beam tune over transverse tunes for three different wire separations.
ances. At Red indicates low dynamic apertures around 3u while blue
not span indicates high dynamic apertures around 11a. The tune
scans are performed with increment Av= 0.01 in trans-
shown in verse directions. It is found that at all wire separations,
rtical and the largest dynamic apertures are distributed nearly along
neighbor- the diagonal, i.e., v - vy ~ 0.02. On the other hand,
eam size. the zone along v- vy ~ 0.03 has the smallest dynamic
apertures at all separations. This scan indicates that the
nominal tune (28.230, 29.216) is close to optimal. Further-
more, a sharper drop in dynamic aperture is observed near
the 5th resonance than at the other resonances as the sepa-
ration drops from 7.3u to 3.8a.
The diffusion coefficients are calculated by loading 103
particles which have identical initial action in horizon-
tal and vertical planes, and averaged over 103 consecu-
tive turns to suppress action fluctuations. The diffusion
coefficients can be calculated numerically from D (J) -
M K--1 limN->o, ((J(N) J(0))2) /N ., where J (0) is
50A and initial action, J (N) action after N turns, and () average
over simulation particles. Figure 5 shows the simulated0.21 022 13,i 17
O019
-9
029 o21 o.22 : asx o.2u osu
Figure 4: (Color) Tune scan for dynamic aperture for wire
current 50A: (top left) dy 3.8&, (top right) dy 5.5u,
and (bottom) dy 7.3u. Working point (28.230, 29.216)
is plotted as a white dot.
Net chromaticities in both planes are set to v1 2 and
vz 2 using chromaticity sextupoles. The tunes are set
to Q = 28.230 and Q = 29.216. Long-term tracking is
carried out over 106 turns corresponding to 13 seconds stor-
age time which is 20% of the RHIC injection period. The
dynamic aperture of the machine is defined as the largest
radial amplitude of particle that survives during the full
106 turns. In this simulation and in the experiments, the
beam-wire separation is entirely in the vertical plane. From
Fig. 3, the dynamic aperture is highly dependent on the an-
gle of the wire position with the horizontal axis - particles
launched with purely vertical amplitudes have smaller dy-
namic apertures than those launched along the horizontal.
The dynamic aperture in the vertical plane is found to be
linearly dependent upon the vertical separation dy.
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Kim, Hyung Jin & Sen, Tanaji. Simulations of beam-wire experiments at RHIC, article, June 1, 2007; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc899106/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.