Tracking studies on the effects of magnet multipoles on the aperture of the RHIC heavy ion collider Page: 1 of 4
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1 PRESENTED AT 1985 PARTICLE ACCELERATOR CONFERENCE, VANCOUVER, B.C.
TRACKING STUDIES ON THE EFFECTS OF MAGNET MULTIPOLES ON THE APERTURE OF THE RHIC HEAVY ION COLLIDER*
G.F. Dell and G. Parzen
Brookhaven National Laboratory
Upton, New York 11973
Tracking studies including the effects of random
raultipoles resulting from construction errors have
been made for RHIC with two independent .tracking pro-
grams at three different tunes. The studies were made
using ten different sets of random errors for each of
the programs. The aperture was defined as the worst
case, and the results of the two programs are in good
agreement. A second set of studies was made for which
the number of dipoles was doubled to determine whether
doubling the number of independent random errors re-
sults in a reduction of the effects or random multi-
poles. The results for the two cases, one dipole per
half cell and two dipoles per half cell, indicate
there is little difference in dynamic aperture.
The present paper describes tracking studies on
RHIC, the Relativistic Heavy Ion Collider being de-
signed at Brookhaven National Laboratory. The ar~ l-
erator is an intersecting storage ring designer to
accelerate fully stripped ions from D+ to A', to ener-
gies of 100 GeV/amu. The lattice design of this a--
celerator is described in another paper at thi.. con-
ference. The goal of the present study is to assess
single particle dynamics with and without random field
errors in a region of tune space that is being consid-
ered for operation. The studies have been made with
two independent tracking programs that Include the
effects of magnet multipoles. The first program is
PATRICIA^, and the second is ORBIT^. The results ob-
tained with the two programs have been in consistent
The lattice consists of six arcs each having
twelve cells with 90° phase advance. Tune changes are
made by varying the strengths of the insertion quad-
rupoles and thus require rematching with a design pro-
gram such as SYNCH. The nominal dipole field is 3.26T;
the dipoles and quadrupoles of the c: ils have coil ID’s
of 8.0 cm. Beam collisions at 0° are made possible by
a set of dipoles on either side of the intersection
point. The dipoles nearest the intersection are common
to both beams and must have large apertures (coil ID =
20 cm). Only one beam passes through the second di-
pole, but since this can be a region of high 8, the
bore of these dipoles is also enlarged (coil ID =
10 cm). In addition, the first three quadrupoles on
either side of the intersection are in a region of
maximum 8 and have increased bores with coil ID's of
The multipoles used in this study are random and
were generated with a simple model assuming 0.002 inch
rms variations in the thickness, width, radial position
and azimuthal position of each current block. The
magnitude of the random errors for a fixed construction
tolerance depends on the coil ID. The random errors
have been scaled as 1/(r/rQ)where Tq is the nom-
inal coil radius and r is the assumed radius. The
multipoles for the nominal coil radii are listed in
*Work performed under the auspices of the U.S.
Department of Energy.
Systematic sextupoles located at the centers of
the quadrupoles in the arcs have been adjusted to give
a chromaticity of zero in both the x and y planes.
The emittances in both planes were equal. All par-
ticles were started with x' = y1 = 0.0. The displace-
ments x and y, with y = (By/Bx)% • x, were increased in
fixed steps until an amplitude was reached where the
particle stopped within 400 turns. Test runs with
1000 turns produced the same stability limit as that
for the 400 turn runs, but 200 turn runs sometimes gave
greater stability limits. It was concluded that 400
turn runs gave reliable results, and such runs have
been used throughout this study.
The a^ and b^ random errors were excluded from
the study. Only random errors were used with the
errors being selected from a gaussian distribution
that was truncated at + 3a. The region of tune se-
lected for this study is 28.800 <_ v <_ 28.833 in both
the x and y planes. The upper tune is a 5/6 resonance,
and the lower tune is a 4/5 resonance.
Table 1(a) Random multi^oles in RHIC quadrupoles
Table 1(b) Random multipoles in
With no multipoles other than chromaticity cor-
recting sextupoles, the dynamic aperture exceeded
30 it mm mradians and corresponds to more than 39 mm at
the center of the cell quadrupoles. Inclusion of mag-
netic multipoles reduces the dynamic aperture. The
goal of the present study is to find a region of tune
space and a combination of multipoles (magnet ID) that
gives the required dynamic aperture.
All tracking studies have been made for ten dif-
ferent sets of random errors for each tracking program.
WSTRtBUTIQN OF THIS BQCUMENT .IS WtUMZD
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Dell, G.F. & Parzen, G. Tracking studies on the effects of magnet multipoles on the aperture of the RHIC heavy ion collider, article, January 1, 1985; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc1093926/m1/1/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.