The acceptance of the SSC (Superconducting Supercollider) clustered lattice Page: 1 of 2
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Submitted to: Proceedings. for Summer ;:udy on the Physics of the Superconducting
-39047 Supercollider, Snowmais, Colorado June 23-July 11, 1986
THE ACCEPTANCE OF THE SSC CLUSTERED LATTICE* F, CC
7 G.F. Dell I BNL-39047
Brookhaven National Laboratory, Upton, New York 11973
Random multipoles in the quadrupole triplets Ql-Q3
adjacent to the interaction regions limit the dynamic
aperture of the SSC storage lattice to 2.5 mm. When
all random multipoles in these triplets are assumed to
be 90% corrected, the dynamic aperture increases to
approximately 5 mm.1 However due to the 1rge beta
functions in the Ql-Q3 triplets, dynamic r -ertures of
5 mm in the arc quadrupoles lose significance, since
they imply amplitudes in the triplets that exceed their
cores. In fact, the dynamic aperture of 2.5 mm obtain-
ed with no =orrection of the triplet multipoles corres-
ponds to amplitudes in the triplets nearly equal to
their inner bore. This consideration has led to the
present study in which the physical apertures of all
elements are included to determine whether correction
of random multipole fields in the triplet quadrupoles
is necessary when betatron amplitudes there are no
more than the inner radius of the beam pipe of = 16 rim.
Tracking has been performed with PATRICIA on the
same five machines used to generate the results of
Reference 1. In all cases aal=abl=0 and (aan,obn) 0
for 2 < n < m with m=5 for quadrupoles and m=10 for
dipoles. Each can and obn for evexy magnet was gener-
ated from a gaussian distribution that was truncated at
+30n~, where the ano are the rm- values of the ran-'om
multipoles listed in the CDR2. No systematic multipole
fields due to magnets were included, but two families
of sextupoles have been used to set the horizontal and
vertical chromaticities to zero at AP/P=0%.
DurinL tracking the influence of random mfltipole
fields was included as a kick given to the test par-
ticle at the center of each quadrupole and at both ends
of every dipole. Prior to each kick, a test was made
to det -cmine whether or not tne radial amplitude of the
particle had exceeded the inner dimensions of the
vacuum chamber. Test particles were launched with
equal horizontal and vertical emittances. The initial
emittance was gradually increased until the test par-
ticle hit the wall of the vacuum chamber before the
specified number of turns had been completed.
For the first part of the study, the acceptance at
AP/P=0% was determined when the degree of correction
of the triplet multipoles was varied from 0 to 100%.
For the second pact of the study, the momentum depen-
dence of the physical aperture was determined for zero
and 90% correction. In all cases the determinations
were made for five independent random multipole distri-
butions (five different machines), and the average
value and rms variation was evaluated. The aperture
determinations were made at vr=78.265, vy=78.283 which
is near one of the nine working points, vx=78.265,
vy=78.285, considered in Reference 1.
The results of the first study--the degree of
multipole correction needed at AP/P=0%--are shown in
Figure 1. The curve indicates that almost no increase
in acceptance (physical aperture) is realized for cor-
rections greater than 50%,-and it even suggests that
operation with no correction of the triplets might be
The dependence of the acceptance on momentum is
plotted on Figure 2 for 90% correction and for no cor-
rection of the triplets. The normalized emittance of
the SSC beam is en(rms area/n)=10-6 m radians3, and the
momentum spread is 0.0175% and 0-005% at injection and
20 TeV, respectively. At injection the beam a in the
arc quadrupoles is: a = (ao2-I y2 ) = 0.65 mm, anr at
AP/P = 0.02%, the results of Figure 2 indicate an
acceptance of +3a for the storage lattice when no cor-
rection is made in the Ql-Q3 triplets. The present re-
sults suggest that operation of the storage lattice
gives an acceptance of at least +3a at 1 TeV and +6a
at 4 TeV. Thus it seems that operation without cor-
rection of random multipoles in the triplets may be
possible and that, i correction is necessary, no more
than 50% is beneficial.
Figure 1. Dependence of the physical aperture
Ar=(e(Bx+ )) measured at the center of arc quadru-
poles on the percentage correction of the random multi-
pole fields in the Q1-Q3 triplets. Corrections of >50%
produce little increase in acceptance.
*Work performed under auspices of the U.S.
Department of Energy.
SSC Conceptual Design Report, SSC-SR-2020,
March, 1986, pg. 158.
Conceptual Design Report, op. cit. pp. 127-128.
Parameter List, SSC Conceptual Design,
SSC-SR-2020A, March, 1986, pg. 1
eP/P(Y)W S E
Figure 2. Momentum dependence of the physical aperture
for 90% correction and for 0% correction of the random
multipoles in the Ql-Q3 triplets. Ar-(e(Bx+By)) is
measured at the center of arc quadrupoles where
Bx=330 m and 8y=110 m for focusing quadrupoles and
Bx=110 m and 8y=330 m for defocusing quadrupoles at
AP/P=0%. All elements have 32 mm ID bore tubes
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Dell, G.F. The acceptance of the SSC (Superconducting Supercollider) clustered lattice, article, January 1, 1986; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc1190331/m1/1/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.