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Conceptual Design of a High Luminosity 510 Me\ Collider *
C. Pellegrini, D. RobinUCLA Dept. of Physics, 405 Hilgard Ave.,
Los Angeles. CA 90024
M. CornacchiaStanford Synchrotron Radiation Laboratory,
Stanford, CA 94309
Abstract
We discuss the magnetic lattice design of a high lumi-nosity 510
MeV electron-positron collider, based on highfield superconduction
bending dipoles. The design crite-ria are flexibility in the choice
of the tune and beta func-
tions at the interaction point, horizontal emittance largerthan
1 mm mrad to produce a luminosity larger than1032cm-2s-1, large
synchrotron radiation damping rate,and large momentum compaction.
The RF system pa-rameter are chosen to provide a short bunch length
alsowhen the beam energy spread is determined by the mi-crowave
instability. A satisfactory ring dynamic aperture,and a
simultaneous small value of the horizontal and ver-tical be ta
function at the interaction point, we expect willbe achieved by
using Cornacchia-Halbach modified sex-tupoles.
IntroductionIn order to study CP violation in the Q-meson
system
it is necessary to have a machine with a large luminosity.The
luminosity in a collider is given by the expression
kg- (1)= Y
where f is the frequency of collisions, N is the num-ber of
particles in each bunch, 6, and by are the hori-zontal and vertical
dimensions of the bunch respectively.Presently the largest
luminosities which have been ob-
tained in electron-positron machines is 1032cm-2s-. Inorder to
make interesting tests of the standard model itwould be desirable
to have luminosities in the range oft033~m-2s-1 to 1034cm- s-l.
This is a very challengingaccelerator problem.
At UCLA we are proposing to build an electron-positronstorage
ring at 51OMeV per beam to be used as a @-factory. The name we have
assigned to it is the Super-conducting Mini Collider @-factory or
the SMC/@-factory.In order to achieve large luminosities in a ring
we haveadopted a certain strategy. First we will buiid a stor-age
ring whose luminosity is about 1032cm-2s-1. \Ve will
Mork supported by DOE contract DEFG03-9OER 40565
then employ new methods to increase the luminosity tothe range
of several times 1033cm-2s-1.
The collider will evolve in three phases. In phase onewe will
use conventional technology and methods whichwe expect wiil achieve
an average luminosity greater than2 x 1032cm-2s-. In phase two we
would like to increase
the luminosity to 1033cm-*s-l To achieve this high lumi-nosity
we will have touse new ideas. One of our favoriteideas to go to
this high luminosity is to run the machine ina quasi-isochronous
mode [l]. The momentum compactionin the ring would be decreased by
changing the strength ofthe quadrupoles. The bunch length would
then decreaseallowing for a more strongly focused beam at the
inter-action point. In phase three we plan to use a
quasi-linearconfiguration where the bunches would be colliding
outsidethe ring in a bypass. In this paper we will discuss only
ourphase one design.
Design Goals of Phase 1As was mentioned in the previous section,
the objective
in phase one is to build a machine whose luminosity 1s2 x
1032cm-2s-1. We have several design goals in phaseone and we list
them here. The first goal is to design ourring with a small
circumference. There are several reasonsfor doing this. First of
all if one looks at the expressionfor the luminosity of a collider
given in equation 1. theluminosity is proportional to the frequency
of collisions,f. One can increase the frequency of collisions by
eitherincreasing the number bunches in the ring or making thering
smaller. The second reason is that if one has a small
ring one then needs a large field in the dipoles to bend
thebeam. increasing the energy loss due to synchrotron radi-ation.
This is an advantage. It will increase the dampingtime which will
help to damp collective instabilities. Xlsthe radiation which the
dipole produces in dispersive re-gions will increase the transverse
emittance of the beamallowing us to put more current in the beam.
The cur-rent is also limited by the beam-beam interaction. In
ourring we have assumed a linear beam-beam tune shift of0.05. The
third reason for choosing a compact ring de-sign is that a compact
ring has a naturally large momen-tum compaction. The threshold peak
current. I,. for thelongitudinal microwave instability which is the
dominantcoherent effect for small rings increases as the
momentum
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compaction goes up.
I, a Q (2)
where LI is the momentum compaction of the ring. This isan
approximate relation valid when the bunch length is onthe order of
the beam pipe radius.
There are two other remns why we chose to build asmall ring and
they are practical reasons. The first ofthese two reasons is we are
trying to make the machine asaffordable ~b possible. By limiting
the number of magne ticelements, we have decreased the cost. In
particular if wedid not have such strong bending dipoles, we might
have toincrease the emittance and reduce the damping time
withwigglers cu htls been proposed in the Frascati machine [2].The
second of these practical reaSOns is that the buildingwhich is to
be built to house this ring is not so large thatit will be able to
fit within its wails a machine of the sizeof that which is to be
built in Rascati.
The second design goal is to have a machine which wasflexible
and that the control of the tune, the bending and
the final focus system were decoupled. In other words wewanted
the arc regions which are to bend the beam around180 degrees to be
unaffected by what ~15shappening in theinteraction region. We
wanted to have the ability to adjustthe tune without affecting the
dispersion in the bends orthe focussing in the interaction region.
In other words wewanted to decouple all three of these functions so
that wecould adjust one parameter while minimizing the effectson
the other parameters.
The third design goal is to build a machine whose dy-namic
aperture was large enough to give a good lifetime.This is somewhat
difficult for machines like this because wehave a large
chromaticity in the ring which is a result of the
large quadrupoie strengths necessary to produce the smallbeam
size at the interaction point. There will then have tobe strong
chromaticity correcting sextupoies in the ring inorder to make the
chromaticity zero. Also nonlinearitiesin the field are enhanced as
a result of the small bendingradius of the dipoles. We expect the
Haibach-Cornacchiasextupoiez. to increase the dynamic aperture and
they willbe discussed later.
The fourth design goal is to build a ring which had
thecapability of decreasing the momentum compaction by sev-eral
orders of magnitude with out significantly changingthe
configuration of the ring. What we mean by signifi-cantly is that
we did not want to change the overall cir-
cumference of the ring. In addition we do not want tochange the
dipoles because they are the most complicatedand expensive magnets
in the ring and we want to buildthem so as to keep them at fixed
strength.
Linear Lattice DesignAs one can see from the artists conceptual
design in
Figure 1, the lattice consists of two straight sections andtwo
180 degree bending sections or bra. In each of the 180degree bends
there are three dipoles which bend the beam60 degrees each. Between
the dipoles there is a quadrupoieand a sextupole. In one of the two
straight sections the
LX, c r1c-?w.!. -< . Llrr*ru L,.CO, rrrs ,r:a,,< CDLLlOEI
. &-r-m J
:! .(I. : .,I 1.
Figure 1: Conceptual Drawing of the UCLA SMC/@-Factory
detecto r will be placed In the interaction region a triplet
isplaced to provide a small beam size. In the other straightsection
the beam will be injected.
Arcs
The arcs consist of three dipoles and two quadrupolesand two
sextupoies. Since we have zero dispersion in thestraight sections
the quadrupoles function is to bend theoff energy particles back to
the on energy ones when theyreach the straight sections. They are
thus both horizon-tally focussing.
The dipoles have a bending field of four tesla. They areparallel
faced magnets to take advantage of the fact thatedge focussing
provides focussing in the verticai plane andhelps to compensate for
the defocussing in thaL plane dueto the quadrupoles. Each dipole
has small field gradient(n= 0.23) which also provides some vertical
focussing. Themagnets are H-type shaped for stability and have
beendesigned by General Dynamics.
Straight Section
The interaction region consists of a triplet and controlsthe
beta function at the interaction point. \Ve canhave4, = 19cm and 0,
= 3.9cm. consistent with a bunch lengthof 3cm. The quadrupole
closest to the interacrion point is30cm away.
The fourth quadrupoie farthest from the Interaction re-gion is
used to vary the tune of the ring. lt does not effectthe dispersion
and changes the final beta very little.
The reference parameters for the ring a re given in Table1. The
current in the ring is1.16A which is rather large.We have
calculated with the help of ZAPIS] the lifetimes ofthe beam due to
such things as Touschek scattering. intra-beam scattering, gas
scattering and beam-beam lifetime.We have found that the limiting
factor at this currenris thegas scattering which fo r a pressure of
1Oiorr IS 1.8hours
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Because of the size of the ring and the amount of syn-C hrl
r
otron radiation. the vacuum system will be difficult.Table 1
-I
Luminosity, cm-s-l
Circumference, mDipole bending radius, mHorizontal betatron
tune, mVertical betatron tune, mMomentum compactionEnergy
loss/turn, KeVHorizontal damping time, msVertical damping time,
msLongitudinal damping time, msNatural emittance, mm
mradVertical/horizontal couplingNumber of particles/bunch
Number of bunches/beamCollision frequency, MHzPI at IP, cmPv at
IP, cm0, at IP, cmuy at IP, cm6v,,buy,RF frequency, MH:Harmonic
number,RF voltage, kVSynchrotron tune,bunch length, cmAverage
current, APeak current, AZ/n, flLifetime: Beam-beam, hoursLifetime:
Touschek. hoursLifetime: Gas. lo-Torr
SMC Parameter ListBeam Energy, Mel/
I
i1IIId
;
1,
5102 x lo=
1i.40.4252.13.850.1114.14.64.22.03.20.24 x 10
117.2193.93.783.0713.053.05500291003.0231.1626932.82.5I.8
Dynamic ApertureThe rings small bending radius enhances
nonlinearities
in the fields. This fact and also the fact that the largenatural
chromaticitv in the ring is quite large and has to becorrected for
by strong chromaticity correctmg sextupolestends to leave the ring
with a small dynamic aperture. Inorder lo avoid a short lifetime
due to quantum fluctuations.it is desirable to have a dynamic
aperture which is at leastten times the rms bunch size in both
planes.
A possible way to increase the dynamic aperture wouldbe LO use
modified sextupoles whose strength is not a ptiresextupole in place
of a normal sextupoie. This posslbilit)has been proposed by hf.
Cornacchia and K. Halbachi4].They have demonstrated that the
dynamic aperture canbe increased. In parrlcular for a ring such a5
ours. Cornac-chia did some calculations of the dynamic aperture for
asextupoie whose fields exoressed in complex notation are
B = -geQ (3)
20
O-
00
0 0
I 1 I 1-l 1 I 1 1 --0 10 20 30 40 50
I I I I 1 I 0
0 Sextupolel0 D Gaussian -
0 0 l Normal00 0
.lY 00 0
Horizontal Dynamic Aperture(mm)
Figure 2: Dynamic aperture due to modified and
normalsextupoles
where 3, = ae(B) and B, = -Im(B). z is the coordi-nate in
complex notation were I = z + iy. The results ofhis calculation can
be seen in Figure 2.
These results are preliminary because the model in thecomputer
code that was used does not provide the properHamiltonian for rings
having a small bending radius. \Vethink that the qualitative
behavior is correct. The sex-tupoles do help increase the dynamic
aperture.
\$e are now adapting a code Krakpot[j] in collabora-tion with E.
Forest which was used to study the dynamic
aperture of the SXLS ring at Brookhaven sacional Lab*ratory.
This program has the ability of implementing thesemodified
sextupoles in the lattice and also has the properHamiitonian.
ReferencesC. Pellegrini and D. Robin. Quasi-Isochronous Stor-age
Ring, Nuclear Insfrumenis and Methods. A301(1991) 27-36
[2] M.E. Biagini, C. Biscari. S. Guiduccl and G. \ig-nola. The
lattice for DA@?: E, the Frascacl @-Fac:or!.project,These
proceedings
[3] 31. Zisman. S. Chattopadhyay and J J. Bisonnano.Zap Users
Manual. Lawrence Berkeiey Laborarorbrep.. LBL-21270. UC-28
(1986)
[4] 31. Cornacchia and K. Halbach. Srudy of Iloa;5edSextupoles
for Dynamic-Aperture Imorovemen: inSvnchrotron Radiation Sources,
.Yucicnr jnstrumcnlsand Methods. A290 (1990)
[5] KR.AKPOT was developed by E. FC~PC: J .\lur:n>and .\l.
Reusch to track parrlcies 12 i3:ooi;habcn sSSLS ring
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