Abstract While RHIC has only just startedrunniug for its heavy ion physics progr~in the fiist run last snmmeq we achieved 100/0of the design luminosity.In this paper we discuss plans for increasingthe luminosi~by a factor of 35 beyond the nominal design. A factor of 4 should be straightforwardby doubling the number of bunches per ring and squeezing the P* horn 2 to 1 m at selected interactionpoints.An additionalf%tor of 8 to 10 could be possible by using electron cooling to counteractintrabeam scatteringandreduce emittancesof the beams

BINP, Russia Usa V Parkhomchuk

BNL D Trbojevic

I Bemzvi

J Kewisch

J M Brerman

M Harrison

S Peggs

T Roser

W Mackay+

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Submitted to:
2001 Particle Accelerator Conferellcfz , .
BNL-67939
June 18-22, 2001: Chxgo. E
UPGRADING RHIC FOR HIGHER LUMINOSITY*
W. MacKay+, I. BemZvi, J.M. Brerman, M. Harrison, J. Kewisch, S. Peggs, T. Roser, D. Trbojevic,
BNL, USA
V. Parkhomchuk, BINP, Russia
Abstract
While RHIC has only just startedrunniug for its heavy
ion physics progr~ in the fiist run last snmmeq we
achieved 100/0of the design luminosity.In this paper we
discuss plans for increasingthe luminosi~ by a factor of
35 beyond the nominal design. A factor of 4 should be
straightforwardby doubling the number of bunches per
ring and squeezing the P* horn 2 to 1 m at selected
interactionpoints.An additionalf%tor of 8 to 10 could be
possible by using electroncooling to counteractintrabeam
scatteringandreduce emittancesof the beams.
1 GOLD-GOLD LUMINOSITY UPGRADE
The RHIC lattice allows for simultaneousopemtion at
six different interaction regions, each with a design
Iuminosiiy of 2 x1026 cm 2 s 1 for gold beams. It is
expected that this design luminosity will be reached
during the FY2001 heavy ion rum The machine
parameters are shown in Table 1 in column “RDM”
(RHIC DesignManual).
lTrT-
Scheme ] Units IRDM lRDM+l RELICIl
&initial n
&fiil 7C : [4
* Im 2 1 1
N~ 60 120 /7X-----
N 109 1 1 1
t 0.0016 m] 0.004
~~* u.rad Im 153 I 95
O* ID I Llu I 1.JU I 7.J
LO I 1027cm-2s-’I 0.8 I 3.2 I 8.3
I <~ I 1027cm-2s-L10.2 I 0.8 I 7 I
Table 1: The luminosity performance of RHIC in
scenarios of Au+Au collisions at 100 GeV/nucleon. The
luminosity averagesgiven for “RDM” and “RDM+” are
averagedover a 10hour store.For the ‘RHIC U“ scenario
luminosityis averagedover 5 hoursdueto the beam-beam
bum-off fkomactualcollisions.
In table 1 (and in the following), &is the normalized
95?40emittance,P* is the H?beta fimction, ~ is the beam-
beam parameterper 1P,NB the numberof storedbunches,
N the numberof ions per bunc~ o’* angularbeam size at
lp, O* rms beam size at the,IP, Lo the initial luminosity
luminosityby abouta factor of four consistsof increasing
the number of bunches from about 60 to about 120 and
decreasing(Y from 2 m to 1 m. This will not requireany
substantialnew hardware. However, due to the larger
beam size in the interactiontripletsthe non-linear local
correction elementswill have to be carefully optimized. It
is expected thatthis level of performancecan be reached
during the FY2003 running period. The machine
parametersfor this enhanced luminosity are shown in
column “IU)M+”.
A furtherincrease of the number of bunches or decrease
of P* is possible andhasbeen studied.However, it would
require substantial upgrades or modifications of the
collider detectors. The former will reduce the time
interval between collisions to less than 100 ns and the
latter would. require additional triplets close to the
collision point. Alternatively the luminosity can be
enhancedby increasingthe numberof ions per bunch or
by de-creasing the transverse emittance of the beam.
However, alreadyat the presentbunch intensityandbeam
emittance the luminosity is expected to decrease very
rapidly during a store due to intrabeamscattering(IRS).
tis is the reason for the large difference between peak
and average luminosity in Table 1. To overcome this
limitation we are proposing to counteract intrabeam
scatteringby electron cooling the gold beams at storage
energy.
Cooling the gold beams at 100 GeV/nucleon requires
electron beam energy of about 50 MeV and an average
beam currentof about 10mA. A detaileddiscussionof the
electron cooling of RHIC can be found in a companion
paper [1]. With electron cooling the beam ernittancecan
be reduced and maintainedthroughoutthe store and the
luminosity increased until non-linear effects of the two
colliding beams on each other limit any fbrtherincrease
(beam-beamlimit). Withthe parametersshown in Table 1
in column “RH.IC H“, a luminosity increase by 35-fold
over RI-UC design luminosity could eventually be
achieved. The RHIC electron cooler could be completed
by FY2006.
Upgradingthe heavy ion beam fi-om gold to uranium
ions at similarbunch intensitieswill requiretAe Electron
Beam lon Source (EBIS), which is presently in
development[2].
~d <b theaverageluminosity.A firstupgradeof the
* Undercontractwith tbe UnitedStatesDepartmentof Energy,Contract
NumberDE-ACO2-98CH1O886
‘mackay@bnLgov
2 LUMINOSITY UP(XADES FOR
POLARIZED PROTON OPERATION
The RHIC spin physics program uses the unique
capability of RHIC to accelemte and collide polarized
proton beams at a center-of-mass energy of up to 500
GeV anda luminosityof up to 2X1032cm-2s-1.
Although the physics potential of this capability still
needs to be exploited thereareupgradesto RHIC thatcan
significantlyextendthephysics reachof thisprogram.
Since the spinphysics programrelies on high precision
measurementsa luminosity upgrade is most usefhl. The
proton beam intensity can be increase~ or the beam
emittance be decreased until the beam-beam limit is
reached which corresponds to a luminosity of about
4X1032cm 2 s ‘. The RHIC electron cooler proposed for
heavy ion operationcould be used at injection energyto
achieve this reduction of the proton beam ernittance.The
machine parametersfor the expected luminosity during
FY2001 (column “lU)M”), the enhanced luminosity as
discussed above for gold beams (column “RDM+”), and
the luminosity at the beam-beam limit (column “RHIC
II”) arelistedin Table2.
~~ I RDM RDM+ RHlcII
& q.lm I 20 20 12
~ m 12 1 1
1~1
Table 2: The luminosity performance of RHIC in
scenarios of p+p collisions at 250 GeV per beam. Note
that for the RHIC II and RDM+ scenarios, we have
assumedthatbeams arecolliding atonly two or th-ee 1P’s
respectively,so the totaltune shiftlimit is still0.024.
Taken together these upgmdes would allow for
polarized proton luminosityat 500 GeV of up to 4X1033
cmzs’, a 20-fold increase over the present luminosity
goal for pp.
It seemsalso possibleto installin one or two interaction
regions an additionalpair of high-field focusing triplets
that would reduce P* to about 30 cm, increasing the
luminosity by an additional factor of 3. Finally, the
number of bunches in each ring could be increasedfrom
120 to 360, increasingthe luminosityby anotherfactor of
3. These two last upgrade options would also requirean
upgradeto the detectors.
It may also be interestingto increasethe center-of-mass
energy of the polarized proton collisions. The arc dipoles
and quadruples in RHIC have a margin of about 30°/0
beyond the opemting field for 250 GeV beam energy.
Exploiting this margin would allow for operation at a
center-of-mass energy of about 650 GeV. One or two
interactionregions would have to be refittedwith higher
field magnetsto produce collisions whereastheremaining
interaction regions could be retuned for simply
transportingthe higher energy beam without producing
collisions.
3 SINGLE BUNCH INTENSITY LIMIT
The beam-beam parameter~ which is proportionalto
N/&,places a fundamentalimit on the single bunch phase
space densityN/s, since ~=1.5rN/&where r is the classical
ion radius.~ has a critical maximumvalue which cannot
be surpasseddueto nonlineardynamics.Note thatneither
the beta function j3*nor the energyy enterthe expression
for ~, thus the single bunch intensity limit cannot be
enhanced or reduced by optics or energy upgrades.Also
note that~ is a %eam-beam” pmeter, not a “tone shiff’
parameter– if thereare Nmhead-on collisions per turn,a
smallamplitudeparticlesuffersa totaltune shiftof
AQ=NP.~
The exact critical maximumvalue ~ depends on many
detailssuch as the number of head-on collisions per tunL
the presence of long range beam-beam interactions,the
betatron and synchrotronstunes, the chromaticity, the
possible presence of externalsources of tune modulation
damping etc. Even without a detailed model of an
upgradedRHIC, it is reasonableto assumethat
~= 0.024ilJP
an approximate value which is justified not only by
general calculations and simulations,but also by direct
experience at the SPS[3], and the Tevatron[4, 5]. It is
unclearhow electroncooling may affect thislimit.
The single bunch intensityknit due to the beam-beam
interactionis dhectly proportionalto the ernittance,which
is nominally expected to increase from about 15 pm to
about 40 pm in the course of a 10-hour store, due to
intrabeam scattering (lBS). Using nominal numerical
values for <. and q the maximum single bunch gold
intensityis foundto be
NC=2.6.10@/15pm)( <JO.004)
This is to be compared with the nominal single bunch
intensityof 109ions per bunchquotedin the MC Design
Manual [6]. The beam-beamlimitis not faraway.
4 LUMINOSITY AT THE BEAM-BEAM
AND ANGULAR APERTURE LJMITS
The lurniuosityper interactionpointis given by
L=N~~2cs’*2(4nf,,v~/?)
Where f,,, is the revolution fkequency.The term in
parentheses is constant at f=ed energy. This
parameterization is appropriate when the maximum
luminosityis simultaneouslylimited -or nearly limited -
by beam-beam effects and by intemction region optics,
since thenthevaluesof{ ando’* arewell known.
The beta functionata distanced horn the 1P,stillin the
driftregion before the firstquadrapole,is given by
~(d)= ~*+d2/~”- d2/(3”
.
Similarly,the maximum value of P in the interaction
region tripletis inversely proportionalto the value of P*.
By anidogy with the equation above, this relationshipis
convenientlydescribedby introducingthe nearlyconstant
“effective tripletdistance” ;, which is definedby
; =(j ~’)””’
The effective triplet distance also relates the angular
beam size atthe IPto themaximumbeam size ‘a, since
~ =;GW
The upper limit of this maximum beam size is
constrainedby the requirementof an apertureatleastn %3
times the rms size of the beam in the tripletquadruples.
Thus, the angularbeam size at the ll? mustbe less thana
critical value a’*. which is proportionalto the “effective
angular aperture”of thetriplet ald, through
.
D’*< G’*C=af~ n
Note that the critical value o’*C is independent of
emittancefor non-pathologicalvaluesof D*.The effective
angularapertureis the principalfigure of meritmeasuring
the potency of I.Poptics schemes.It is improved by using
largerbore quadruples (increasinga ) or by moving the
tripletcloser to the D?(decreasing ~ ).
At RHIC, the Effective tripletdistance, ; is 36 ~ the
triplet bore radius, z is 65 mm and this leads to a
maximum angularbeam size a’*, of 226 prat a limit
which will be slightly violated if a gold beam with an
emittanceof&=40 n pm is storedin a latticewith ~%=1m.
Withthesevalues,and f,,v=78.3 M..z,we get
L=(NB/120)(&.004)2(o’*/226pmd)24.6.1028cm-2s-*
The next natumlquestionto ask is what are the limits
on NB.The image currentof the beam which flows in the
vacuum chamber walls causes resistiveheating. This is
not a concern in the sections of beam pipe at room
temperature,but has the potentialto be a seriousproblem
when the heat is deposited at cryogenic temperatures.A
maximumaveragecryogenic heatload of about 0.5 to 1.0
Watt per meter can be tolerated during continuous
running.An analysis [7] lead to the engineeringdecision
to use stainlesssteelbeam pipes withouta copper coating.
Fig. 1 shows the extension of that analysisto the RHIC
upgrades.The linearpower load depends stronglyon the
RMS Gaussiazzbunch length, and on the number of
bunches.
The calculation assumes that all ion bunches have
exactly the same charge, and that they are spread
uniformly around the circtierence. la this case the
power spectrum is a series of narrow lines uniformly
spacedby NBf~~,, undera Gaussianenvelope which is the
Fourier transform of the bunch shape. The total linear
power load is just a sum over all these spectral lines,
convoluted with the vacuum chamber resistanceat those
frequencies– a resistancethatis dominatedby skindepth
effects. As the number of bunches increases,the spacing
between spectrallines increaseslike NB, but the power in
each harmonic increaselike NB2.Thus when the bunches
are Iongitachxdly spaced by very many bunch lengths–
for example,when NB=360– the linearpower load is just
proportionalto NB,as is intuitivelyexpected.
Fig. 1 shows thatthis scaling breaks down when there
are 2520 bunchesin anion ring, andthe bunch spacing is
only 1.52 m, except for very shortbunchlengthslesstha.q
say, 0.25 m. The suppressionof the linear power load
which is implied for longer bunch lengthsis weakenedin
more realisticsituations– for example,when an abortgap
is present and when the bunch populations are not all
equal.Nonetheless,it is possibleto storeasmany as 2520
bunches in the ion rings without violating the maximum
heatload limit, andwithoutlosing much luminosityto the
hourglasseffect.
Otherpossible limits,which will not be discussedhere,
are heating of the Beam Position Monitor signal cables
andthe electroncloud effect.
Figure 1. Linear power load deposited at cryogenic
temperaturesin the stainlesssteelvacuumchamber,dueto
beam image currentswith 109gold particlesper bunch.
5 REFERENCES
[1] 1. Ben-Zvi et al., “Electron Cooling for RH.IC”,Proc.
of the Part.Ace. Conf. 2001, Chicago (2001).
[2] J. Allesi et al., “Progress in he Operation of a High
IntensityEBIS at BNL”, Proc. of the Part.Ace. Conf.
2001, Chicago (2001).
[3] PhillipJ. Brytrrtand Kjell Johnse~ “The Principlesof
Circular Accelerators and Storage Rings”, Cambridge
Univ. Press(1993). ‘
[4] Steven D. Holmes, “Tevalron PerformanceGoals for
the Coming Decade”, Proc. of the Part.Ace. Conf 1999,
p. 43, New York City (1999).
[5] V. Shiltsev et al., “Compensation of Beam-Beam
Effects in the Tevatron Collider with Electron Cooling”,
Proc. of the Part.Ace. Conf. 1999, p. 3728, New York
City (1999).
[6] ltHIC DesignManual,BNL, 1993.
htqx//www.agsrhichome.bnl.gov/NT-share/rhicdm
[7] A.G. Ruggiero, S. Peggs, “Vacuum Pipe Heating in
RHIC”, RHIC/AP/46, BNL, 1994.


Upgrading RHIC for higher luminosity

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Upgrading RHIC for higher luminosity

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