FUTURE HERA HIGH LUMINOSITY PERFORMANCE
G. H. Hoffstaetter, F. Willeke, Deutsches Elektronen–Synchrotron, Notkestr. 85, 22603 Hamburg, Germany

Abstract
After the design luminosity has been exceeded in theelectron–proton collider HERA, the interaction regions arebeing rebuilt to obtain smaller  at the two interaction
points (IP). This should increase the luminosity by abouta factor of yielding L:  32 cm 2 s 1 . To
achieve this, it can not be avoided that the beam–beamtune shift of the e–beam is increased and that the vertical  of the protons becomes comparable to the proton
bunch length. This implies new beam dynamical conditions. In accelerator studies, the beam–beam limits of thetwo HERA beams have been explored and the new low
emittance optics has been implemented and tested with apolarized positron beam. Based on these tests, the future
performance limits of the HERA e–p collider is discussed.

41= 0 74 10LUMINOSITY UPGRADEHERA exceeded its design goals in 2000 with a luminosityof L:  32 cm 2 s 1 and an integrated luminosity of167 pb . A large further increase in luminosity requires an
upgrade of the interaction region (IR) since the beam crosssections at the IP are limited by the aperture in the low–
quadrupoles. Other ways of increasing the luminosity
are not favorable since the lepton intensity is not far frombeing limited by the available rf power and there is no cost
efficient way to increase the space charge–limited proton
brightness in the acceleration chain.
The North and South IRs around the colliding beam experiments ZEUS and H1 have been rebuilt [1, 2] to movethe first focusing magnets for electrons from 7 m to 2 mdistance from the IP and to move the first focusing magnets for protons from 28 m to 11 m. The proton beam can
now be strongly focused to x
: m and y: mat the IP. The previous values have been x
m and
: m.
y
The new lattice is based on superconducting combined–
function magnets installed inside the detectors to separate
the beams completely after 8 m and to focus the electrons
vertically. To avoid backgrounds for the experiments, thesynchrotron radiation generated by these magnets is absorbed far from the IP, which requires sufficient apertures
for the radiation fan in the IR magnets. The first lens forthe protons is a new type of septum quadrupole which consists of a half quadrupole with a mirror plate. The newfeature is a deep triangular cut–out in the mid–plane of themirror plate for the lepton beam with a separation of only
60 mm from the proton orbit [3]. The magnets have high= 0 2 10= 2 45=05= 0 18=7(2 3)10 @ = 134rmm sofield quality of B=B 'that the dynamic aperture is not affected by field errors.
In order to make space for the superconducting magnets,
the compensating solenoids in the detectors have been removed. The non–compensated solenoid fields affect the
spin polarization of the lepton beam. Nevertheless, electron
polarization can be maintained due to the newly installed
spin rotator pairs which provide longitudinal polarizationfor H1 and ZEUS. The new nominal HERA parameters are:Energy–p/e (GeV)
Emit. hor/vert (nm) at IP hor/vert (m)Aperture hor/vert ()p per bunch and e-cur.
3)
Tune shift hor/vert (Bunch Length (mm)10p9205.1/5.1
2.45/0.1812/12
1.03 11
1.6/0.4
191e
27.5
20/3.40.63/0.26
20/20
58 mA
34/51
10.3

10

These parameters would lead to a luminosity of 0:74 1032 cm 2s 1 which includes a reduction by 0.92 due tothe increase of the beta functions along the proton bunch
during collision (the hourglass effect).

2

ACCELERATOR STUDIES

Before the upgrade, accelerator studies have been carriedout to verify the new parameters and dynamical conditions[4]. The new low emittance optics of the leptons with a–tron phase advance of 72Æ per FODO cell and an rf frequency shift of 300 Hz has been implemented and tested.
The emittance value of 22 nm and the corresponding increase in specific luminosity was verified. The normalized dynamic aperture, one of the critical issues, was measured and was found to be similar as in the old Æ lattice(Ax  x). High spin polarization of 60% has been obtained in this configuration. We conclude that there should
be no problems with the new lepton optics [5].
In a beam–beam study, the protons were collided withlepton bunches of different intensities inducing : times
as large proton beam–beam tune shift values than expected
for the upgraded optics [6]. While there was an enhancement of a factor 2–4 in tail population (x >  px ), the coreof the proton beam and therefore the specific luminosity remained unaffected during 10 h of collisions. We thus conclude that there should be a sufficient margin in the proton
beam–beam tune shifts.
The vertical beam–beam tune shift of the lepton beam
will increase by 50% compared to the year 2000 operation. Therefore, the tune shift limit has been explored by60

12085ey83:2 nm

64ex

32 nm

2181.5

22.5

343.5

ey

Ls (1029 cm 2 s 1mA 2 )measured

6421.5

22.5

343.5

ey

Figure 1: Top: Measured emittances of the lepton beam asa function of the vertical beta function. Bottom: Measured
and computed specific luminosity.

=25


increasing the lepton y [4c)]. Values of ex: m (corresponding to the expected horizontal tune shift for 140 mA
of protons) and ey
2 f ; : ; ; ; g have been implemented and collided with a 90 mA proton beam. The beam
sizes were not matched. We observed a monotonously increasing blow–up of the vertical lepton emittance with in
creasing y by factors up to 8. At the value of ey: mwhich corresponds to a beam–beam tune shift of :, theblow–up factor was : . Figure 1 (top) shows the measured
vertical emittance as a function of the beam–beam tune
shift. Figure 1 (bottom) shows the measured specific luminosity and the luminosity computed from the measured
beam emittances. These measurements justify that no emittance blow–up should be expected for the nominal valuesof the upgraded lattice.
All the critical beam dynamic issues for the HERA luminosity upgrade have been addressed in accelerator studies.
There appears to be no beam dynamics problem to achieve
the nominal parameters and there might be additional margin for a further increase in luminosity.

(m)

1 15 2 3 4=150 069

153 LUMINOSITY LIMITS

12The upgraded lattice provides a physical aperture of 
for the protons, while it has been before the upgrade. The –functions of the protons at the IP could
thus be some 30% smaller than the nominal values yield
ing px
cm, py: cm. Thus, the new latticepermits proton –functions as small or even smaller thanthe bunch length of the protons. The proton bunch lengthis ultimately limited by intra–beam scattering and grows
slowly due to residual rf noise [7]. Currently it’s RMS

10= 170= 12 5= 42= 1735

computed
1value is about 15 cm at the beginning of a store and reaches
28 cm after 10 h storage. This implies that maximum luminosity will be achieved with a noticeable variation ofalong the bunch length. Also the electron beam could befocused stronger at the IP quadrupoles. This would however increase the chromatic error of these quadrupoles anddecrease the dynamic aperture from 18ex to roughly 12when the beta functions are reduced to ex
cm,andeycm. Several problems can occur when the electron and proton beta functions are pushed to these ultimate
limits: (1) The fact that the bunch length of the protons issimilar to the vertical beta function reduces the luminosity, (2) it influences the beam–beam tune shift, and (3) itchanges the strength of resonances driven by the beam–
beam force; (4) for proton emittances of :  mm mrad,
which have often been achieved in the past, the horizontal
beam size of the proton beam becomes smaller than that of
the electrons which enhances nonlinear effects on the electron beam.
For the smallest possible  values and for this small
proton emittance, the luminosity, including an hourglass
reduction factor, would ultimately be:
nominal: L reduction ultimate: L reduction:  320.92:  320.86

0 74 101 3 10Also the beam–beam tune shift can change due to the hourglass bunch–length effect. For HERA the beam–beam tune
shift for particles in the center of the bunch and at the head or tail of the bunch are shown for the initial parameters with which operation will start in 2001. These are thenominal parameters with currents reduced to :  11
protons per bunch and 50 mA of positrons. These shifts
can be compared to those for the ultimate parameters withthe smallest possible  and small proton emittances andto those for the extreme conditions of the performed accelerator studies:

50 73 10 0x

initial p
ultimate pstudies p
initial eultimate estudies e0.00160.00220.0022
0.024
0.034
0.041

 5x



0.000810.00060
0.0017
0.024
0.036
0.041

 0y

0.000440.000590.00061
0.045
0.069
0.085

 5y



0.000110.001470.00080
0.044
0.070
0.083

The tune shifts computed without consideration of thehourglass effect are indicated by an index 0.
The beam–beam resonances also change due to the hourglass effect. The formulas for the resonance strength contain high powers of the beta functions and some of the resonances can therefore strongly increase with increasing beta
functions for particle collisions which occur not exactly at
the IP but in the head or tail of the proton bunch. We therefore list the resonance strength computed without hourglass
effect as well as the maximum resonance strength for particles between  s along the bunch. These numbers can becompared with the resonance strength which were encountered in the extreme conditions of the performed beam–

5beam studies:Æ (4Qex + 2Qey )Æ (2Qex + 8Qey )initial0.000200.000012

ultimate
0.000310.000018

studies
0.000450.000036

Other beam–beam resonances of reasonable order are notclose to the lepton working point. For the protons there are
7th and 10th order resonances close to the working point.
For these resonances maximum resonance strength over thebunch length can differ significantly from the resonancestrength computed without the bunch–length effect. The
strength (given in units of 8 ) for initial parameters, forultimate parameters, and for the accelerator studies are indicated by the superscripts i, u, and s are:10Æ (10Qpx )Æ (8Qpx + 2Qpy )Æ (6Qpx + 4Qpy )Æ (4Qpx + 6Qpy )Æ (2Qpx + 8Qpy )Æ (10Qpy )Æ (14Qpx )Æ (12Qpx + 2Qpy )Æ (10Qpx + 4Qpy )Æ (8Qpx + 6Qpy )Æ (6Qpx + 8Qpy )Æ (4Qpx + 10Qpy )Æ (2Qpx + 12Qpy )Æ (Qpy )

Æ0i

175
73
43
24
1422
3.1
2.9
4.4
5.9
2.6
1.2
0.37
0.33

i
Æmax

u
Æmax

s
Æmax

175
73
55
55
65
251
3.1
2.9
4.4
5.5
7.0
8.8
8.5
22

230
97
65
60
68300
4.1
3.8
5.8
5.8
6.0
8.06.622220
9960
44
3268
4.1
3.7
5.8
5.3
4.3
3.2
1.4
1.7

Most of the resonance strength which would occur in theultimate case have already been reached in our accelerator
studies. The resonances which are stronger for ultimate parameters than in the studies would not be stronger without
the bunch–length effect. Reducing the bunch length would
therefore not only reduce the hourglass reduction of the luminosity, it would also reduce the resonance strengths to alevel for which a stable operation of the proton beam underluminosity conditions was already demonstrated.

4 ULTIMATE LUMINOSITY
Since the beam dynamics seams to be acceptable for thesmallest possible beta functions, the luminosity in HERA
appears to be limited by the aperture of the protons in thelow –quadrupoles and by the dynamic aperture of theelectron beam.
Under extreme conditions the hourglass effect can leadto a decrease of the luminosity with a reduction of  . For < cm. For the minimal
HERA this would happen for py
py: cm the luminosity is therefore reduced but notlimited by the hourglass effect.
The vertical beam–beam tune shift of the leptons becomes ey:and should be tolerable according
to the beam–beam studies. The 12ex electron dynamic
aperture margin is small and it remains to be investigatedwhether this is sufficient. There is no reason not to achieve

8= 12 5= 0 069

the full lepton beam current of 58 mA since the available
rf power is sufficient. In order to reach the proton design
intensity, many small improvements in the entire accelerator chain will be necessary. This requires much effort but is
not fundamentally difficult the ultimate parameters which
differ from the nominal parameter list would therefore be:

Energy–p/e (GeV)
Emit. hor/vert (nm) at IP hor/vert (m)Aperture hor/vert ()3)Tune shift hor/vert (10p920
3.57/3.57
1.7/0.125
10/10
1.7/0.5e27.5
20/2.70.42/0.17
12/12
47/69

With these ultimate values the luminosity could be as large
as L:  32cm 2 s 1 , which includes a noticeable
hourglass reduction factor of : . The required emittancecoupling of the electron beam of 13.5% has been achieved
under the extreme conditions of the mentioned accelerator
studies, where the horizontal emittance was exnm,since it was not reduced by an additional rf frequency shift
but only by the Æ focusing scheme. If this ultimate coupling value can not be reached for  ex
nm due toemittance blowup, the ultimate luminosity might be several
10% smaller, so that L:  32cm 2 s 1 constitute
upper limits of what can be reached. In order to get close
to these values the full design beam intensities must be attained, there may not be any additional dynamic effects dueto the beam–beam and the hourglass effect, the enhanced
beta should not lead to intolerable synchrotron radiation
tails inside the detectors, and the reduced dynamic aperture
has to be sufficient for safe operation.

= 1 3 100 86= 32

72= 20= 1 3 105CONCLUSIONS

We conclude that the performance goal of the HERA luminosity upgrade of L
: 32 cm 2 s 1 is not unrealistic
and we are confident that it will be achieved. However wealso conclude that it will be very difficult to obtain a substantially larger luminosity. A luminosity value of about
L:  32 cm 2 s 1 constitutes an upper limit, which
willbe hard to reach. The available aperture margins however will be helpful to compensate a possible shortfall ofbeam intensity in the short term.

= 0 74= 1 3 106REFERENCES[1] U. Schneekloth (ed.), Report DESY–HERA–98–05 (1998)[2] M. Seidel, Proc. of PAC99, New York (1999)[3] Parker et al., Proc. of EPAC98, Stockholm (1998)[4] G. H. Hoffstaetter (ed.), HERA Accelerator Studies a) ’98, b)’99, and c) ’00, DESY–HERA–99–03, 00–02, and 00–07.
[5] G. H. Hoffstaetter, E-Proc. EPAC 2000, Vienna (2000)[6] M. Bieler et al., Proc. LHC beam–beam workshop, CERN(1999)[7] S. Ivanov, Report in preparation (2001)