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HERA LuminosityZEUS Weekly Collaboration Meeting
January 22, 2007 F. Willeke, DESY MHE
PART I• HERA Overview• HERA Luminosity Production 2004-2006• Low Energy Proton Running
PART II• Accelerator Physics of Luminosity Tuning, selected topic
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Electron-Hadron Collider HERAElectron-Hadron Collider HERADouble Storagering with 6.3km Circumference920GeV Protons - 27.5GeV Leptons
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HERA Double Ring Collider 820 GeV Protons (actual 920 GeV) 30 GeV Leptons e+ or e- (actual 27.5 GeV) Spatial resolution 10-18m Björn Wiik (1937-1999)
Ultimate experimental demonstration of QCD required a Lepton-Proton Collider with 320 GeV center of mass Energy
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HERA Milestones1981 Proposal1984 Start Construction1991 Commissioning, first Collisions1992 Start Operations for H1 and ZEUS,
1st Exciting Results with low Luminosity1994 Install East spin Rotators longitudinal polarized leptons for
HERMES1996 Install 4th Interaction region for HERA-B1998 Install NEG pumps against dust problem, Reliability Upgrade2000 High efficient Luminosity production rate:100pb-1y-1
180pb-1 e+p Precision Measurement on proton structure 2001 Install HERA Luminosity Upgrade, Spin Rotators for H1 and ZEUS2001/2 Recommissioning, HERA-B physics Run2003 1st longitudinal polarization in high energy ep collisions
Start-up of the HERA II Run2007 HERA operation ends
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HERA FootprintHERA Footprint
H1
ZEUS
HERMES
HERA-B HERA
PETRA
778 m
6336 m long
DE
SY
Polarized ElectronsProtons
H1
ZEUS
HERMES
HERA-B HERA
PETRA
778 m
6336 m long
DE
SY
Polarized ElectronsProtons
240 m
circumference
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InjectorsInjectors ProtonsMagnetron H- SourceRFQ to 180keVAlvarez Linac to 50MeVCharge conversion injection
DESY III p to 7.5GeV/cPETRAII to 40GeV/c
Leptonsthermionic guns-band LINAC ~300MeVe+ converters-band LINAC 450MeVe+ accumulator 450MeVDESYII 12.5Hz Synchrotron
7GeVPETRA II 12GeV
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810 m10 m detectordetector
IPIP
NEW IR NEW IR schematicallyschematically
Top ViewTop View
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Basic Concept: low Quadrupole Magnets closer to the Interaction Point, using novel magnet
technology
IR
TOP VIEW
Half Quadrupoles for p-focusing Superconducting Separator/Quads
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Improved Absorber 4 NR11m:
Status: eingebaut
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HERA II Beam Currents
P-limitations
Losses in transfering
From PETRA
(PR-Weg)
Lepton Limitations
RF Breakdowns
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HERA Luminosity Production 2004-2007
2004
2005
2006
2007
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Specific Luminosity 2004-2007Qy
Qx
Operation with Mirror
Tunes
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Modeling of HERA Specific LuminosityEffects investigated to explain/cure difference:• Beam optics e: ok
• Beam optics p: ok
• Chromatic beta beat p After switching to mirror tunes: 5%, corrected
• Assuming incorrect phase advance
Models well the difference, but can not be verified experimentally
• larger satellite resonances, uncorrectable, -3%
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Low Proton Energy Running
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Adiabatic damping and aperture limitations
~-1
max~a2/
*~1/max
xy~1/
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Proton beam-beam Tuneshift
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Electron Beam Size Matching
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20
Electron Beam-Beam Tune shift
0 500 10000.01
0.015
0.02
0.025
ex Ep Ee0
Ep
GeV
0 500 10000.02
0.03
0.04
0.05
ey Ep Ee0
Ep
GeV
We make the conservative assumption, that the tuneshift should be not larger than for the920GeV/27.5GeV values
ex Ep Ee min ex Ep Ee ex 920GeV 27.5 GeV( )
Under these circumstances, the number of protons per bunch becomes proton and electron energy dependent.
Np Ep Ee min Np02 e Ee xp Ep xp Ep yp Ep ex 920GeV 27.5GeV( )
re xe Ep Ee
400 600 800 10000
5 1010
1 1011
Np Ep Ee0
Ep
GeV
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Luminosity as a function of Proton Energy
L Ep Ee Np Ep Ee Iep Ep nbc Rhg Ep Ee
4 e nb xp Ep yp Ep
0 100 200 300 400 500 600 700 800 900 10000
0.8
1.6
2.4
3.2
4
4.8
5.6
6.4
7.2
8
L Ep Ee0 1031 cm 2 s 1
Ep
GeV
Lumi-scaling with Energy
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Design of low energy collision scheme Reduce GM magnets in strength and leave all p-magnets in the nominal proton- positron/electron positions Positron Lattice unchanged, positron IR quads unchanged Positron optics in the arc: assume 60 degree positron/proton IP (-7.5mm radially) Optical Parameters:
xp=4.9m xe = 1.20myp=0.36m ye = 0.52mNp=16 mm xe = 40nm
ye = 6 nm
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Ip=100mA
Ie=40mA
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IR Top View
P-Magnets: Nominal positron/electron positions
E-Magnets: Nominal positron positions
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IR Top View Close-up
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All p-magnets are now at nominal positions
P-magnets axis
GM GM GN GN GN GA GB GB GB9 QR QR QR QR
~4mm
P-Trajectory
IP
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P-Optics
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PART II
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VersatileToolbox for Accelerator Optimisation “BUMPS”Closed Orbit bump tool box:
• adjusting transverse position and angle in the IP• adjusting the beams on the photon monitor• optimized spurious dispersion waves and width of
synchro-betatron amplitudes• injection bumps for adjusting position and angle at
the injection septum• Polarimeter bumps:adjusting the position and angle
of the beam at calorimeters• H1 VFPS Bumps: make room in the beam pipe for off
momentum protons by moving the circulating beam off center
• Vertical dispersion bumps for adjusting the vertical beam emittance to match the two beam sizes at the IR
• Decoupling bumps: small vertical beam offset of the arcs to produce
• Weak skew quadrupoles in the arc by feed-down of sextupole fields
• Harmonic bumps to compensate the detrimental content of the distribution small dipole perturbations around the machine in order to achieve high spin polarization
• Phase bumps: global compensation of higher order Chromaticity and dynamic beta
• Tilt bumps:adjusting the x-y beam ellipse tilt at the IP• Background bumps: adjust beams in the centre of
quadrupoles to avoid additional synchrotron radiation• Chromaticity bumps: adjust the sextupoles to
compensate the chromaticity
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Closed Orbit
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Closed Orbit Bump
3 short dipoles (“kicks”) are necessary in general to make a local orbit distortion
A superposition of two 3-bumps allows to control the besides the amplitude also the slope a some position
Such bumps are called
Symmetric 4 Bump x’=0
Antisymmetric 4 bump x=0, x’≠0
(if centred around a symmetric lattice point)
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Luminosity Tuning and Luminosity Scans
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Angle Bumps in the IP
222222
222
22222
21
0
2
2
22
22
21
0
2
)(2)(
exp
2exp
)(2exp
ypyesypxe
cpe
sxpxe
xpxes
sxpxe
fNNL
sdsLL
ssdsLL
s
s
s
Assume that the proton beam is cut in slices of length ds which collide with the e-beam with an offset of =s (short bunches assumed)
s=20cm, xp,e=110m, xxp2+xe
2s
xp,e=30m y << ((yp2+sye
2)0.5/ss)= 2.110-4
Vertical angles in the order of
20 rad significant
@ p-orbit change of 0.8mm in low Quad
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IP Beam Angels and Luminosity Difference Electrons/Positrons
IP16mm
24 mm
e+e-
P(e-)
P(e+)
Lumimonitor
R(positrons)= 95%
R(Electrons)=98%
Luminosity difference is 3%
Not quite negligible
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H4A-Bumps and Synchro-betatron Oscillations Transverse ad longitudinal motion are intrinsically strongly
coupled. This coupling my drive synchro-betatron resonances
Resonances: small distortions, which are in phase with the oscillation
amplitudes and have large impact:• amplitude growth (beam loss)• oscillation energy exchange between different planes
Longitudinal oscillation energy: dEs=E∙10-3
Transverse energy: dEt= E∙x’=E 10-4
Resonant coupling between transverse and longitudinal directioncan cause large growth of transverse emittance
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Operation with the new LatticeLuminosity Optics
3Qx
4Qx
Q x- Q
y
Injection Tune:Dynamic Aperture Sufficient High specific Luminosity But in Collisions Tune footprint limited by strong resonances Poor PolarizationCollision Tunes:good polarization (50% in collisions with 3 rotators)Dynamic Aperture small (6-7) frequent sudden lifetime breakdown non-reproducible orbit effects reduced specific luminosity (15%) Frequent beam loss when switching tunes, Squeeze with C.T. very difficult
Qx + 2Q
y
Qx0.50
0.5
Qy
0
Qxbb =0.036 Qy
bb=0.072
Q x -2 Q y
4QyQx +
2Q
s
3Qy
2Qx + 2Q
y
BETATRON TUNE DIAGRAM
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Results of Particle Tracking with Synchrotron and Betatron Oscillations
(6D)1000 turns @21ms, (transverse Radiation Damping time x=12ms)
2 Sextupole Families, 20 sextupoles per family/octant Result:
Dynamic Aperture severely reduced near single resonances
The strongest resonances are the Qx-2Qy resonance driven by sextupole fields and
the 2nd synchro-betatron resonance
Qx+2Qs
Tracking Calculations using the code ‘Six-track’ performed by W. Decking
Study of Resonances
Survival plot
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Coupled 6-D motion with cavities and sextupolesCoupled 6-D motion with cavities and sextupoles
322322
2
61
21
21
611
21
21
WVxpxmxkpH
Strong linear coupling between horizontal and longitudinal motion
chromatics
NonlinearitiesTransverse motion Nonlinearities
longitudinal motion
Linear opticsLongitudinal focussing
Approximations:
v = c
p2x/neglectedSquare root expanded1/(1+) expanded into 1-
32
30
0
22
00
61
21
cos261cos2
21
WVa
EeU
Lh
EeU
Lha
s
s
Canonical coordinates
x,p,
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Decoupled Motion Decoupled Motion (Ripken, Barber, Mais, Wke,’90)(Ripken, Barber, Mais, Wke,’90)
3332
3
2222
222
22
222
61
61
2161
21
21
21
21
21
21
21
21
21
21
mWD
xm
xDDpWxmDpD
xDDpWxmDp
xDDpV
VD
xDDpVxkp
K
Transverse linear optics
Longitudinal linear optics
Linear coupl. by dispersion in cavities
Chromatics
2nd satellite driving terms
Nonlinearities trans.
Nonlinearities longitudinal.
)sin(2
))'()(cos()'()(' 1
x
xxxxx
Q
QssssdsD
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Example: Qx+2Qs resonance driving term driven by dispersion in sextupoles
))2)2()(2)((exp()(8
)()()(21
))2)2()(2)((exp()(8
)()()()(21
))2)((exp())2)((exp(
))((cos)))(sin())((cos(/2)()(
12
12
2,0,2,1,
2/12/112
22
LsqQQssi
sssDsW
dsk
LsqQQssi
ssssDsW
dsk
LsqmQnQmniJJk
LsqmQnQmniJJk
sssJsDsWWDp
sxsxx
sqs
sxsxx
xsqc
mnq qnmqssxsxsxnmqsnmqcsxsxsxqc
ssxxxxxxx
Resonances are driven by certain harmonics of the non-linear Forces (called ‘driving terms’) which oscillate close to the betatron/synchrotron frequency
Near a resonance, there is rapid exchange of energy between the oscillation in different planes and in some cases ‘unlimited’ growths of oscillation amplitudes
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H4A Bumps & Dispersion
IP
Dispersion kicks from off centre passage through IR quads add: large dispersion wave
Dispersion Waves:Large contributions to Satellite Driving Term
2))(2)(cos())(cos(ˆ LsssDdsL sL
xx
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Built-up of satellite driving terms around HERA for various optics solutions
Before Upgrade After Upgrade
After Upgrade Improved chromatics
After Upgrade Improved D.A.
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Re-evaluating synchro-betatron resonances without closed orbit distortions
3000 3500 4000 45005
0
55
5
xi
mm
48002600 i 0 1000 2000 3000 4000 5000 6000 70001
0
1
21.667
0.437
Di
6.336 1030 si
0 1000 2000 3000 4000 5000 6000 70000.2
0
0.2
Dp i
si
Zero closed orbit Undistorted Dispersion Function
0 2000 4000 6000 80000
0.1
0.2
0.3
0.4
0.5
0
h ca12s j
2 h ca12cj
2
h sex12sj
2 h sex12cj
2
h chr12s j
2 h chr12cj
2
h 12A j
6.336 1030 s j
Built-up of Satellite resonance driving terms
f12=295.8Hz
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Re-evaluating synchro-betatron resonances with an asymmetric Bump around IP North
3000 3500 4000 45005
0
55
5
xi
mm
48002600 i0 1000 2000 3000 4000 5000 6000 7000
1
0
1
21.699
0.485
Di
6.336 1030 si
0 1000 2000 3000 4000 5000 6000 70000.2
0
0.2
Dp i
si
0 2000 4000 6000 80000
0.1
0.2
0.3
0.4
0.5
0
h ca12s j
2 h ca12cj
2
h sex12sj
2 h sex12cj
2
h chr12s j
2 h chr12cj
2
h 12A j
6.336 1030 s j
5mm asymmetric hor. bump at IP North Dispersion with 10cm beat
f12=590 Hz
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Long Bumps In HERA with its‘ long periodic structures in the arc,
distortions can potentially accumulate which leads to strong performance reduction
large accelerators need a distributed corrector system
On the other hand, this sensitivity to small distortions can be used for tuning and corrections:
Long, but small amplitude bumps • Beam size optimization (emittance correction)• Coupling correction (also beam size)• Resonance compensation
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Lepton Beam EmittanceStochastic emission of synchrotron radiation photons (Quantum effect)
Stochastisc Excitation of the beam oscillations amplitudes
Design Trajector (Orbit)
Trajectory for off-
energy particlex
D·
Dipolmagnet
Dispersion
trajectory D p/p
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Radiation Damping
ptrans.
p=ħω
eUhf sin()
Hard limit formaximum achievableenergy HERA27.5GeV P=5.16MWPower Loss
P ~ E4 / ρ2
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Lepton Emittance
Equilibrium between quantum excitation of betatron oscillations and radiation damping
1
1
1)'((
1084.3
,
2
322
13
2
yx
q
q
J
ds
dsDDD
H
mCJHC
If dipole fields have gradient, this is more complicated
excitation
damping
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Dispersion Accumulation of a closed orbit exited by one kick
x
rcmD
QklN
D
Q
kl
Q
klQD
Q
Qkl
Q
QklD
Q
QQklD
Q
QxklD
Q
Qx
fodo
ikiijkjjk
ikiijkjjk
k
ikjkijkiijjk
ikijkjkiijjk
k
iikjiiijjk
k
iikiiki
k
jijjii
ˆ2501ˆsin8
ˆˆ
sin8
cos
sin8
2cos
sin8
22coscos
sin8
2cos2cos
sin4
coscos
sin2
cos)(
sin2
cos
2
22
22
2
D ~ L
A free betatron oscillation in in phase with the dispersion oscillation generated by the corresponding orbit offset in quadrupoles
Accumulative built-up of Spurious dispersion
)(sin4
))'((sin)'()()'()()'()'('))(cos()()(
)(
)(sin4
)()'(cos)'()(cos)'()'(')()()(
)()()(sin4
)''()'(cos)'()(cos)''()'()''()()'(''')(
)sin(2
)'()(cos)'()'()()'(')(
)sin(2
)'()(cos)'()()'(')(
2
20
2
00
0
2
2
Q
ssssssksdssss
sD
Q
QssQsssksdssssD
ssshQ
QssQssshsksssdsdssD
Q
QsssxskssdssD
Q
Qssshssdssx
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Closed Orbit Impact on Horizontal Emittance
~ ‹ D2/›= ‹ D02/∙ (1+ D/D0+D2/D0
2 ) ›D ~ D∙cos()≈ 0∙ ( 1+1/2 ‹ D2/D0
2 › )
Since D0 is relatively large, (80cm), the direct impact of closed orbit effects on horizontal emittance is small
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Built up of synchro-betatron resonance driving terms due to an oscillatory contribution to the dispersion
Since the longitudinal phase advance is small, the driving field component is sampled with the betatron frequency
Spurious dispersion contributions accumulate around the ring
~ L2 Large effects !!
2))(2)(cos())(cos(ˆ LsssDdsL sL
xx
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rad kick IP North
3000 3500 4000 45005
0
55
5
xi
mm
48002600 i
0 1000 2000 3000 4000 5000 6000 70001
0
1
21.557
0.291
Di
6.336 1030 si
0 1000 2000 3000 4000 5000 6000 70000.2
0
0.2
Dp i
si
0 2000 4000 6000 80000
0.1
0.2
0.3
0.4
0.5
0
h ca12s j
2 h ca12c j
2
h sex12sj
2 h sex12cj
2
h chr12s j
2 h chr12c j
2
h 12A j
6.336 1030 s j
Closed orbit with 1mm oscillation Dispersion with 30cm beat
Built-up of driving term
f = 1315 Hz
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Vertical Beamsize of the Leptons The lepton vertical beam size in HERA is due to:• Small systematic effects from the non-planar spin
rotator• Global coupling of horizontal beta motion into the
vertical plane• Local coupling of horizontal dispersion into the
horizontal plane
• Spurious vertical Dispersion due to closed orbit distortions and LONG BUMPS
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Vertical Emittance Generation by Closed Orbit and Bumps
)sin(2
'cos)()(''
)()()(''
(..))()()(''
)()()(''
y
yxy
coxyy
cocoxcoyy
cococo
Q
QyDsmskdsD
yDsmskDskD
OyyDsmyskDskD
EyxsmyskdEdysky
Need to take into account the sextupoles
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Long Bump Emittance Tuning in HERA
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