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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

7

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

10

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

13

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

18

Electron Beam Size Matching

19

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

42

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

47

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

51

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

52

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

56