1. 1 HERA Luminosity ZEUS 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

2. 2 Electron-Hadron Collider HERA Double Storagering with 6.3km Circumference 920GeV Protons - 27.5GeV Leptons

3. 3 HERA Double Ring Collider 820 GeV Protons (actual 920 GeV) 30 GeV Leptons e + or e - (actual 27.5 GeV) Spatial resolution 10 -18 m HERA Double Ring Collider 820 GeV Protons (actual 920 GeV) 30 GeV Leptons e + or e - (actual 27.5 GeV) Spatial resolution 10 -18 m Björn Wiik (1937-1999 ) Ultimate experimental demonstration of QCD required a Lepton-Proton Collider with 320 GeV center of mass Energy

4. 4 HERA Milestones 1981 Proposal 1984 Start Construction 1991 Commissioning, first Collisions 1992 Start Operations for H1 and ZEUS, 1st Exciting Results with low Luminosity 1994 Install East spin Rotators longitudinal polarized leptons for HERMES 1996 Install 4 th Interaction region for HERA-B 1998 Install NEG pumps against dust problem, Reliability Upgrade 2000 High efficient Luminosity production rate:100pb -1 y -1 180pb -1 e + p Precision Measurement on proton structure 2001 Install HERA Luminosity Upgrade, Spin Rotators for H1 and ZEUS 2001/2 Recommissioning, HERA-B physics Run 2003 1 st longitudinal polarization in high energy ep collisions Start-up of the HERA II Run 2007 HERA operation ends

5. 5 HERA Footprint 240 m circumfer ence

6. 6InjectorsInjectors Protons Magnetron H - Source RFQ to 180keV Alvarez Linac to 50MeV Charge conversion injection DESY III p to 7.5GeV/c PETRAII to 40GeV/c Leptons thermionic gun s-band LINAC ~300MeV e+ converter s-band LINAC 450MeV e+ accumulator 450MeV DESYII 12.5Hz Synchrotron 7GeV PETRA II 12GeV

7. 7

8. 8 10 m detector IP NEW IR schematically Top View

9. 9 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. 10 Improved Absorber 4 NR11m: Status: eingebaut

11. 11 HERA II Beam Currents P-limitations Losses in transfering From PETRA (PR-Weg) Lepton Limitations RF Breakdowns

12. 12 HERA Luminosity Production 2004-2007 2004 2005 2006 2007

13. 13 Specific Luminosity 2004-2007 Qy Qx Operation with Mirror Tunes

14. 14 Modeling of HERA Specific Luminosity Effects 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%

15. 15 Low Proton Energy Running

16. 16 Adiabatic damping and aperture limitations ~ -1 max ~a 2 / *~1/ max x y ~1/

17. 17 Proton beam-beam Tuneshift

18. 18 Electron Beam Size Matching

19. 19

20. 20 Electron Beam-Beam Tune shift

21. 21 Lumi-scaling with Energy

22. 22 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 = 1.20m yp =0.36m ye = 0.52m Np =16 mm xe = 40nm ye = 6 nm

23. 23 I p =100mA I e =40mA

24. 24 IR Top View P-Magnets: Nominal positron/electron positions E-Magnets: Nominal positron positions

25. 25 IR Top View Close-up

26. 26 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

27. 27 P-Optics

28. 28 PART II

29. 29 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

30. 30 Closed Orbit

31. 31 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, x0 (if centred around a symmetric lattice point)

32. 32 Luminosity Tuning and Luminosity Scans

33. 33 Angle Bumps in the IP 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 =110 m, x xp 2 + xe 2 s xp,e =30 m y << (( yp 2 +s ye 2 ) 0.5 /ss)= 2.1 10 -4 Vertical angles in the order of 20 rad significant @ p-orbit change of 0.8mm in low Quad

34. 34 IP Beam Angels and Luminosity Difference Electrons/Positrons IP 16mm 24 mm e+ e- P(e-) P(e+) Lumimonitor R(positrons)= 95% R(Electrons)=98% Luminosity difference is 3% Not quite negligible

35. 35 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: dE s =E 10 -3 Transverse energy: dE t = E x=E 10 -4 Resonant coupling between transverse and longitudinal direction can cause large growth of transverse emittance

36. 36 Operation with the new Lattice Luminosity 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 Polarization Collision 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 Q x + 2Q y QxQx 0.50 QyQy 0 Q x bb =0.036 Q y bb =0.072 Q x -2 Q y 4Q y Q x + 2Q s 3Q y 2Q x + 2Q y BETATRON TUNE DIAGRAM

37. 37 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 Q x -2Q y resonance driven by sextupole fields and the 2 nd synchro- betatron resonance Q x +2Q s Tracking Calculations using the code Six-track performed by W. Decking Study of Resonances Survival plot

38. 38 Coupled 6-D motion with cavities and sextupoles Strong linear coupling between horizontal and longitudinal motion chromatics NonlinearitiesTransverse motion Nonlinearities longitudinal motion Nonlinearities longitudinal motion Linear optics Longitudinal focussing Approximations: v = c p 2 x/ neglected Square root expanded 1/(1+ ) expanded into 1- Canonical coordinates x,p,

39. 39 Decoupled Motion (Ripken, Barber, Mais, Wke,90) Transverse linear optics Longitudinal linear optics Linear coupl. by dispersion in cavities Chromatics 2nd satellite driving terms Nonlinearities trans. Nonlinearities longitudinal.

40. 40 Example: Q x +2Q s resonance driving term driven by dispersion in sextupoles 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

41. 41 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

42. 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.

43. 43 Re-evaluating synchro-betatron resonances without closed orbit distortions Zero closed orbit Undistorted Dispersion Function Built-up of Satellite resonance driving terms f 12 =295.8Hz

44. 44 Re-evaluating synchro-betatron resonances with an asymmetric Bump around IP North 5mm asymmetric hor. bump at IP North Dispersion with 10cm beat f 12 =590 Hz

45. 45 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

46. 46 Lepton Beam Emittance Stochastic emission of synchrotron radiation photons ( Quantum effect) Stochastisc Excitation of the beam oscillations amplitudes Design Trajector (Orbit) Trajectory for off- energy particle x D· Dipolmagnet Dispersion trajectory D p/p

47. 47 Radiation Damping p trans. p=ħω eU hf sin( ) Hard limit for maximum achievable energy HERA 27.5GeV P=5.16MW Power Loss P ~ E 4 / ρ 2

48. 48 Lepton Emittance Equilibrium between quantum excitation of betatron oscillations and radiation damping If dipole fields have gradient, this is more complicated excitation damping

49. 49 Dispersion Accumulation of a closed orbit exited by one kick 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

50. 50 Closed Orbit Impact on Horizontal Emittance ~ D 2 / = D 0 2 / (1+ D/D 0 + D 2 /D 0 2 ) D ~ D cos( ) 0 ( 1+ 1 / 2 D 2 /D 0 2 ) Since D 0 is relatively large, (80cm), the direct impact of closed orbit effects on horizontal emittance is small

51. 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 ~ L 2 Large effects !!

52. 52 rad kick IP North Closed orbit with 1mm oscillation Dispersion with 30cm beat Built-up of driving term f = 1315 Hz

53. 53 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

54. 54 Vertical Emittance Generation by Closed Orbit and Bumps Need to take into account the sextupoles

55. 55 Long Bump Emittance Tuning in HERA

56. 56