1. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-1 TLS and TPS Vertical Beam Size Control and Beam Stability Issues C.C. Kuo NSRRC XBPM and Beam Stability Mini Workshop September 11-12, 2008 NSRRC

2. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-2 Outline 1.Challenges of a high-performance light source 2.Sources of the beam perturbations 3.Emittance coupling control 4.Orbit stability and beam instabilities control

3. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-3 Challenges of a high-performance LS High brilliance, low emittance, low emittance coupling ratio, high nonlinear lattice effects Small beam size, stringent stable beam orbit High current, low beam impedance, good vacuum Many insertion devices with small sizes of vacuum pipes High reliability, reproducibility and flexibility Reasonable beam current lifetime and top-up injection NSRRC TLS TPS [photon/sec/mm 2 /mrad 2 /0.1%bandwidth]

4. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-4 TLS and TPS Optical functions TLS: 25.6 nm-rad @1.5 GeVTPS: 1.6 nm-rad @ 3GeV

5. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-5 TLS and TPS Parameters TLSTPS Energy (GeV)1.53.0 Beam current (mA)300400 Circumference (m)120518.4 Nat. emittance  x (nm-rad) 25.61.6 Cell / symmetry / structure6 / 6 / TBA24 / 6 / DBA Straights6m*612m*6+7m*18 Betatron tune x / y 7.18 / 4.1326.2 / 13.25 Mom. comp. (  1,  2 ) 6.678×10 -3, -3.89×10 -3 2.4×10 -4, 2.1×10 -3 Nat. energy spread  E 7.45×10 -4 8.86×10 -4 Damping time (ms) (  x /  y /  s ) 7.2 / 9.3 / 5.512.20 /12.17 / 6.08 Nat. chromaticity  x /  y -15.3 / - 7.9-75 / -27 RF frequency (MHz)500 RF voltage (MV)1.63.5 Harmonic number200864 SR loss/turn, dipole (keV)128852.6 Synchrotron tune s 1.52×10 -2 6.09×10 -3 Bunch length (mm)6.52.86

6. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-6 Electron beam size Emittance ratio=1% due to betatron coupling Source pointσ x (μm)σ x ’ (μrad)σ y (μm)σ y ’ (μrad) TPS 1.6 nm- rad 12 m straight center 165.112.4 9.8 1.6 7 m straight center 120.817.2 5.1 3.1 Dipole39.776.1 15.8 1.1 TLS 25.6 nm- rad 6 m straight center 526.950.3 27.7 9.5 Dipole125.1287.8 55.8 8.5

7. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-7 Sources of the beam perturbations Emittance coupling change Collective instabilities – single-bunch and coupled-bunch, longitudinal and transverse Beam-ion instabilities Orbit perturbations

8. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-8 Emittance Coupling Sources Linear betatron coupling due to skew quadrupole errors from (1) quadrupole rotation errors and (2) vertical closed orbit distortion in sextupoles. Linear betatron coupling from solenoid field. Spurious vertical dispersion caused by (A)(1) vertical bend error from bending rotation errors and (2) vertical closed orbit errors in the quadrupoles (B)dispersion coupling due to skew quadrupole errors in the dispersive region which are from (3) quadrupole rotation errors in the dispersive region and (4) vertical closed orbit distortion in sextupoles in the dispersive region.

9. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-9 the minimum separation of the normal mode tunes is. Coupling ratio is defined as:. Betatron Coupling driving strength ： Betatron Coupling

10. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-10 Betatron coupling Two major sources: (1)Quad rotation (2)Vertical orbit through sextupoles TPS TLS Qaud roll=0.1 mrad rms

11. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-11 Spurious Vertical Dispersion Vertical dispersion generated from all error sources can be expressed as: TPS: TLS: Unit: mm, mrad

12. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-12 Spurious Vertical Dispersion TPS: TLS: Unit: mm, mrad TPS TLS Dipole roll=0.2 mrad rms Quad roll=0.1 mrad rms

13. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-13 Cross Orbit Response Matrix Vertical orbit and dispersion response,

14. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-14 Response Matrix skew quads and sextupoles only TPS: M: 16296 X 24 or 48 K: 24 or 48 skew quads V: 16296 (96*168+168) 168 Monitors, 4 correctors per section, 96 in total. Using SVD method to get K as wanted correction. TLS: M: 1176 X 8 K: 8 skew quads V: 1176 (24*48+48) 48 Monitors, 4 correctors per section, 24 in total. Using SVD method to get K as wanted correction. M : unified response matrix for a set of horizontal steering and installed (or virtual) skew quads V : measured normalized vertical orbit and dispersion, K : skew quad array in the ring can be obtained using SVD for a linear equation such that the betatron coupling and vertical dispersion can be minimized simultaneously.

15. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-15 Experimental results (TLS) Coupling ratio is defined as: C.C. Kuo, et. al EPAC2002 No de-convolution yet

16. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-16

17. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-17

18. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-18 C.C. Kuo, et. al EPAC2002 TLS results

19. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-19 Vertical beam size from interferometer at NSRRC um Top-up FBs ON 2008/8/29

20. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-20 Sensitivity to alignment in TPS Error Type (rms) G  (%) Quadrupole Rotation: 0.1 mrad5.04E-021.40E-031.53E-01 Vertical Sextupole Position: 0.1 mm5.04E-023.00E-037.07E-01 Spurious dispersion Betatron coupling Increase tune separation to 0.1 will reduce K by a factor about 4

21. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-21 CORRECTION OF VERTICAL DISPERSION AND BETATRON COUPLING Lattice: TPS 79H2 Using cross-plane response matrix and SVD method to correct both betatron coupling and vertical dispersion with a set of skew quadrupoles. With 48 skew quads, <1% emittance ratio can be achieved, and the maximum strength is < 5.4x10 -3 m -1 100 machines Before correction 100 machines After correction

22. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-22 Efforts for Beam Stabilization in TLS 1. Orbit stability: Elimination of sources Feedback system 2.Coupled-bunch instability: RF gap voltage modulation ( ~ Oct. 2004) Superconducting RF ( Dec. 2004 ~) Coupled-bunch feedback systems (FPGA-based processor) Transverse (Nov. 2005), 300 mA top-up Longitudinal (Feb. 2006)

23. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-23 TLS orbit

24. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-24 Orbit at NSRRC: COD before correction (compared with model simulation with errors input) in SRRC Storage ring at commissioning stage in1993. Corrected COD is shown. Qx=7.18, Qy=4.13 47 BPM, 24HC, 30 VC

25. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-25 32 micron, rms (H) and 40 micron, rms (V) after correction

26. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-26 Some examples related to orbit perturbations at NSRRC Cooling water temp. variation While adjusting PID controller Orbit oscillations due to cooling water temp. Vertical orbit changes during crane motion Orbit drift during ID gap change w/ and w/o feedback One turn

27. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-27 Orbit feed-forward for ID gap change: H. Chang, SRRC

28. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-28 Girder Displacement Main cause: air temperature Sensitivity to air temp.: ~10 μm / ℃ Induced beam orbit drift: 20-100 μm / ℃ Current status: < ± 0.1 μm per 8 hr shift Air temp. : < ± 0.1 ℃ (utility control system improved) Thermal insulator jacket J.R. Chen et. al.

29. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-29 Magnet (Water Temp.) Caused by the temperature fluctuations of magnet cooling water Magnet deformed ~10μm/ ℃ Induced beam orbit drift: 5-50 μm / ℃ Current status Cooling water temp.: ~ ± 0.1 ℃ J.R. Chen et. al.

30. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-30 Expansion of Vacuum Chamber Caused by synchrotron light irradiation. Sensitivity to water temp.: ~10 μm / ℃ Move the girder (~0.3μm/ ℃ ) and BPM (~1μm/ ℃ ) Induced beam orbit drift: ~10-30 μm / ℃ Current status Vacuum cooling water temp.: ~ ± 0.5 ℃ J.R. Chen et al.

31. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-31 TLS beam response to ground wave and mechanical vibration V=500 m/s

32. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-32 tens micron Closed Orbit : tens micron rms w.r.t. target orbit with DC correction schemes. Orbit distortions: < 10 micron rms during insertion gap scan can be compensated for using look-up correction tables. Beam orbit stability: a few micrometer level (peak-to- peak) with a global feedback system. (temperature control, electricity upgrade, etc.) Closed Orbit and Orbit Stability (low frequency)

33. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-33 TLS orbit log (0.1Hz sampling) 2008/08/29 mm K.T. Hsu will talk about high frequency behavior mm

34. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-34 TLS instabilities and cures

35. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-35 TLS - Transverse Performance Beam Spectrum Courtesy by K.T. Hsu

36. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-36 TLS - Transverse Performance Transverse Feedback OFF Transverse Feedback ON Synchrotron Radiation Monitor Courtesy by K.T. Hsu

37. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-37 Loop Closed Loop Open Snapshot of Synchrotron Radiation Beam Profile (w/o Longitudinal Feedback) Grow/Damp test results @ 300 mA Horizontal Vertical Horizontal Modal Spectrum Courtesy by K.T. Hsu

38. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-38 TLS - Longitudinal Performance Courtesy by P.J. Chou and M.H. Wang

39. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-39 TLS - Longitudinal Performance Evolution of the stable longitudinal mode during user shift No longitudinal feedback SRF 5 ~ 10 increase in threshold current Courtesy by K.T. Hsu

40. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-40 Conventional RF cavity + RF gap voltage modulator => Longitudinal stable beam Superconductor RF cavity => Longitudinal stable beam no feedback Time dependence of beam profile (SR monitor @  ≠ 0) TLS - Longitudinal Performance Time dependence of beam profile (SR monitor @  ≠ 0) Courtesy by K.T. Hsu

41. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-41 Streak Camera Observation Loop Open Loop Closed One Turn Loop Closed -> Open -> Closed One Turn Loop Open Snapshot of the Synchrotron Radiation Beam Profile Loop Closed Loop Open Courtesy by K.T. Hsu TLS performance with longitudinal feedback

42. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-42 Photon Beam stability through 50 um pinhole 2008/08/29 Top-up 300 mA, Orbit feedback ON Transverse and longitudinal feedbacks ON

43. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-43 TLS operation

44. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-44 TLS photon beam stability

45. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-45 TLS orbit reproducibility from pinhole monitor

46. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-46 TPS orbit

47. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-47 TPS COD Correction Scheme Precision ~ 15  m 7 BPM each cell 3 HC(+1) and 4 VC(+1) each cell for SVD but all sextupoles are with HC and VC. CV CH CV CH CV CH CV SQ

48. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-48 COD Error Sources and Amplification Factor Error Source (rms) 3 sigma truncated Girder displacement x, y (mm)0.1 Girder roll θ (mrad)0.1 Quad and sext displacement x,y w.r.t. girder (mm) 0.03 Dipole displacement x,y (mm)0.5 Dipole roll θ (mrad)0.1 Dipole field error (10 -3 )1 BPMs displacement x, y (mm)0.1 Amplification factorAx rms (max) Ay rms (max) Quad displacement55 (97)40 (51) Girder displacement30 (54)8 (10) Dipole roll θ-5.8 (7.8) Dipole field error1.1 (1.9)- COD due to Errors: Horizontal: 3.8 mm r.m.s. Vertical : 2.2 mm r.m.s.

49. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-49 COD Correction Before Correction COD and Optics correction After Correction XC=2,4,6/YC=1,3,5,7 HorizontalVerticalHorizontalVertical COD at BPMs mm (r.m.s.)3.792.220.08070.0676 Max. COD mm21.119.270.3710.338 Max. Cors Strength mrad 0.4020.245 Mean Cors Strength mrad 0.07880.0484

50. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-50 Correction Capability and Residual COD

51. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-51 Ground vibration effects To guarantee the photon brilliance, beam orbit disturbance due to ground wave need to be controlled. V H Amplification v=500 m/sec, girder transmission = 1

52. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-52 TPS Collective Effects SC RF cavities will not cause coupled bunch instability in nominal operation. Resistive wall impedance will cause transverse coupled bunch instability. To stabilize the beam requires positive chromaticity( > 5), not recommended. At present the microwave instability is the dominant limitation of single bunch current. The more insertion devices we install, the more detrimental the transverse instabilities are. Active transverse feedback system is required for stable operation. We must strive to keep good vacuum condition in the storage ring. P.Chou

53. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-53 Major sources of broadband impedance and microwave instability threshold Total broadband impedance: |Z/n|= 0.36  A. Rusanov (K. Oide’s code)

54. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-54 summary The beam size control including coupling correction, instability cures or feedback system in TLS and TPS are discussed. Some orbit perturbation issues included in this talk. Orbit feedback issues will be covered by Kuotung Hsu. With a set of skew quadrupoles in the ring, one can control both betatron coupling and vertical dispersion. ID gaps and phases will change coupling strength and orbit. Both TLS and TPS need transverse feedback systems to stabilize the beam in the transverse planes. In TLS, we need longitudinal feedback system for high current operation (>200 mA) even we replaced the room- temperature cavity with superconduting type. With SRF in TPS, we might not need longitudinal feedback system if the vacuum components are well taken care of.

55. NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-55 Thank you