1. Electron Cloud Studies at KEKB
J.W. Flanagan
Cornell LEPP
Also: K. Ohmi, E. Benedetto, H. Fukuma, Y. Funakoshi, S. Hiramatsu, T. Ieiri, H. Ikeda, K. Kanazawa, Y.Ohnishi, K. Oide, E. Perevedentsev, M. Tobiyama, S. Uehara, S. Uno, S.S. Win, Others…

2. Overview
Brief summary of beam measurements made at KEKB, in particular as they may relate to ones which can be made at CESR
Size (Fukuma)
Tune shift (Ieiri)
Coupled-bunch mode spectra (Tobiyama)
Single-bunch head-tail sideband signal
Focus on this – would like to try to see at CESR
Luminosity-related measurements

3. Electron cloud-induced beam blow-up
Vertical beam blow-up has been observed at KEKB LER (positron ring) at bunch currents above a threshold of ~0.35 mA/bunch, at a spacing of 4 rf buckets (~8 ns).
Blow-up due to photo-electrons kicked from wall by synchrotron radiation, which form clouds that interact with the positron beam.
Bunch-current blowup threshold can be raised by the use of solenoids around the beam pipe.
Currently about 95% of drift space in LER is covered.

4. LER Electron-cloud suppression solenoids
Fukuma et al., “Study of Vertical Beam Blow-up in KEKB LER,” HEAC01 proceedings

5. Blow-up measured by SR interferometer
Fukuma et al., “Study of Vertical Beam Blow-up in KEKB LER,” HEAC01 proceedings

6. Bunch-by-bunch beam size along train as measured by gated camera
Fukuma et al., “Study of Vertical Beam Blow-up in KEKB LER,” HEAC01 proceedings

7. Gated Camera Observations of Trailing Witness Bunch
J.W. Flanagan et al., Proc. EPAC00 (2000) 1119

8. Detection of photoelectrons at wall
Ohnishi et al., “DETECTION OF PHOTOELECTRON CLOUD IN POSITRON RING AT KEKB,” HEAC01

9. Tune Shift Measurements T.Ieiri, et al., PRST-AB 5, 094402 (2002)
Train Bunches
Witness Bunches

10. Tune Shift after Train
w/o Solenoids
T.Ieiri

11. Width of Tune Spectrum T.Ieiri
 Damping Rate is proportional to Frequency Width
 Spectrum Width depends on various effects
Wb: Radiation damping + Head-tail damping (Chromaticity, Impedance) + Beam-Beam + Electron Cloud
Wc: Feedback damping + Current ripple Nonlinear magnetic field
W0: RBW (Resolution Band Width)
T.Ieiri

12. Width vs Bunch Current T.Ieiri w/o Solenoids I_train=380 mA
ξx=1.7
ξy=4.8
 電流バンチとCloud密度 増加でwidth減少
T.Ieiri

13. Beam spectrum measurements
Bunch Oscillation Recorder
Digitizer synched to RF clock, plus 20-MByte memory.
Can record 4096 turns x 5120 buckets worth of data.
Calculate Fourier power spectrum of each bunch separately.
Inputs:
Feedback BPMs
6 mm diameter button electrodes
2 GHz （4xfrf) detection frequency, 750 MHz bandpass
Fast PMT

14. Coupled-Bunch Measurements M. Tobiyama et al
Coupled-Bunch Measurements M. Tobiyama et al., PRST-AB 9, (2006)
Abstract :
A coupled bunch instability caused by an electron cloud has been observed in the KEKB LER. The time evolution of the instabilities just after the turning-off the transverse bunch feedback was recorded with several weak solenoid-field conditions, which are used to suppress the vertical blowup of the beam size due to the electron cloud.
The mode spectra and their growth rates of the coupled-bunch instabilities were compared with simulations of electrons moving in drift space, a weak solenoid field and a strong bending field.
Mode spectra without a solenoid field support the model where the instability is dominated by the electron clouds in the drift space with a lower secondary yield of photoelectron 2,max = 1.0 rather than 1.5. With the solenoid field, the behavior of unstable modes and the growth rate with the strength of solenoid field also support the simulation with lower secondary emission yield.

15. Analysis Procedure

16. Horizontal Mode Spectra
Bsol=0%
Bsol=10%
Bsol=20%
Bsol=100%

17. Horizontal: Time evolution
Bsol=0%
Bsol=10%
Bsol=20%
Bsol=100%

18. Horizontal: Effect of Chromaticity
xx=-0.3
xx=-0.7

19. Vertical Mode Spectra
Bsol=0%
Bsol=10%
Bsol=20%
Bsol=100%

20. Vertical: Time Evolution
Bsol=0%
Bsol=10%
Bsol=20%
Bsol=100%

21. Vertical: Effect of Chromaticity
xy=5.2
xy=4.2

22. Single-bunch measurements: synchro-betatron sidebands
Vertical betatron sidebands found at KEKB which appear to be signatures of fast head-tail instability due to electron clouds.
J.W. Flanagan, K. Ohmi, H. Fukuma, S. Hiramatsu, M. Tobiyama and E. Perevedentsev, PRL 94, (2005)
Presence of sidebands also associated with loss of luminosity during collision.
J.W. Flanagan, K. Ohmi, H. Fukuma, S. Hiramatsu, H. Ikeda, M. Tobiyama, S. Uehara, S. Uno, and E. Perevedentsev, Proc. PAC05, p. 680 (2005)
Further studies have been performed:
Single beam studies:
Varying RF voltage
Varying chromaticity
Varying initial beam size below blow-up threshold (emittance)
In-collision studies:
Looking at specific luminosity below sideband appearance threshold
Looking at specific luminosity closer to head and tail of LER bunch

23. Fourier power spectrum of BPM data
V. Tune
Sideband Peak
LER single beam, 4 trains, 100 bunches per train, 4 rf bucket spacing
Solenoids off: beam size increased from 60 mm ->283 mm at 400 mA
Vertical feedback gain lowered
This brings out the vertical tune without external excitation

24. Spectra of Bunches 1-10 Bunch 1 Bunch 6 Bunch 2 Bunch 7 Bunch 3

25. Synchro-betatron sideband characteristics
Sideband appears at beam-size blow-up threshold, initially at ~nb+ns, with separation distance from nb increasing as cloud density increases.
Sideband peak moves with betatron peak when betatron tune is changed.
Sideband separation from nb changes with change in ns. (Flanagan et al., EPAC06)

26. Mode spectrum using model wake and airbag charge distribution.
Model focusing wake
a=wR/2Q
Mode spectrum using model wake and airbag charge distribution.
Sideband-betatron peak separation dependence on synchrotron tune reproduced.

27. Simulations of electron cloud induced head-tail instability E
Simulations of electron cloud induced head-tail instability E. Benedetto, K. Ohmi
Simulation (PEHTS)
(HEADTAIL gives similar results)
Betatron sideband
Tail of train
Head of train
Head-tail regime
Incoherent regime

28. Feedback does not suppress the sideband
Bunch by bunch feedback suppresses only betatron amplitude.
Betatron sideband
Simulation (PEHTS)
Sideband signal is Integrated over the train

29. PMT setup Partially block beam image with
black cardboard, and measure light
intensity of the visible part with a
PMT. The PMT signal is buffered
and then recorded using a feedback
BOR digitizer/memory board.
y: 100 mV/division
x: 10 ns/division

30. Beam Blow-up Measurement 4-bucket spacing, 600 bunches
4 trains, 150 bunches/train, 4 rf bucket spacing
Vertical beam size at IP (mm)
Blow-up threshold
250 mA, 0.42 mA/bunch
LER Beam Current (mA)

31. PMT Spectra
FB BPM Spectra
100 mA, 2.3 mm
200 mA, 2.7 mm
250 mA, 2.9 mm
Blow-up Threshold
300 mA, 3.6 mm
450 mA, 4.9 mm
Tune
Tune

32. Summary of BPM + PMT measurements
Sideband peak appears in both BPM and PMT measurements.
Two different types of detector
Sideband peak appears in both instruments only at and above the beam-size blow-up threshold of beam current
Other measurements show that the amplitude of the sideband peak at constant beam current is affected by the strength of the solenoid field. Stronger solenoid field  smaller sideband peak.

33. Time series data
BPM Data
(Position)
PMT Data
(Size)

34. Time Development of Instability: 512-turn slices
BPM data

35. Blow-up Pattern Analysis: PMT data
Find a bunch with characteristic
blow-up pattern, and take spectra of
3 stages separately. Then average
the 3 spectra over all bunches that
have this pattern.

36. Summary of time domain data
Sideband oscillation has a burst-like structure.
Sideband peak is present at a low level, then grows and damps in a burst lasting ~500 turns (5 ms).
During this burst, beam size grows ~5% from its already blown-up state
Immediately after burst is complete, sideband peak is absent, until beam size damps back down.

37. Threshold dependence on synchrotron tune
dns Data: 23 Dec 2003
Vc = 8 MV
Vc = 6 MV 25
Bunch 1
Tune
Tune
Data taken at 8 MV and 6 MV.
Sequence: 8 MV×2, 6 MV×2, 8 MV×2, 6 MV×1
Synch. Tune = 8 MeV, 6 MeV (measured from spectral peak).
Peak frequency bin in sideband region found, peak height averaged for 8 MV and 6 MV subsets separately.

38. Sideband Peak Height Near Threshold at Different ns

39. Effect of changing RF voltage 200 bunches/train, 4-bucket spacing, 0
Effect of changing RF voltage 200 bunches/train, 4-bucket spacing, 0.6 mA/bunch, xy = 4.27 νy
Sideband
Tail Head
Vc = 8 MV
FB gain = dB
Tail Head
Vc = 6 MV
FB gain = dB
Tune

40. Effect of varying synchrotron tune (RF voltage)
Sideband-tune separation does not change
Or does it? Hard to tell.

41. Model Spectrum
Dns

42. Effect of changing RF voltage
Separation is found to be close to Dns towards the head of the train, and it decreases going towards the back of the train, where the cloud density is higher.
Dns
Dns

43. Effect of changing RF voltage
Sideband onset is delayed along train (~3 bunches).
Confirms previous results.
Betatron peak growth is not delayed.
Note that it peaks just before sideband appears

44. Effect of Changing ns (RF Voltage)
Conclusion:
Threshold and separation between betatron peak and sideband peak are found to depend on ns, in agreement with model.

45. Effect of Changing Chromaticity
An effect predicted by head-tail theory is that the e-cloud density threshold for the onset of the instability should go up if the vertical chromaticity is raised.
Feedback gain was changed at each beam current to make ny visible. To make sure this did not affect results, also took data at same chromaticity and two different feedback gains.

46. Sidebands at Different xyny
Noise
Sideband
xy = 1.27
xy = 4.27
FB Gain = dB
FB Gain = dB
Joining/Splitting?
xy = 6.27
xy = 6.27
FB Gain = dB
FB Gain = dB

47. Sideband Peak Heights
xy=1.27
xy=4.27
xy=6.27, FB gain = -14.9dB
xy=6.27, FB gain = dB
Note: For KEKB, Dxy ~ 3 should correspond to a change in cloud-density threshold of ~10%

48. Simulated E-cloud build-up at KEKB Wang et al., PRSTAB 5 124402 (2002)
Bunch:

49. Effect of Changing Chromaticity
The lower the chromaticity, the earlier in the train the sideband appears. (No change is seen for two different feedback gains at xy=6.3, as expected.) Raising xy from 1.3 to 4.3 pushes the onset of the instability back ~10 bunches along the train, as does further increasing xy from 4.3 to From simulations of electron cloud build-up (L.F. Wang, et al., PRSTAB (2002)), these would correspond do changes in the electron cloud density of ~20-40%.
In numerical simulations (K. Ohmi, Proc PAC, Chicago, p (2001)), changing xy from 0 to 12 raises the threshold by a factor of 2, from 5x1011 electrons/m3 to 1x1012 electrons/m3. Scaling from this, each change in xy used in the machine study would be expected to change the threshold by ~20.
Basic agreement between simulations and experimental results.

50. Effect of Forced Excitationnx ny
Side-band
Experiment performed on a non-colliding bunch during physics operation, with the cloud-suppression solenoids on. A test bunch was inserted between two bunches (high cloud region).
Test bunch was excited near the vertical tune. Bunch-by-bunch feedback was turned off for this bunch.
As the excitation amplitude increased, in addition to the betatron peak amplitude increasing, the sideband amplitude decreased, dropping below detectable levels at the highest excitation amplitude.
Mechanism under investigation

51. Sidebands in Collision
How do sidebands behave in collision?
They are present, but smeared out compared to their appearance in non-colliding bunches. nx ny
Sideband ny
Sideband

52. Specific Luminosity Studies
Electron cloud instability in a bunch depends on
Cloud density encountered by bunch
Bunch current of the bunch itself (must be sufficient to pinch the cloud)
But this may be a weak dependence.
Two studies reported on at PAC05:
Constant cloud, decaying bunch current.
Inject extra test bunch into regular physics pattern, let it decay from 1.2 mA to zero.
Space between test bunch and preceeding bunch is 2 rf buckets (~4 ns).
Decaying cloud, constant bunch current.
Inject extra test bunch, let it decay, and look at observer bunch behind it.
Space between observer bunch and test bunch preceeding it is again 2 rf buckets (~4 ns).
In both cases, have one colliding test/observer bunch and one non-colliding test/observer bunch.
Compare spectrum of non-colliding bunch, and specific luminosity of colliding bunch.

53. Zero-Degree Luminosity Monitor (ZDLM) S. Uehara and S. Uno (Belle)
Set just downstream of quadrupole QC2RP near interaction point.
Detects recoil electrons emitted to the zero-degree angle and deflected to the outside by Q magnetic fields
Pb Glass 50 x 70 x 190 mm & a PMT
Record Hit Timings
Monitor Rates

54. ZDLM Bunch-by-Bunch Luminosity Display

55. Decaying Cloud, Constant Bunch Current Study
Test Bunch
Constant
Observer Bunch
Fill Pattern:
Buckets: 4 3 4 3 2 2 3
Regular physics pattern bunches
Average spacing: 3.5 buckets
Bunch current: Constant 1.2 mA
(using continuous injection)

56. Sideband Peak Tune Tune of sideband peak drifts down as cloud decays.
Sideband peak tune constant if cloud constant, even if bunch current decays.
Decaying Cloud
Constant Bunch
Constant Cloud,
Decaying Bunch

57. Decaying Cloud, Constant Bunch Current Sideband Peak Heights
Sidebands disappear below test bunch current of ~0.4 mA

58. Decaying Cloud, Constant Bunch Current Specific Luminosity
Specific luminosity of observer bunch is lower than that of regular bunches above 0.4 mA, but is the same below 0.4 mA.
Consistent with sideband behavior, and explanation that loss of specific luminosity is due to electron cloud instability.

59. Decaying Cloud, Constant Bunch Current (Second Attempt)

60. Ratio of specific luminosities at varying cloud density

61. Sideband Integrated Power (05.6.26)
DAQ Down

62. Constant Cloud, Decaying Bunch Current Study
Test Bunch
Fill Pattern:
Buckets: 4 3 4 3 2 2 3
Regular physics pattern bunches
Average spacing: 3.5 buckets
Bunch current: 1.2 mA constant
(using continuous injection)

63. Constant Cloud, Decaying Bunch Current Sideband Peak Heights
Sidebands disappear below test bunch current of ~0.75 mA

64. Constant Cloud, Decaying Bunch Current Specific Luminosity
Specific luminosity of observer bunch is lower than that of regular bunches above 0.75 mA, but is the same below 0.75 mA.
Again, consistent with sideband behavior, and explanation that loss of specific luminosity is due to electron cloud instability.
Also consistent with streak camera observations of vertical bunch size: bunch larger above ~0.8 mA.
H. Ikeda et al., PAC05 poster RPAT052.

65. Constant Cloud, Decaying Bunch Current Study II (Higher cloud density)
Test Bunch
Fill Pattern:
Buckets: 4 3 4 3 2 2 3
Regular physics pattern bunches
Average spacing: 3.5 buckets
Bunch current: 1.2 mA constant
(using continuous injection)

66. Sideband Integrated Power (Higher cloud, decaying bunch)

67. Difference in specific luminosities at higher cloud density (Run 1)

68. Difference in specific luminosities at higher cloud density (Run 2)

69. Higher cloud density, decaying current
Sidebands disappear at around a bunch current of 0.8 mA.
Specific luminosity of high-cloud and low-cloud bunches do not merge at that point, however.
Possible that sidebands continue, but below noise level.
Or possible indication of the presence of an incoherent component below the sideband threshold (non-linear focusing by cloud leading to non-Gaussian beam tails, e.g.)
Alternatively, simple tune shift due to focusing effect of cloud?

70. Dependence of Lum. On Tune
Luminosity drops about 1% for a change of in tune.
Tune of high-cloud bunch is 0.01 greater than that of no-cloud bunch, while luminosity is 20% lower.
Hard to trust extrapolation
Specific Luminosity
During study
Specific Luminosity
Tuning after study
LER Vertical Tune

71. Decaying Cloud, Decaying Bunch Current Study
Lead Bunch
Decaying
Test Bunch
Fill Pattern:
Buckets: 4 3 4 3 2 2 3
Regular physics pattern bunches
Average spacing: 3.5 buckets
Bunch current: 1.2 mA constant
(using continuous injection)

72. Sideband power (Decaying Cloud, Decaying Bunch)

73. Specific luminosities for decaying cloud, decaying bunch

74. Sideband Power at low cloud density, decaying bunch

75. Difference in specific luminosities at low cloud density, decaying bunch

76. Summary of Luminosity Studies
For high bunch-current beams and a varying cloud density, the luminosity loss accompanies the appearance of betatron sidebands, indicating the onset of head-tail instability.
For high cloud density and varying bunch currents, even low-current bunches have a similar luminosity loss as high-current bunches.
Sidebands not visible at low currents: signal present but below noise threshold? (Measured signal proportional to square of bunch current.)
Or else indication of incoherent effects below head-tail instability threshold, as predicted by simulation.

77. Collision Offset Study
Background: We get the best luminosity with a non-zero horizontal offset at the interaction point.
Question: Could this be due to electron cloud blow-up in the tail of the LER bunch?
Indications are yes (Ieiri et al., PRSTAB 8, (2005))

78. Collision Offset Study T. Ieiri et al., PRSTAB 8, 124401 (2005)
Measurements of total luminosity, beam-beam kick, and beam-beam tune shift made at different horizontal collision offsets showed lower luminosity at tail of bunch than at head of bunch, attributed to effects of electron cloud on positron beam.
Measurements made with all bunches at same current:
High-cloud, high “observer” bunch current
Los-cloud, low “observer” bunch current

79. Follow-up Collision Offset Study
Use bunch-by-bunch luminosity monitor.
Vary cloud density by letting pilot bunch in front of observer bunch decay.
Vary observer bunch current while keeping pilot bunch current constant.

80. Collision Offset Study
LER
HER
+25 mm
0 mm
-25 mm
-40 mm
LER
HEAD in
Collision
LER
TAIL in
Collision

81. Decaying Cloud, Constant Current
LER
HEAD in
Collision
LER
TAIL in
Collision
Low
Cloud
Density
High
Cloud
Density
Low
Cloud
Density
High
Cloud
Density

82. Constant Cloud, Decaying Current
LER
HEAD in
Collision
LER
TAIL in
Collision

83. Implications
Tune shifts due to cloud should increase towards the tail of the bunch due to pinching.
As the bunch current decreases, the pinching effect should become weaker.
This would imply that the luminosity difference between the head and tail of the bunch should decrease as the bunch current decreases.
The fact that this does not happen suggests that simple tune shift is not the dominant mechanism for luminosity loss under high-cloud, low bunch current conditions.
e- cloud
e+ bunch

84. Collision Offset Study
Conclusion:
Under high-cloud conditions, specific luminosity appears to be lower towards the tail of the LER bunch than towards the head.
Under low-cloud conditions, there is no specific luminosity difference between the head and tail of the LER bunch.
Agrees with Ieiri’s results
In addition, we find that under high-cloud but low-bunch-current conditions, the luminosity difference between the head and the tail of the bunch is the same as for a high-current bunch.
This suggests that the mechanism of luminosity loss for high-cloud/low-current conditions is not primarily due to simple tune shift. If it were, then the difference between the head and tail of the bunch would be expected to decrease as the bunch current decreases, due reduced cloud pinching.

85. Summary
Electron cloud-related beam dynamics observables include beam size, tune shift, tune spread, and coupled-bunch effects, which all react to the presence of solenoids.
Above the blow-up threshold, single-bunch synchro-betatron sidebands indicative of head-tail instability appear. Below threshold, possible indications of incoherent effects as well.
Much to measure.

86. Still time to register!

87. Spares

88. Effect of Changing Emittance
At a low current (200 mA) below the blow-up threshold, the vertical emittance of the beam was adjusted via dispersion bumps that are used for luminosity tuning. The beam size was set to 1, 2.3, and 3.2 mm (as expressed at the interaction point) in successive runs, and at each initial beam size the beam current was then ramped up to 600 mA while recording beam sizes and spectra.
The instability threshold does not depend on initial beam size.