1. e+/e- Vertical Beam Dynamics during CHESS Operation-Part II
Introduction
e+ turn-by-turn vertical dynamics
e- turn-by-turn vertical dynamics
Summary
R. Holtzapple, J. Kern, and E.Tanke
November 16, 2006

2. I. Introduction e+/e- CHESS 9x6 Pattern Single bunch currents
Turn-by-turn vertical beam distribution measurements made at the top, middle, and bottom of a CHESS fill.
Similar analysis was done on 11/2/06.
e+ current/bunch
Lifetime grows along the train.
e- current/bunch.

3. II. e+ turn-by-turn measurements
e+ single bunch vertical bunch distributions from the PMT array.
9,000 turns of all 54 e+/e- bunches.
High I File:924 Ie+=3.7mA/bunch
Note difference in sv
e+ Bunch 1 Train 1
1st ten turns (movie)
e+ Bunch 6 Train 2
1st ten turns (movie)

4. e+ Vertical Position
Mean vertical position for 9,000 turns for 54 bunches.
Low frequency vertical oscillation is denoted for all 54 bunches.
Low I File:921
Ie+=3.1mA/bunch (movie)
High I File:924
Ie+=3.7mA/bunch (movie)
Medium I File:920
Ie+=3.5mA/bunch (movie)

5. e+ vertical position oscillation-FFT of vertical position for 9,000 turns
FFT of the vertical position.
The vertical position oscillation frequency is denoted in the FFT spectrum.
High I File:924
Ie+=3.7mA/bunch (movie)
Medium I File:920
Ie+=3.5mA/bunch (movie)
Low I File:921
Ie+=3.1mA/bunch (movie)

6. e+ high frequency vertical motion-FFT Power
High I File:924 Ie+=3.7mA/bunch
Medium I File:920 Ie+=3.5mA/bunch
Low I File:921 Ie+=3.1mA/bunch

7. e+ high frequency vertical motion-FFT Frequency of Oscillation
Detailed View
Dfosc=2.5kHz
High I File:924 Ie+=3.7mA/bunch
Detailed View
Dfosc=2.0kHz
Medium I File:920 Ie+=3.5mA/bunch
Dfosc=1.75kHz
Oscillation frequency shift, Dfosc, along the trains is current dependent.
Large frequency jump is occasionally noted.
Low I File:921 Ie+=3.1mA/bunch

8. e+ FFT power dependence on vertical position oscillation amplitude–High I
Bunch 3
Peak
yavg=1.78mm
Std=0.013mm
Bunch 41
Peak
yavg=1.77mm
Std=0.015mm
Bunch 13
Peak
yavg=1.73mm
Std=0.018mm
Noisy FFT spectrum background
File:924 Ie+=3.7mA/bunch
Noisy FFT spectrum correlates to increased vertical position oscillation amplitude.

9. e+ FFT power dependence on vertical position oscillation amplitude–Medium I
Bunch 12
Peak
yavg=1.700mm
Std=0.014mm
Bunch 24
Peak
yavg=1.668mm
Std=0.016mm
Many peaks and noise in FFT spectrum.
Bunch 1
Peak
yavg=1.718mm
Std=0.011mm
File 920 Ie+=3.5mA/bunch
Increase of vertical position oscillation amplitude noted in FFT spectrum

10. e+ FFT power dependence on vertical position oscillation amplitude–Low I
Bunch 1
Peak
yavg=1.611mm
Std=0.013mm
Bunch 9
Peak
yavg=1.623mm
Std=0.014mm
Bunch 24
Peak
yavg=1.586mm
Std=0.015mm
No real peak in FFT spectrum but noisy FFT spectrum background
File:921 Ie+=3.1mA/bunch
Noisy FFT spectrum correlates to increased vertical position oscillation amplitude.

11. e+ high frequency vertical motion High I File:924 Ie+=3.7mA/bunch
High FFT noise
Bunch 49
yavg=1.735mm
Std=0.017mm
e+ high frequency vertical motion
High I File:924 Ie+=3.7mA/bunch
Several bunches oscillate over a wide frequency spectrum-particularly bunches 12,31,49 (noisy FFT spectrum). The bunches have large oscillation amplitudes.
The peak oscillation frequency of fosc=195.2kHz=1/2*frev appears for the last bunch in a train. These bunches have a large oscillation amplitude that does not correlate with FFT noise.
Bunch 12
yavg=1.726mm
Std=0.017mm
High FFT noise
Low FFT noise
Bunch 3
yavg=1.780mm
Std=0.013mm

12. e+ vertical position oscillation amplitude
High I File:924
Ie+=3.7mA/bunch
Medium I File:920
Ie+=3.5mA/bunch
Low I File:921
Ie+=3.1mA/bunch
e+ vertical position oscillation amplitude (standard deviation of vertical position) does not correlate with FFT power. Instead, the amplitude increases with FFT noise.

13. e+ sv along the train sv 9,000 turns for 54 bunches.
Significant vertical beam size growth along each train-especially at high I
Low I File:921
Ie+=3.1mA/bunch (movie)
High I File:924
Ie+=3.7mA/bunch (movie)
Medium I File:920
Ie+=3.5mA/bunch (movie)

14. e+ high frequency sv oscillation frequency-FFT of sv for 9,000 turns
FFT of sv for all 54 bunches
No clear oscillation frequency in the vertical beam size-incoherent oscillation.
High I File:924
Ie+=3.7mA/bunch (movie)
Medium I File:920
Ie+=3.5mA/bunch (movie)
Low I File:921
Ie+=3.1mA/bunch (movie)

15. e+ high frequency sv oscillation frequency - FFT of sv - High I
Bunch 31
Peak
sv=0.328mm
Std=0.021mm
Bunch 15
Peak
sv=0.172mm
Std=0.009mm
Bunch 5
Peak
sv=0.236mm
Std=0.012mm
File 924 Ie+=3.7mA/bunch
Noisy FFT spectrum correlates with an increased sv.

16. e+ high frequency sv oscillation frequency - FFT of sv – Medium I
Bunch 6
Peak
sv=0.372mm
Std=0.021mm
Bunch 13
Peak
sv=0.223mm
Std=0.014mm
Bunch 43
Peak
sv=0.170mm
Std=0.009mm
File 920 Ie+=3.5mA/bunch
Noisy FFT spectrum correlates with an increased sv.

17. e+ high frequency sv oscillation frequency- FFT of sv - Low I
Bunch 25
Peak
sv=0.159mm
Std=0.009mm
Bunch 54
Peak
sv=0.221mm
Std=0.013mm
Bunch 6
Peak
sv=0.301mm
Std=0.018mm
File 921 Ie+=3.1mA/bunch
At low I the vertical beam size growth is reduced (still correlates with FFT noise). sv is largest for last bunch in each train.

18. e+ sv oscillation amplitude
High I File:924
Ie+=3.7mA/bunch
Medium I File:920
Ie+=3.5mA/bunch
Low I File:921
Ie+=3.1mA/bunch
e+ sv oscillation amplitude (standard deviation of sv) correlates with FFT power.

19. III. e- turn-by-turn measurements
e- single bunch vertical bunch distributions from the PMT array.
9,000 turns of all 54 e+/e- bunches.
High I File:923 Ie-=4.3mA/bunch
Note difference in sv
e- Bunch 1 Train 1
1st ten turns (movie)
e- Bunch 5 Train 6
1st ten turns (movie)

20. High I File:923 e- Vertical Position
Mean vertical position for 9,000 turns for 54 bunches.
High I File:923
Ie-=4.3mA/bunch (movie)
Medium I File:922
Ie-=4.1mA/bunch (movie)
Low I File:919
Ie-=3.8mA/bunch (movie)

21. e- high frequency vertical position oscillation-FFT of vertical position for 9,000 turns
High I File:923
Ie-=4.3mA/bunch (movie)
Medium I File:922
Ie-=4.1mA/bunch (movie)
Low I File:919
Ie-=3.8mA/bunch (movie)
FFT of the vertical position.
Vertical position oscillation signal is prominent in the FFT spectrum.

22. e- high frequency vertical position oscillation-close up of the oscillation frequency foscillation
Medium I File:922
Ie-=4.1mA/bunch (movie)
Low I File:919
Ie-=3.8mA/bunch (movie)
High I File:923
Ie-=4.3mA/bunch (movie)
Vertical position oscillation frequency shifts along the train.

23. e- high frequency vertical position oscillation-FFT Power
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Low I File:919
Ie-=3.8mA/bunch
FFT power increases along the train

24. e- high frequency vertical position oscillation-Frequency of Oscillation
Detailed View
Dfosc=1.5kHz
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Oscillation frequency shift, Dfosc, along the trains is current dependent.
Large frequency jump is occasionally noted
Dfosc=1.5kHz
Low I File:919
Ie-=3.8mA/bunch
Dfosc=1kHz
Detailed View

25. e- high frequency vertical position oscillation - FFT of vertical position – High I
Bunch 31
Peak
yavg=2.631mm
Std=0.022mm
Bunch 33
Peak
yavg=2.619mm
Std=0.024mm
Bunch 35
Peak
yavg=2.665mm
Std=0.034mm
File:923 Ie-=4.3mA/bunch
Vertical position oscillation amplitude correlates with FFT power.

26. e- high frequency vertical position oscillation - FFT of vertical position – Medium I
Bunch 31
Peak
yavg=2.715mm
Std=0.021mm
Bunch 33
Peak
yavg=2.708mm
Std=0.024mm
Bunch 35
Peak
yavg=2.736mm
Std=0.031mm
File:922 Ie-=4.1mA/bunch
Vertical position oscillation amplitude correlates with FFT power.

27. e- high frequency vertical position oscillation - FFT of vertical position – Low I
Bunch 13
Peak
yavg=2.651mm
Std=0.021mm
Bunch 15
Peak
yavg=2.647mm
Std=0.025mm
Bunch 17
Peak
yavg=2.685mm
Std=0.035mm
File:919 Ie-=3.8mA/bunch
Vertical position oscillation amplitude correlates with FFT power.

28. e- vertical position oscillations amplitude correlation FFT Power
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Correlation between e- vertical position oscillation amplitude and FFT power. Signature of coherent oscillation.
Low I File:919
Ie-=3.8mA/bunch

29. e- sv along the train sv 9,000 turns for 54 bunches.
Vertical beam size growth along each train.
High I File:923
Ie-=4.3mA/bunch (movie)
Medium I File:922
Ie-=4.1mA/bunch (movie)
Low I File:919
Ie-=3.8mA/bunch (movie)

30. e- high frequency sv oscillation frequency-FFT of sv for 9,000 turns
High I File:923
Ie-=4.3mA/bunch (movie)
Medium I File:922
Ie-=4.1mA/bunch (movie)
Low I File:919
Ie-=3.8mA/bunch (movie)
FFT of sv for all 54 bunches
Strong sv oscillation signal.

31. e- high frequency sv oscillation frequency-FFT of sv-Close up of the oscillation frequency foscillation
High I File:923
Ie-=4.3mA/bunch (movie)
Medium I File:922
Ie-=4.1mA/bunch (movie)
Low I File:919
Ie-=3.8mA/bunch (movie)
sv oscillation frequency shifts along the train.

32. e- high frequency sv oscillation-FFT Power
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Low I File:919
Ie-=3.8mA/bunch
FFT power of sv grows along the train except for bunch 6 in trains 1,4,7 (note different fosc for these bunches on the next page).

33. e- high frequency sv oscillation-Frequency of Oscillation
Dfosc=1.5kHz
Detailed View
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Dfosc=1.5kHz
Low I File:919
Ie-=3.8mA/bunch
Dfosc=2.0kHz
An oscillation frequency shift, Dfosc, is noted along the trains.
A large frequency jump is noted for bunch 6 in trains 1, 4, and 7.

34. e- high frequency sv oscillation - FFT of sv – High I
Bunch 13
Peak
sv=0.224mm
Std=0.021mm
Bunch 15
Peak
sv=0.256mm
Std=0.029mm
Bunch 17
Peak
sv=0.288mm
Std=0.035mm
File:923 Ie-=4.3mA/bunch
sv oscillation amplitude correlates with FFT power

35. e- high frequency sv oscillation - FFT of sv – Medium I
Bunch 31
Peak
sv=0.217mm
Std=0.023mm
Bunch 33
Peak
sv=0.239mm
Std=0.029mm
Bunch 35
Peak
sv=0.282mm
Std=0.036mm
File:922 Ie-=4.1mA/bunch
sv oscillation amplitude correlates with FFT power

36. e- high frequency sv oscillation - FFT of sv – Low I
Bunch 6
Peak
sv=0.225mm
Std=0.022mm
Bunch 8
Peak
sv=0.241mm
Std=0.027mm
Bunch 10
Peak
sv=0.290mm
Std=0.037mm
File:919 Ie-=3.8mA/bunch
sv oscillation amplitude correlates with FFT power.

37. e- sv oscillation amplitude correlation with FFT Power
Direct correlation between sv oscillation amplitude (standard deviation of sv) and FFT power- coherent oscillation of sv oscillation amplitude.
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Low I File:919
Ie-=3.8mA/bunch

38. e- sv correlated with FFT Power
Direct correlation between sv oscillation and FFT power- sv growth due to coherent instability
High I File:923
Ie-=4.3mA/bunch
Medium I File:922
Ie-=4.1mA/bunch
Low I File:919
Ie-=3.8mA/bunch

39. IV Summary e+ turn-by-turn vertical dynamics:
The e+ vertical position oscillation is denoted in the FFT spectrum of the vertical position. The vertical position oscillation frequency shifts along the train. Occasionally, a large jump in the oscillation frequency was noted. As the bunch current is increased the oscillation frequency shift increases along the train. The vertical position oscillation amplitude is not dependent on the FFT power but correlates with noise in the FFT spectrum.
Significant e+ sv growth along each train was measured and is dependent on the bunch current. No clear oscillation frequency of sv was measured and sv’s growth correlates with the noise in the FFT spectrum This is a signature that an incoherent instability causes the sv growth along the train. In addition, the e+ sv oscillation amplitude correlates with FFT power.
e- turn-by-turn vertical dynamics:
The e- vertical position oscillation is prominent in the FFT spectrum and the oscillation frequency shifts along the train increase slightly with current. Occasionally, a large jump in the oscillation frequency was noted for bunch 6 in trains 1,4,7. The vertical oscillation amplitude correlates with the FFT power which is a signature of a coherent oscillation.
A sv growth and oscillation along the e- trains was measured. The sv oscillation frequency shifts along the train. The sv oscillation amplitude (standard deviation of sv) correlates with the FFT power. A direct correlation between sv and FFT power suggests a coherent instability is the cause of the sv growth along the trains.
Differences from 11/2/06 results are denoted in red.