e-/e+ Vertical Beam Dynamics with 6 and 12Wigglers On

e-/e+ Vertical Beam Dynamics with 6 and 12Wigglers On
Content I. Introduction II. e+ 6 wigglers on/6 wigglers off III. e+ 12 wigglers on IV. e- 6 wigglers on/6 wigglers off V. e- 12 wigglers on R. Holtzapple, G.Codner, M.Palmer, and E.Tanke 9/6/2006

e+/e- vertical distributions
I. Introduction: Goal: Examine e+/e- turn-by-turn vertical beam dynamics for 45 bunch train at CESR-c operating point. e+/e- vertical beam dynamics were measured in: 6 wiggler magnet configuration-14-15E/W on, 19E/W triplets are off 12 wiggler magnet configuration-14-15E/W and 19E/W triplets are on Vertical feedback was adjusted under certain current conditions. PMT calibration for the analysis is 10mm/pixel for both e- and e+. The calibration was measured to be 10.4mm/pixel for e+ and 8.6mm/pixel for e- on 9/18/2006. e+/e- vertical distributions e- 12 wigglers on I=1.25mA/bunch (movie) e+ 12 wigglers on I=0.84mA/bunch (movie)

II. e+ 6 wigglers on/6 wigglers off
Significant tune shift, Qy and Qx, along the 45 bunch trains

Bunch current is not uniform along the train at high current.

File 548 bunch 34 Movie Unstable outliers Detailed view

Detailed view

FFT Vertical position Ie+=0.25mA/bunch
File:545 e+ 6 wigglers on, 6 wigglers off Vert. Vertical position movie The vertical position oscillation frequency, fosc=235.8kHz, is determined from the FFT of the vertical position. There is a correlation between standard deviation of the vertical position (vertical position oscillation amplitude) and FFT power of mean position.

File:545 e+ 6 wigglers on, 6 wigglers off Vert. Fdbck@-1
FFT sv Ie+=0.25mA/bunch File:545 e+ 6 wigglers on, 6 wigglers off Vert. Bunch 2 movie sv movie A dramatic jump in vertical beam size occurs at bunch 3 and slow decays by bunch 11. This jump correlates with a peak in FFT spectrum at f=235.8kHz. From bunch there are only small fluctuations in sv. The standard deviation of sv (sv oscillation amplitude) is fairly constant along the train. Bunch 3 movie

File:542 e+ 6 wigglers on, 6 wigglers off Vert. The vertical position oscillation frequency is fosc=235.8kHz. The vertical position oscillation amplitude increased with bunch current and correlates with FFT power. Bunch 41 has a broad frequency spectrum. Vertical position movie

FFT sv Ie+=0.6mA/bunch File:542 e+ 6 wigglers on, 6 wigglers off Vert. Detailed view sv movie From the FFT of sv, a broad frequency spectrum is detected for bunch 41. Bunch 41 has a large vertical position and sv oscillation amplitude. A 45% decrease in sv for bunch 3 (compared to I=0.25mA/bunch). sv growth along the 45 bunch trains starts at bunch 23.

Bunch 36 fosc=307.2kHz fosc=236.6kHz
At the onset of the beam blow-up at bunch 41, two peaks in the FFT spectrum is observed at fosc=236.6kHz (cycles/turn=0.396) and fosc=307.2kHz (cycles/turn=0.213). Bunch 36-movie Bunch 41-movie Bunch 42-movie

File:552 e+ 6 wigglers on, 6 wigglers off Vert. Main peak Secondary peak Turn on vertical feedback: Vertical feedback reduces the vertical position oscillation amplitude. The oscillation amplitude correlates with FFT power. The vertical position oscillation frequency has two peaks, at fosc=236.6kHz (0.396 cycles/turn), and fosc=354.9kHz (0.091 cycles/turn). Vertical position movie

FFT sv Ie+=0.63mA/bunch File:552 e+ 6 wigglers on, 6 wigglers off Vert. FFT spectrum peak correlates with maximum sv measured for bunch 3. Feedback reduces bunch 3 sv slightly. Vertical feedback eliminated the sv growth near the end of the train. sv movie

File:539 e+ 6 wigglers on, 6 wigglers off Vert. Slight increase in current and vertical feedback results in: A reduction the vertical position oscillation amplitude. An increase in the secondary oscillation frequency signal. The oscillation amplitude increases with FFT power. Vertical position movie

FFT sv Ie+=0.7mA/bunch File:539 e+ 6 wigglers on, 6 wigglers off Vert. Peak in the FFT spectrum correlates with bunch 3 sv. sv growth along the train start at bunch 25. No clear oscillation frequency in the vertical beam size in detected. Signature of incoherent oscillation. sv movie

File:550 e+ 6 wigglers on, 6 wigglers off Vert. Increase in vertical feedback results in: Reduction in vertical position oscillation amplitude. The amplitude increases with FFT power. Increase in secondary oscillation frequency in the FFT spectrum. Vertical position movie

FFT sv Ie+=0.70mA/bunch File:550 e+ 6 wigglers on, 6 wigglers off Vert. Further reduction in sv of bunch 3. The peak in the beam spectrum is no longer present. sv growth along the train starts at bunch 31 (moved later in the train). sv movie

File:548 e+ 6 wigglers on, 6 wigglers off Vert. Coherent vertical position oscillation at fosc=236.7kHz Incoherent vertical position oscillation At I=0.75mA/bunch turning off the vertical feedback resulted in: An increase in the vertical position oscillation amplitude at fosc=236.7kHz A vertical position oscillation for bunches 25,35,36, and where: -the oscillation amplitude does not correlate with FFT power. -A wide spectrum of frequency oscillations are present in the FFT spectrum. Vertical position movie

fosc fosc FFT sv Ie+=0.75mA/bunch
File:548 e+ 6 wigglers on, 6 wigglers off Vert. fosc fosc Incoherent sv oscillation sv movie At I=0.75mA/bunch and no vertical feedback: sv growth along the train starts at bunch 16. Two oscillations frequencies are present, at fosc=236.6kHz and fosc=306.5kHz. Along the train the vertical position oscillation amplitude increases until a significant sv blows-up occurs. The process repeats three times over the 45 bunches.

Bunches 26-34 Spectrum and bunch distribution leading up to beam blow-up for I=0.75mA/bunch and vertical feedback off. Bunches 1-24 Bunch 34 I=0.86mA Movies Bunch 35 I=0.62mA Characteristics of sv blow-up along the train: Increase in FFT power at fosc=236.6kHz and fosc=306.5kHz. Increase in vertical position oscillation amplitude (bunch 34). Substantial increase in sv (bunches 34-36). Stable vertical position and sv (bunch 37). Repeat process. Bunches 37-43 Bunch 36 I=0.52mA Bunch 37 I=0.84mA

Summary e+ vertical dynamics with 6 wigglers on/off
As the bunch current increases, the vertical tune shift along the 45 bunch train increases. A vertical position oscillation along the 45 bunch train is always present at bunch currents measured. The position oscillation amplitude increases with current and decreases with vertical feedback. The FFT power from the vertical position correlates with the vertical oscillation amplitude. At low current, a substantial sv increase was measured for bunches As the current and vertical feedback is increased, the sv for these bunches is reduced. As the bunch current is increased, sv growth along the 45 bunch train occurs. If vertical feedback is turned off, a large vertical position oscillation amplitude causes a significant increase in sv. This sv blow-up appears to be incoherent due to the lack of structure in the FFT spectrum.

III. e+ 12 wigglers on Along the 45 bunch train,
DQy (12 wigglers on) > DQy (6 wigglers on/off)

Large fluctuations in bunch current along the train at higher bunch current.

Detailed view

File:570 e+ 12 wigglers on Vert. Vertical position oscillation at fosc=234.7kHz. Oscillation amplitude correlates with FFT Power. Large vertical position oscillation amplitude for bunches 3-7. Vertical position movie

FFT sv Ie+=0.25mA/bunch File:570 e+ 12 wigglers on Vert. Bunch 1 Dist. Movie Dramatic jump in sv for bunches 3-7 which correlates with a peak in the beam spectrum at fosc=235.1kHz. Equilibrium sv is larger with 12 wigglers on (sv=0.31mm) than with 6 wigglers on/off (sv=0.26mm). No sv growth along the train after bunch 7. sv movie Bunch 3 Dist. Movie

File:564 e+ 12 wigglers on Vert. Increasing the current and with vertical feedback off causes a: An increase in the vertical position oscillation amplitude. The amplitude as a frequency of fosc=234.6kHz and correlates with FFT power. The last bunch in the train has a large oscillation amplitude over a wide frequency spectrum. Vertical position movie

FFT sv Ie+=0.75mA/bunch File:564 e+ 12 wigglers on Vert. sv movie At higher current, sv for bunch 3 is reduced. A gradual sv growth occurs at ~bunch 30. No single sv oscillation frequency is in the beam spectrum leading up to the bunch 45 sv blow-up.

File:565 e+ 12 wigglers on Vert. Turn vertical feedback on results in: A substantial reduction in the vertical position oscillation amplitude (fosc=234.2kHz). The amplitude still correlates with FFT power. A second oscillation frequency is detected at fosc=209.36kHz (0.463 cycles/turn). Vertical position movie

Vertical Feedback on/off
FFT sv Ie+=0.75mA/bunch File:565 e+ 12 wigglers on Vert. sv growth occurs at bunch 31 but at a slower rate compared to no feedback on. The reduction of the vertical position oscillation amplitude eliminates the sv blow-up at the end of the train. sv movie I=0.75mA/bunch Vertical Feedback on/off

File:562 e+ 12 wigglers on Vert. Vertical position movie Slightly higher I and turning off vertical feedback results in: A large vertical position oscillation amplitude that does not correlate with FFT power. A position oscillation (coherent) amplitude that correlates with FFT power and an oscillation amplitude (incoherent) that does not correlate with FFT power.

FFT sv Ie+=0.84mA/bunch File:562 e+ 12 wigglers on Vert. sv growth along the train starts at ~bunch 21. Two main peaks in the beam spectrum at fosc=235.4 and 310kHz. Large vertical position oscillation amplitude leads to a sv blow-up occurs at several locations in the 45 bunch train. sv movie

Spectrum and bunch distribution leading up to beam blow-up with I=0
Spectrum and bunch distribution leading up to beam blow-up with I=0.84mA/bunch and vertical feedback off Bunches 20-27 Bunches 28-37 Bunch 36 I=0.66mA Movies Bunch 37 I=0.92mA Characteristics of sv blow-up along the train: Increase in FFT power at fosc=236.6kHz and fosc=306.5kHz. Increase in vertical position oscillation amplitude (bunch 36-37). Substantial increase in sv (bunches 38). large vertical position oscillation amplitude but reduced sv (bunch 39). Repeat process. Bunches 39-43 Bunch 38 I=0.91mA Bunch 39 I=0.91mA

File:560 e+ 12 wigglers on Vert. Turn on vertical feedback: Large reduction in vertical position oscillation amplitude (fosc=234.6kHz). Oscillation amplitude correlates with FFT spectrum that grows along the train. Vertical position movie

FFT sv Ie+=0.84mA/bunch File:560 e+ 12 wigglers on Vert. sv growth occurs at bunch w/o feedback). No clear sv oscillation frequency is denoted in the FFT spectrum. sv movie

File:558 e+ 12 wigglers on Vert. Increase current and feedback: Vertical position oscillation amplitude is reduced (fosc=234.2kHz). Amplitude correlates with FFT power. Vertical position movie

FFT sv Ie+=0.90mA/bunch File:558 e+ 12 wigglers on Vert. At high I with feedback on: sv growth starts at bunch 22. No distinct sv oscillation frequency is apparent in the beam spectrum. No significant change in sv along the 45 bunch train due to the increase vertical feedback. sv movie

Summary e+ vertical dynamics with 12 wigglers on
The vertical tune shift along the 45 bunch train increases with current. DQy(12 wigglers) > DQy(6 wigglers on/off). At low current, the sv blows-up for bunches As the bunch current is increased, sv for bunches 3-7 decreases. A coherent vertical position oscillation along the 45 bunch train is always present (at all currents measured). The position oscillation amplitude increases with current and decreases with vertical feedback. The FFT power from the vertical position correlates with the vertical oscillation amplitude. As the bunch current is increased, sv growth along the 45 bunch train occurs. If vertical feedback is turned off, the vertical position oscillation amplitude increases and results in a significant increase in the sv. This sv blow-up appears to be incoherent due to the lack of structure in the FFT spectrum.

e+ comparison of sv with wigglers on/off
sv blow-up occurs at bunch 3 with wigglers on/off. The equilibrium sv is larger with 12 wigglers on. sv(12 wigglers) > sv(6 wigglers on/off) sv reduction for bunch 3 with current. sv growth occurs at bunch 16 with 6 wigglers on/off and at bunch 31 with 12 wigglers on. Significant incoherent contribution with 6 wigglers on/off.

sv (12 wigglers on) > sv (6 wigglers on/off).
sv growth along the train occurs roughly at the same location (~bunch 31).

IV. e- 6 wigglers on/6 wigglers off

Summary of the vertical position and sv along the 45 bunch trains with 6 wiggler magnets on/off.
Vertical position change and sv growth occur at the same location along the 45 bunch train.

FFT Vertical position Ie-=0.25mA/bunch
File:532 e- 6 wigglers on, 6 wigglers off Vert. No large vertical position oscillation for bunch 3. Vertical position oscillation amplitude increases along the train at ~bunch 29. The amplitude correlates well with FFT power (fosc=237.4kHz) Vertical position movie

FFT sv Ie-=0.25mA/bunch File:532 e- 6 wigglers on, 6 wigglers off Vert. sv growth occurs at ~bunch 29 with no clear oscillation frequency in the vertical beam size except for the last few bunches. No distinct sv oscillation frequency is apparent (incoherent instability). sv movie

File:535 e- 6 wigglers on, 6 wigglers off Vert. Vertical position movie Increase the current per bunch with feedback constant: Now two vertical position oscillation frequencies are present, fosc=237kHz(0.393 cycles/turn) and fosc=206.9kHz (0.47 cycles/turn). The oscillation amplitude increase with FFT power.

FFT sv Ie-=0.75mA/bunch File:535 e- 6 wigglers on, 6 wigglers off Vert. Significant sv growth along the train starting at bunch 30 with no sv oscillation frequency in the FFT spectrum until the last 3 bunches. sv movie

File:528 e- 6 wigglers on, 6 wigglers off Vert. Increasing the current results in: A vertical position oscillation amplitude increase at fosc=236.2kHz (0.395 cycles/turn) and 202.7kHz (0.47 cycles/turn). Vertical position changes at bunch 34. The oscillation amplitude correlates with FFT power. Vertical position movie

FFT sv Ie-=1.25mA/bunch File:528 e- 6 wigglers on, 6 wigglers off Vert. sv movie sv growth along the train starts at bunch 30 with no clear frequency of oscillation for the vertical beam size-Incoherent oscillation. sv growth > sv growth

Comparison of sv with 6 wigglers on/off
For all bunch currents, sv growth starts at ~bunch 30. sv(I=0.75mA/bunch)>sv(I=1.25mA/bunch)>sv(I=0.25mA/bunch)

Summary e- vertical dynamics with 6 wigglers on/off
The vertical tune shift along the 45 bunch train initially is negative and then turns positive. The positive tune shift correlates with the vertical beam size growth along the train (~bunch 30). The vertical position oscillation is a coherent oscillation that is present at all currents measured. The FFT vertical position power correlates with the vertical oscillation amplitude. sv growth occurs along the train, which starts at bunch 30, is due to a incoherent oscillation and is present at all currents measured. sv growth coincides with a shift in the vertical position in the bunches.

v. e- 12 wigglers on Slight positive shift in Qy along the 45 bunch train.

Summary of the vertical position and sv along the 45 bunch trains with 12 wiggler magnets on.

Non-uniform bunch current along the 45 bunch train at high current.

File:572 e- 12 wigglers on Vert. Low I with vertical feedback off: Vertical position oscillation occurs at bunch 12 (fosc=237.8kHz) and the oscillation amplitude correlates with FFT power. The oscillation dies out near the end of the train (~bunch 40). Vertical position movie

FFT sv Ie-=0.25mA/bunch File:572 e- 12 wigglers on Vert. sv growth along the train starts at ~bunch 10. Two oscillation frequencies are presents in the beam spectrum at fosc=237.8kHz (0.391 cycles/turn) and 305.3kHz (0.218 cycles/turn). A broad beam spectrum is observed for bunches 25 and 34 which correlates with the peak in sv. sv movie

File:574 e- 12 wigglers on Vert. At low I with vertical feedback on: Vertical position oscillation occurs later in the train (~bunch 26) and the oscillation amplitude correlates with FFT power (fosc=238.1kHz) but with a reduced amplitude. Again, the oscillation dies out near the end of the train (~bunch 44). Vertical position movie

FFT sv Ie-=0.25mA/bunch File:574 e- 12 wigglers on Vert. Fdbck@400
sv growth along the train starts at ~bunch 22. Three oscillation frequencies are presents in the beam spectrum at fosc=238.1kHz (0.390 cycles/turn), 304.5kHz (0.22 cycles/turn), and 359.2kHz (0.08cycles/turn). Maximum sv correlates with maximum vertical oscillation amplitude. Wide frequency spectrum is not as evident with feedback on. sv movie

FFT Vertical position Ie-=0.75mA/bunch File:578 e- 12 wigglers on
Vert. At I=0.75mA/bunch with vertical feedback on: Vertical position oscillation occurs at ~bunch 26 in the FFT. The oscillation amplitude increases with FFT power Two oscillation frequencies are present, fosc=237.8kHz (0.391cycles/turn) and 207.7kHz (0.468cycles/turn). Vertical position movie Bunches 41-45

FFT sv Ie-=0.75mA/bunch File:578 e- 12 wigglers on Vert. sv growth along the train starts at two locations, at bunch 15, and bunch 30. Many oscillation frequencies are presents in the beam spectrum. At higher current, sv growth along the train starts earlier and has a steeper slope. sv(I=0.75mA/bunch) > sv(I=0.25mA/bunch) sv movie

File:555 e- 12 wigglers on Vert. Increased current with vertical feedback on: The vertical position oscillation amplitude increased. The oscillation amplitude correlates with FFT power. The vertical position initially decreases. At ~bunch 26 the vertical position increases. Two oscillation frequencies are present, fosc=237.4kHz (0.392 cycles/turn) and 207.3kHz (0.469 cycles/turn). Vertical position movie

FFT sv Ie-=1.25mA/bunch File:555 e- 12 wigglers on Vert. Fdbck@400
sv growth along the train has two slopes: 1) gradual increase-bunches 1-29 (coincides with vertical position decrease). 2) steeper slope-bunches (coincides with vertical position increase). Several oscillation frequencies are presents in the beam spectrum. sv is larger at low current (I=0.75mA/bunch) than at high current (I=1.25mA/bunch). sv movie

Summary e- vertical dynamics with 12 wigglers on
The vertical tune shift along the 45 bunch train is positive. The vertical position oscillation is always present (even with vertical feedback on). The oscillation amplitude correlates with FFT power. sv growth along the 45 bunch train is observed at all bunch currents with feedback on and off. Vertical feedback reduces the sv growth along the train and shifts the growth to a later point in the train. The vertical position oscillation correlates with sv growth.

e- comparison of sv with wigglers on/off
sv blow-up occurs earlier with 12 at wigglers on. The equilibrium sv is larger with 12 wigglers on. sv(12 wigglers) > sv(6 wigglers on/off). sv growth occurs earlier with 12 wigglers on. sv(12 wigglers) > sv(6 wigglers on/off).

Initially, sv(12 wigglers on) > sv(6 wigglers on/off). sv growth along the train occurs roughly at the same location (~bunch 31). sv growth rate with 6 wigglers on/off is greater than with 12 wigglers on.

e-/e+ Vertical Beam Dynamics with 6 and 12Wigglers On

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e-/e+ Vertical Beam Dynamics with 6 and 12Wigglers On

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