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

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.

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)

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)

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)

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

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

e+ FFT power dependence on vertical position oscillation amplitude–High I Bunch 3 Peak Power=23@244.3kHz yavg=1.78mm Std=0.013mm Bunch 41 Peak Power=88@245.2kHz yavg=1.77mm Std=0.015mm Bunch 13 Peak Power=275@246.2kHz 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.

e+ FFT power dependence on vertical position oscillation amplitude–Medium I Bunch 12 Peak Power=85@245.6kHz yavg=1.700mm Std=0.014mm Bunch 24 Peak Power=165@195.2kHz yavg=1.668mm Std=0.016mm Many peaks and noise in FFT spectrum. Bunch 1 Peak Power=37@244.7kHz yavg=1.718mm Std=0.011mm File 920 Ie+=3.5mA/bunch Increase of vertical position oscillation amplitude noted in FFT spectrum

e+ FFT power dependence on vertical position oscillation amplitude–Low I Bunch 1 Peak Power=28@244.3kHz yavg=1.611mm Std=0.013mm Bunch 9 Peak Power=407@244.0kHz yavg=1.623mm Std=0.014mm Bunch 24 Peak Power=40@195.2kHz 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.

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

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.

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)

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)

e+ high frequency sv oscillation frequency - FFT of sv - High I Bunch 31 Peak Power=283@260.3kHz sv=0.328mm Std=0.021mm Bunch 15 Peak Power=12@195.2kHz sv=0.172mm Std=0.009mm Bunch 5 Peak Power=116@195.2kHz sv=0.236mm Std=0.012mm File 924 Ie+=3.7mA/bunch Noisy FFT spectrum correlates with an increased sv.

e+ high frequency sv oscillation frequency - FFT of sv – Medium I Bunch 6 Peak Power=78@312.8kHz sv=0.372mm Std=0.021mm Bunch 13 Peak Power=73@195.2kHz sv=0.223mm Std=0.014mm Bunch 43 Peak Power=8@195.2kHz sv=0.170mm Std=0.009mm File 920 Ie+=3.5mA/bunch Noisy FFT spectrum correlates with an increased sv.

e+ high frequency sv oscillation frequency- FFT of sv - Low I Bunch 25 Peak Power=55@286.2kHz sv=0.159mm Std=0.009mm Bunch 54 Peak Power=91@260.3kHz sv=0.221mm Std=0.013mm Bunch 6 Peak Power=204@260.3kHz 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.

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.

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)

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)

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.

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.

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

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

e- high frequency vertical position oscillation - FFT of vertical position – High I Bunch 31 Peak Power=459@242.8kHz yavg=2.631mm Std=0.022mm Bunch 33 Peak Power=1300@241.3kHz yavg=2.619mm Std=0.024mm Bunch 35 Peak Power=4905@241.7kHz yavg=2.665mm Std=0.034mm File:923 Ie-=4.3mA/bunch Vertical position oscillation amplitude correlates with FFT power.

e- high frequency vertical position oscillation - FFT of vertical position – Medium I Bunch 31 Peak Power=261@242.2kHz yavg=2.715mm Std=0.021mm Bunch 33 Peak Power=1543@241kHz yavg=2.708mm Std=0.024mm Bunch 35 Peak Power=4335@241.1kHz yavg=2.736mm Std=0.031mm File:922 Ie-=4.1mA/bunch Vertical position oscillation amplitude correlates with FFT power.

e- high frequency vertical position oscillation - FFT of vertical position – Low I Bunch 13 Peak Power=228@242.2kHz yavg=2.651mm Std=0.021mm Bunch 15 Peak Power=2424@241kHz yavg=2.647mm Std=0.025mm Bunch 17 Peak Power=4387@241.1kHz yavg=2.685mm Std=0.035mm File:919 Ie-=3.8mA/bunch Vertical position oscillation amplitude correlates with FFT power.

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

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)

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.

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.

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).

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.

e- high frequency sv oscillation - FFT of sv – High I Bunch 13 Peak Power=880@242.8kHz sv=0.224mm Std=0.021mm Bunch 15 Peak Power=2892@241.3kHz sv=0.256mm Std=0.029mm Bunch 17 Peak Power=6002@241.7kHz sv=0.288mm Std=0.035mm File:923 Ie-=4.3mA/bunch sv oscillation amplitude correlates with FFT power

e- high frequency sv oscillation - FFT of sv – Medium I Bunch 31 Peak Power=812@242.2kHz sv=0.217mm Std=0.023mm Bunch 33 Peak Power=3602@241.0kHz sv=0.239mm Std=0.029mm Bunch 35 Peak Power=6415@241.2kHz sv=0.282mm Std=0.036mm File:922 Ie-=4.1mA/bunch sv oscillation amplitude correlates with FFT power

e- high frequency sv oscillation - FFT of sv – Low I Bunch 6 Peak Power=148@243.1kHz sv=0.225mm Std=0.022mm Bunch 8 Peak Power=3570@241.2kHz sv=0.241mm Std=0.027mm Bunch 10 Peak Power=3998@241.2kHz sv=0.290mm Std=0.037mm File:919 Ie-=3.8mA/bunch sv oscillation amplitude correlates with FFT power.

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

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

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.