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Analyze of Synchrotron Sidebands with ICA

Analyze of Synchrotron Sidebands with ICA. Honghuan Liu Indiana University March 15 th 2012. Outline. The analytic solution of the signal with synchro-betatron coupling. Discuss using ICA to separate synchrtron sidebands .

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Analyze of Synchrotron Sidebands with ICA

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  1. Analyze of Synchrotron Sidebands with ICA Honghuan Liu Indiana University March 15th 2012

  2. Outline • The analytic solution of the signal with synchro-betatron coupling. • Discuss using ICA to separate synchrtron sidebands. • Apply this method to the singals with both synchro-betatron coupling and horizontal and vertical betatronhttp://www.xixise2.com/coupling. • Summary

  3. Signal with Synchro-betatron Coupling • If there is synchro-betatron coupling, the signal is written like this way where is betatron tune, synchrotron tune, a and b are parameters. i=1, 2, … M, M is the number of BPMs. j=1, 2, … N, N is the number of tracking turns.

  4. Using the following formulas, We obtain the following analytic result Where J is the Bessel function.

  5. Estimate the value of b Betatron tune is given by Compare with the signal, we find out that

  6. Use AGS as an example. Read the data from mad file of AGS, Take , the value of b is

  7. Compare PCA and ICA • To see the virtue of ICA, let’s compare ICA with PCA. • Choose the following parameters: a=0.005m, b=0.5, =8.70, =0.02, M=100, N=1000. • Use both PCA and ICA to analyze the original data, we get the following two graphs. These graphs are the fft on source signals obtained by PCA and ICA separately.

  8. Analyze data with ICA • Compare the betatron amplitude obtained from ICA with the analytic amplitude. • Some parameters are chosen to be a=0.005m, b=0.5, M=100, N=2000, =8.7.

  9. =0.02, tau=50. The ratio of the amplitude obtained by ICA to the analytic amplitude.

  10. =0.01, tau=100. The ratio of the amplitude obtained by ICA to the analytic amplitude.

  11. =0.005, tau=200. The ratio of the amplitude obtained by ICA to the analytic amplitude.

  12. The region of b to separate betatron motion and first order synchrotron sidebands. • Quantity standard of separating a source. a. b. If there are more than two frequency components in a mode, the fft amplitude of the second highest peak is smaller than 10% of the main peak.

  13. The maximum b value of separating all betatron motion and first order sidebands vs time lag.

  14. Betatron Coupling and Synchro-Betatron Coupling • Consider both the betatroncoupling and the synchro-betatroncoupling in the signal. The signal is • Expand the signal, we obtain

  15. We consider the case of and

  16. Analyze data with ICA • Find out how the maximum b value of separating each frequency component depends on time lag. • Since first order sidebands are not symmetric, we analyze each component separately. • Some parameters are a=0.005m, c=0.001m, =8.70, =8.85, M=100, N=2000.

  17. The maximum b of separating each component vs time lag. =0.01.

  18. The maximum b of separating each component vs time lag. =0.005.

  19. Find out how the maximum b value of separating each frequency component depends on - . • Find out how the maximum b value of separating all betatron motion and first order sideband. • Some parameters are a=0.005m, c=0.001m, =8.70 is fixed, =0.01, tau=100, M=100, N=2000.

  20. The maximum b of separating each component vsbetatron tune difference.

  21. The maximum b of separating all components vsbetatron tune difference.

  22. Find out how the maximum b value of separating each frequency component depends on c/a. • Some parameters are a=0.005m is fixed, =8.70, =8.85, =0.01, tau=100, M=100, N=2000.

  23. The maximum b of separating each component depends on c/a.

  24. Summary • ICA can separate betatron motion and first order sidebands. • The separation ability of ICA are independent on time lag times synchrotron tune.

  25. The difference between two betatron tunes affect the separation ability of ICA, but when this difference is big enough, it does affect the separation of each component. • When c/a >0.1, c/a does not affect the separation ability of ICA.

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