1. First analysis results of EXT MW0-4 X,Y,- 10,-10 wire-size measurements to reconstruct the 4D betatron phase-space

2. Questions opened by the First analysis results of EXT MW0-4 X,Y,- 10,-10 wire-size measurements to reconstruct the 4D betatron phase-space

3. 1-Principle

4. Coupling Measurements: waist scan method - 1 Transfer Matrix: normal quad: R tot = RQ skew quad: R tot = RQ K Coupling terms Measurable terms The squares of the measured beam sizes,  11 M,  13 M,  33 M, at a wire scanner position can be expressed as a parabolic function of the strength of the scanned quad, described by 3 fit parameters A, B, C:  ij =A ij (k-B ij ) 2 +C ij  13 M can be measured using a tilted wire scanner, u (10 o ), applying method described in I. Agapov, G. Blair, M. Woodley, PRST-AB 10 112801 (2007) P. Emma, M. Woodley, ATF-99-04: where  is the angle between x and tilted wires

5. Coupling Measurements: waist scan method - 2 With normal quad scan: With skew quad scan:

6. 2-Measurements

7. - Measurements performed on 28th May 2009 by G.W., Y.R., M.W., F.Z. - Dispersion measurements and corrections - QK1X scans: at -20, -10, 0, 10, and 20 A, 3 measurements each time - MW0X: y, +10 o, -10 o - MW1X-MW4X: x, y, +10 o, -10 o MW1X_xMW2X_xMW3X_xMW4X_x -20132+/-1596+/-3163+/-784+/-4 -10145+/-8103+/-3167+/-881+/-1 0146+/-9102+/-11158+/-379+/-4 10152+/-13102+/-5163+/-779+/-5 20148+/-5108+/-12167+/-1084+/-2 MW0X_+10MW1X_+10MW2X_+10MW3X_+10MW4X_+10 -2040.0+/-4.743.6+/-2.321.9+/-5.350.2+/-1.346.6+/-0.3 -1033.0+/-2.542.2+/-1.127.1+/-2.148.6+/-2.433.2+/-2.4 044.4+/-3.847.8+/-2.032.2+/-2.744.4+/-4.213.5+/-1.0 1059.5+/-5.059.8+/-6.139.9+/-1.344.5+/-5.015.8+/-2.4 2078.5+/-2.676.5+/-3.650.2+/-3.437.8+/-1.532.9+/-0.6 MW0X_yMW1X_yMW2X_yMW3X_yMW4X_y -2026.7+/-1.917.7+/-0.722.8+/-0.911.9+/-0.320.5+/-0.7 -1016.2+/-0.813.9+/-0.920.9+/-1.38.4+/-0.38.4+/-0.1 019.0+/-0.916.4+/-1.028.5+/-1.46.9+/-0.49.2+/-0.3 1033.9+/-1.122.5+/-0.929.1+/-0.98.5+/-0.322.0+/-1.6 2052.8+/-4.735.1+/-3.339.0+/-3.48.7+/-0.434.9+/-1.2 MW0X_-10MW1X_-10MW2X_-10MW3X_-10MW4X_-10 -2021.9+/-0.721.6+/-0.636.1+/-3.616.1+/-0.76.6+/-0.2 -1010.9+/-0.718.8+/-0.820.7+/-1.216.6+/-0.66.5+/-0.6 013.4+/-2.715.5+/-0.922.2+/-2.420.3+/-2.714.7+/-0.3 1021.8+/-0.214.8+/-1.918.8+/-2.319.1+/-1.525.3+/-1.5 2031.9+/-3.420.6+/-2.031.2+/-1.422.3+/-1.332.6+/-2.6

8. 3-First "difficulty"

9. The measurements we get from x and y are corrected from the moving 45 o axis, but not for +10 o and -10 o. Question: -How are oriented wire on each wire-scanners? Answer: the same for all the WS Beam direction Correction to apply to -10 o : cos(35 o ) With  =80 o Correction to apply to +10 o : cos(55 o ) With  =100 o

10. 4- Graphical representation

11. x +10 o -10 o y MW0X MW1X MW2X MW3X MW4X

12. 5- Coupling

13. From I. Agapov, G. Blair, M. Woodley, PRST-AB 10 112801 (2007), pp 8-9 Simple deductions - If the major axis of the beam lies along the horizontal axis  =0 - if ≠0, then =cste with  - if  (80 o )=  (100 o ) then =0

14. Coupling reconstruction applying MW1X MW2X MW4XMW3X from +10 o (  100) and -10 o  =80) measurements

15. Coupling reconstruction applying MW1X MW2X MW4XMW3X abs(1- + / - )

17. 6- Questions 1 - Stupid mistakes from me... (after several verifications, no major bugs found) 2 - Are the named +10 0 and -10 0 wires invert / Was there an error in the positionning of the wires for the scan of the beam? 3 - Several other errors during data acquisition?.... 4 - other  Test of 2

18. Coupling reconstruction applying from +10 o (  100) and -10 o  =80) measurements with inversion of named +10/-10 wires MW1X MW2X MW4X MW3X

19. 7- Interpretations Coupling reconstruction applying inversion of +10/-10 wires Results should look like b1: 2 options: 1 - Consider b1 is true:  +10 and -10 are invert + half of the data are "wrong" but what I mean by "true"?  2 - Should I believe this equation? fig. a fig. b

20. 8- A bit of geometry

21. Are you agree with this? The tranverse profile of a gaussian beam can be represent by an ellipse of major axis  x and minor axis  y  x =5  y =1

22. From I. Agapov, G. Blair, M. Woodley, PRST-AB 10 112801 (2007), pp 8-9 From P. Emma, M. Woodley, ATF-99-04

23. If no coupling, =0 o B A C 

24. From P. Emma, M. Woodley, ATF-99-04 If no coupling, =0 o B A C  A’ B’

25. From P. Emma, M. Woodley, ATF-99-04 If no coupling, =0 o B A C’  A’ B’  !!!??? C

26. What I know about an ellipse general equation: reduce equation: o xx r  yy

28. But what do the wire scanners measure?: projections the tilted wires don’t measure the beam sizes, but the projection of r, such as: is maximal  

29. But what do the wire scanners measure: projections

30. From P. Emma, M. Woodley, ATF-99-04 Is it the philosophy of this?

31. The measurements MW1X MW2XMW3X MW4X -20A -10A 0A 10A 20A