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

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

1-Principle

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 (2007) P. Emma, M. Woodley, ATF-99-04: where  is the angle between x and tilted wires

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

2-Measurements

- 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 /-1596+/-3163+/-784+/ /-8103+/-3167+/-881+/ /-9102+/ /-379+/ / /-5163+/-779+/ /-5108+/ /-1084+/-2 MW0X_+10MW1X_+10MW2X_+10MW3X_+10MW4X_ / / / / / / / / / / / / / / / / / / / / / / / / /-0.6 MW0X_yMW1X_yMW2X_yMW3X_yMW4X_y / / / / / / / / / / / / / / / / / / / / / / / / /-1.2 MW0X_-10MW1X_-10MW2X_-10MW3X_-10MW4X_ / / / / / / / / / / / / / / / / / / / / / / / / /-2.6

3-First "difficulty"

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

4- Graphical representation

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

5- Coupling

From I. Agapov, G. Blair, M. Woodley, PRST-AB (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

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

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

6- Questions 1 - Stupid mistakes from me... (after several verifications, no major bugs found) 2 - Are the named and 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? other  Test of 2

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

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

8- A bit of geometry

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

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

If no coupling, =0 o B A C 

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

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

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

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  

But what do the wire scanners measure: projections

From P. Emma, M. Woodley, ATF Is it the philosophy of this?

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