J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 1 Exercising emittance measurements in the ATF EXT line Upgrade of Annecy meeting slides …. J. Brossard / C. Rimbault / P. Bambade (LAL)

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 2 ATF EXT line description & wire scanner position 5 positions for wire scanners Diagnostic section (  x =  y =  ) Each position is equipped with 3 wire scanners oriented at 0, 90 and 10° for y,x and 10° beam-size measurement. Wire thickness = 10  m & 50  m 90° 10° 0° Diagnostic section (  x =  y =  )

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 3 Evolution of Horizontal & Vertical sqrt(beta) and phase functions along EXT line for nominal and modified EXT line. QM7

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 4 Horizontal & Vertical beam size at wire-scanner positions for nominal and modified EXT mad deck.  x =sqrt(  x  x )  y =sqrt(  y  y )  x = m  x=   x(s)  y = m  y=   y(s) Wire thickness = 50  m Wire thickness = 10  m

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 5 Exercice : Run MAD with QM7 = Nominal value & QM7 = QM7-20% Remark : Only the K1 value is modified What about the dipole kick induce by the x-offset position in the quad ? At each wire scanner the beam matrix is computed (output from MAD). A relative gaussian error on  11  33  13 is added (for 1000 succesives « measurements »): At present time, we assume that :  13 =  10° Where  varie from 0 to 30 Assuming no x-y coupling for nominal case ( =0)

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 6 The Least Means Square Method (LMS) is used to find « the LMS solution ». The « 2D-emittance » reconstruction method is base on 3 different over-estiminated linear systems : Example for  x measurement Measurement of  x at the 5 wire scanners (obtained with MAD deck where QM7=QM7-20%) R ij Linear transport coefficent (using QM7 nominal value) Beam matrix element at the reference input point A.  10° measurements to defined  4  5  7 and  8  y measurements to defined  6  9 and  10 Then the 2D projected emittance  x and  y are computed using :

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 7 2D projected emittances

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 8 4D intrinsinc emittances If is diagonalisable then Then the 2D projected emittance  x and  y are computed using :

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 9 Rejection level : 4D intrinsinc emittances BUT …. Preliminary results…. Some mathematical point in MATLAB need to be understand.

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 10 2D projected emittances

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 11 END Next step : Modified the  10° measurement simulation using a tracking particles.

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 12 4d-beam matrix at point A : 4d-beam matrix at point B : Where is the 4D-linear optic matrix from point A to point B. 4d - reconstruction method based on 5 wire scanner measurements

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 13 4d - reconstruction method based on 5 wire scanner measurements If the 4d-linear transport matrix from point A to B is uncoupled Then =(x-beam B) 2 =(y-beam B) 2 -> For « n » points (B,C,…Z), where the x beam size is measure, we have : If we know how to solve this linear system then, we can compute the horizontal emittance : Similar analysis can be performed to estimate :  4, to  10 … and   y can be estimated.

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 14 4d - reconstruction method based on 5 wire scanner measurements If n<3 No solution. If n==3 and M x -1 exist then the solution is known and unique. If n>3 the sytem is « overestimated » and the Least Mean Square (LMS) method can be used to find the « LMS » solution. (in ATF n==5) First question : How sensitive to wire scanner errors this method is ? Second question : What happen if the QM6 quadrupole strength is reduce by 20% ?

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 15 Assumption : the relative error level on « measurements » at position MW0X, MW1X, MW2X, MW3X and MW4X is identical, and tested for values ranging between 0 and 30% The minimum relative error level for y-beam size measurement is at least equal to 13% (D/4~1.25 microns) Where « r » comes from a gaussian distribution having zero mean and X/100 rms First question : How sensitive to wire scanner errors this method is ?

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 16 First question : How sensitive to wire scanner errors this method is ? For each error level, 1000 « measure » have been tested. The plot shows the mean and +/- 1 rms mean value rms value The maximum relative errors (define by the rms value) on  11,  12,  22,  33,  34 and  44 values are approximatively between -30% and +30%

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 17 A part of the 1000 tested « measurements » lead to a unphysical results. In the current analysis, this rejection level is always lower than 4%. First question : How sensitive to wire scanner errors this method is ? Impact on horizontal and vertical emittance reconstruction …  This method leads to underestimate vertical and horizontal emittance. The underestimation of horizontal emittance is higher than the vertical one.

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 18 Second question : What happen if the QM6 quadrupole strength is reduce by 20% ? QM6 is the first bending magnet (with quadrupole part) after the kicker. The quad. strength of this element might have been over-estimated…(TBC) The maximum error level on  11,  12,  22 and  44 is similar to the previous analysis (i.e : +/- 30%) The maximum error level on  33 and  34 reach +100 or +200% !!!

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 19 Second question : What happen if the QM6 quadrupole strength is reduce by 20% ? In presence of WS error, the - horizontal emittance is sligthly underestimated - vertical emittance is greatly over-estimated. Impact on horizontal and vertical emittance reconstruction … The rejection part increase… to reach 40% for error measurement of 30 % Absolute values (m.rad) Absolute values (m.rad) relative values (%) + 30%

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 20 Preliminary Quadrupole Strengh Variation method - 1 MW2X MW3X    (mm 2 )   x = mm.mrad   x = mm.mrad 5 positions for wire scanners QD6X

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 21 Preliminary Quadrupole Strengh Variation method positions for wire scanners QD6X MW2X MW3X   y = e-05 mm.mrad   y = e-05 mm.mrad    (mm 2 )

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 22 Conclusions and perspectives Conclusions and persepctives - For the nominal ATF-EXT line, the LMS* method based on the 5 existing wire scanners induced an underestimation of the vertical and horizontal emittance (function of WS error level). - If the QM6 quadrupole strength is underestimated (by 20%) then the LMS method based on the 5 existing wire scanner induced a « small » horizontal emittance reduction and a « large » vertical emittance estimation (function of WS error level). For QM7 quadrupole strength underestimation an symetric (x-y) effect is observed (see extra slide). - Compare the error sensitivity of the LMS reconstruction method with a « quadrupole strength variation » method. Questions - What are the real « quadrupole strength » of QM6 and QM7 (seen by the extracted bunch) ? - Is it possible to determine WS positions leading to less error sensitive reconstruction method ? - What is the sensitivity of « quadrupole strength variation » method ? (which quad ? which WS ?, new quad position ?, new WS position ? ….). - Is it possible to realize more than 3 measurement per WS to reduce the error level ? - others ideas ? … * LMS : Least Mean Square

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 23 References Many thanks to Mark Woodley for the input MAD file (see : References : ATF Internal reports : ATF-99-01, ATF-00-06, ATF-99-17, ATF-99-08, ATF-00-01…

J. Brossard, C. Rimbault a P. Bambade LAL / / 8-9 nov LAL 24 Extra-slide QM6 quadrupole strength is reduce by 20%  QM7 quadrupole strength is reduce by 20%  (see M. Alabau Pons & al. Talk) + 10% + 30% Absolute values (m.rad) Absolute values (m.rad) Relative values (%)