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Exercising emittance measurements in the ATF EXT line. J. Brossard / C. Rimbault / P. Bambade (LAL) http://flc-mdi.lal.in2p3.fr/. Upgrade of Annecy meeting slides …. ATF EXT line description & wire scanner position. 90°. 5 positions for wire scanners. - PowerPoint PPT Presentation
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J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ LAL 1
Exercising emittance measurements
in the ATF EXT line
Upgrade of Annecy meeting slides ….
J. Brossard / C. Rimbault / P. Bambade (LAL) http://flc-mdi.lal.in2p3.fr/
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ LAL 4
Horizontal & Vertical beam size at wire-scanner positions
for nominal and modified EXT mad deck.
x=sqrt(xx)
y=sqrt(yy)
x=2.10-9 mx= x(s)
y=2.10-11 my= y(s)
Wire thickness = 50 m
Wire thickness = 10 m
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ 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°
)*100( 111111
Nomgauss
Nom f
)*100()*
100( 331133111313
NomNomgauss
NomNomgauss
Nom ff
)*100( 333333
Nomgauss
Nom f
Where varie from 0 to 30
Assuming no x-y coupling for nominal
case ( =0)
Nom13
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ 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%)
Rij 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 :
29106 . y
2231 . x
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ LAL 7
2D projected emittances
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ LAL 8
4D intrinsinc emittances
If is diagonalisable then
Then the 2D projected emittance x and y are computed using : AAA
y 4433int, .
AAAx 2211int, .
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ LAL 10
2D projected emittances
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ LAL 11
END
Next step : Modified the 10° measurement simulation using a tracking particles.
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ LAL 13
4d - reconstruction method based on
5 wire scanner measurements
4443
3433
2221
1211
00
00
00
00
RR
RR
RR
RR
RIf the 4d-linear transport matrix from point A to B is uncoupled
Then 2Bx
2By
=(x-beam size @ B)2
=(y-beam size @ B)2
-> For « n » points (B,C,…Z), where the x beam size is measure, we have :
2231 .AAAA
x 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 / [email protected] / 8-9 nov 2007 @ LAL 14
4d - reconstruction method based on 5 wire scanner measurements
If n<3 No solution.
If n==3 and Mx-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 / [email protected] / 8-9 nov 2007 @ 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)
idealXsim r )1(%
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 / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ LAL 20
Prelim
inary
Quadrupole Strengh Variation method - 1
MW2XMW3X
(mm
2)
(mm
2)
x = 0.00201428 mm.mradx = 0.00201837 mm.mrad
5 positions for wire scanners
QD6X
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ LAL 21
Prelim
inary
Quadrupole Strengh Variation method - 2
5 positions for wire scanners
QD6X
MW2XMW3X
y = 2.0164e-05 mm.mrady = 2.01626e-05 mm.mrad
(mm
2)
(mm
2)
J. Brossard, C. Rimbault a P. Bambade LAL / [email protected] / 8-9 nov 2007 @ 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 / [email protected] / 8-9 nov 2007 @ LAL 23
References
Many thanks to Mark Woodley for the input MAD file
(see : http://www.slac.stanford.edu/~mdw/ATF/EXT.mad)
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 / [email protected] / 8-9 nov 2007 @ 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 (%)