MERIT analysis - Beam spot size
Goran Skoro
More details: http://hepunx.rl.ac.uk/uknf/wp3/shocksims/mermar/
UKNF Meeting, Oxford, 16 September 2008
MERcury Intense Target
Purpose: To provide a proof-of-principle for the NF/MC 4-MW target concept. To study the effects ofhigh-magnetic fields on the beam/jet interaction.
1234
Syringe PumpSecondaryContainment
Jet Chamber
ProtonBeam
Solenoid
“Each beam pulse is a separate experiment”
Estimate of energy density is based on the beam optics calculations
Beam size has to be measured for each pulse
The MERIT Experiment
Beam monitoring
MERITCamera 484
Camera 454 Camera 414
Beam monitoring (example)
CERN software for online (and offline) beam monitoring
X, Y projections
At the beginning (May, 2008), the goals of this analysis were:
To make a better fitting algorithmTo find x,y positions of the beamTo find ratios of the x,y sigmas
Problem: saturation
For most shots the light intensity is saturated
Find a shadow Fit a tail2nd approach:
Devils Tower Wyoming
Distribution looks like this
To extract ASCII from SDDS
How to extract a beam size?
z(x,y) distribution is in a saturation here
1st approach: To fit projections*
Mean = 0.31(7) mmSigma = 6.42(12) mm
X
Y
X
Y
2nd approach: To fit shadows**
Mean = -4.64(3) mm
Mean = 0.16(4) mm
Mean = -4.71(3) mmSigma = 2.21(3) mmSigma = 2.22(4) mm
Sigma = 4.82(5) mm
We have 3 beam ‘cameras’ -> 3 images for each beam pulse
Shot from Camera 484
* Projection for X is
yn
ii
y
yxzn
xP1
),(1
)(
similarly for Y.
, ** Shadow for X is ),1()],,(max[)( yi niyxzxS similarly for Y.
,
Fitting: Procedure
Simple fitting function: Gaussian + ‘background’
Fitting algorithm (how to avoid gaps; how to choose initial value of the ‘background’ term, etc…) was based on the analysis of the 15-20 randomly selected images (after this, completely ‘blind’ analysis -> no parameters tuning)
In total: 520 beam pulses* x 3 cameras x 2 projections = 3120 distributions have been fitted
Result: Table – ntuple (part of it shown below)
Fitting: ProcedureCamera
414Camera
454Camera
484TARGET
BEAM
Camera 414
Camera 454
Camera 484
Date(ddmmyyyy)
Time(hhmmss)
Xmean
(mm)Xmean
(mm)Ymean
(mm)Ymean
(mm)Sigmax
(mm)Sigmax
(mm)Sigmay
(mm)…………………
……………………
……………………
……………………
……………………
……………………
…This will be used to reconstruct the Run number and to attach this table to the ‘global’ table with experimental results.
This will be used to recognize a shot with the ‘suspicious’ fitting result and to fit it ‘manually’.
* Period: 23 Oct 2007 – 11 Nov 2007
Xmean (mm) Xmean (mm) Xmean (mm)
Ymean (mm) Ymean (mm) Ymean (mm)
Rela
tive
inte
nsit
y
Camera 414
Camera 414
Camera 484
Camera 454
Camera 454
Camera 484
454 484
TARGET
BEAM
414
Results: Shadows Distributions of the Gaussian means
Distributions of the Gaussian sigmas
x (mm)
Rela
tive
inte
nsit
y
Camera 414
Camera 414
Camera 484
Camera 454
Camera 454
Camera 484
x (mm) x (mm)
y (mm) y (mm) y (mm)
(empty shots, beam on the edge
of the ‘visible field’, etc…)
-Suspicious results
Find the corresponding
event in the table (Slide 6) and fit it
manually (if possible)
454 484
TARGET
BEAM
414
Results: Projections
Xmean(shadow)/Xmean(projection)
Rela
tive
inte
nsit
y
Camera 414
Camera 414
Camera 484
Camera 454
Camera 454
Camera 484
454 484
TARGET
BEAM
414
Cross-checking: Projections vs Shadows
Distributions of the ratios (shadow/projection) of the Gaussian
means
Xmean(shadow)/Xmean(projection)Xmean(shadow)/Xmean(projection)
Ymean(shadow)/Ymean(projection)Ymean(shadow)/Ymean(projection)Ymean(shadow)/Ymean(projection)
Everything is (more or less) symmetrical
around 1. As expected, both approaches
return similar values of x/y means.
Rela
tive
inte
nsit
y
Camera 414
Camera 414
Camera 484
Camera 454
Camera 454
Camera 484
x(shadow)/x(projection) x(shadow)/x(projection) x(shadow)/x(projection)
454 484
TARGET
BEAM
414
y(shadow)/y(projection) y(shadow)/y(projection) y(shadow)/y(projection)
Distributions of the ratios (shadow/projection) of the Gaussian
sigmas
Distributions are not symmetrical around 1 (shifted towards left). It means that sigmas for projections are, in general, bigger than sigmas for shadows.
Cross-checking: Projections vs Shadows
Distributions of the ratios of the Gaussian sigmas
Rela
tive
inte
nsit
y
454 484
TARGET
BEAM
414
jy
iy
jx
ix
,
454
414
x
x
484
454
x
x
454
414
y
y
484
454
y
y
Nice agreement with ‘Beam Optics’
values
Results: Shadows
BO ~ 1
BO ~ 1.33
Rela
tive
inte
nsit
y
454 484
TARGET
BEAM
414
iy
ix
414
414
y
x
454
454
y
x
484
484
y
x
Distributions of the ratios of the Gaussian sigmas
Results: Shadows
‘Beam Optics’ value = 1.3
‘Beam Optics’ value = 1.7
Beam position on target
* From ‘Beam Spot Information’ talk, I. Efthymiopoulos, VRVS Meeting, November 30, 2007
454 484
TARGET
-5.77 m -4.17 m 0.0
454 484
TARGET
BEAM
414
EXP
Taken online (estimated by the eye from the screen data)
FIT
Calculated by using:
1) the fitted beam positions for Camera454 and Camera484 (see Slide 4, for example);
2) the Camera454, Camera484 and target positions*
EXP
FIT
EXP
FIT
454 484
TARGET
BEAM
414R
ela
tive
inte
nsit
yDistributions of the ratios
of the Gaussian sigmas
484
454
x
x
484
454
y
y
484
484
y
x
Mean = 1.07
Mean = 1.41
Mean = 1.80
‘Beam optics’ ~ 1
‘Beam optics’ ~ 1.33
‘Beam optics’ = 1.7
Beam position on target
So far, everything (sigmas ratios, beam positions) looks nice…
… except the absolute values of the beam widths!!! Beam optics calculations: beam sigmas are much smaller
Projections
If we assume that the ‘light intensity’ (from the screens) is proportional to beam intensity (before we reach a ‘saturation intensity’) we can, at least, estimate the correction factor when fitting the projections.
Similar results have been obtained by fitting of shadows.
Objections:
1) Saturation is a problem (‘we could have many sigmas hidden here’)2) Shadows approach looks problematic for the highest beam intensities (only a few points left to fit tails)
This is not a problem (intensity is below the saturation level) and a projection approach will give us correct value of beam width(s)
This is a problem (intensity is 10x higher than the saturation level)
Results: Beam size vs beam intensity
Simulation: Saturation effects
(1)
(2)
(3)
Intensity = 10x ‘saturation intensity’
Intensity = 100x ‘saturation intensity’
Intensity <= ‘saturation intensity’
x = y = 2 mm
x = y = 2 mm
x = y = 2 mm
It is obvious that an extraction of projections from (2) and (3) will not give us gaussians
Projections
X, Y (mm)
(1) x,y = 2.00 (2)
(2) x,y = 2.97 (3)
(3) x,y = 3.78 (4)
Inte
nsi
ty
But, what will happen if we try to fit corresponding projections by using gaussian(s)?
Simulation: Saturation effects
Intensity = 10x ‘saturation intensity’
Intensity = 100x ‘saturation intensity’
Intensity <= ‘saturation intensity’
x = 3 mmy = 1.5 mm
x = 3 mmy = 1.5 mm
x = 3 mmy = 1.5 mm
- In our case, expected value of sigma_x/sigma_y ~ 2
‘Symmetry’ between x and y is broken
Sig
ma_fi
t/sig
ma_i
np
ut
Intensity / ’Saturation intensity’
- Previous slide is for sigma_x = sigma_y
- By plotting sigma_output/sigma_input as a function of intensity we can estimate a correction function
Next step: To find a value of ‘saturation intensity’ in our case
xy
Results: Beam intensity below 0.2 Tp454 484
TARGET
BEAM
414
There are 10 -15 shots (23 Oct 2007) where beam intensity is below 0.2 Tp. The distributions (few examples are shown below) look like perfect double-Gaussians for all shots.
Camera 484
No saturation here BUT sigmas are ~2x bigger than expected from BO calculations!!!
Results of fitting of the shadows
X (mm)
Y (mm)
(1) x = 2.93 (2)
(2) x = 3.26 (2)
(3) x = 3.22 (3)
(1) y = 1.90 (1)
(2) y = 2.05 (2)
(3) y = 1.66 (2)
454 484
TARGET
BEAM
414
For low beam intensity shots, in around 50% of the cases the situation is similar to (1) and (2). Even when we have a beam shot similar to case (3) the x/y widths ratio is close to 2. The plot above shows the results of the fitting of these 3 distributions.
(1)
(2)
(3)
Saturation
Saturation (but not so clear)
‘Proper’ Gaussian
Camera 484
It looks that saturation starts somewhere here
Rela
tive
inte
nsit
y
Results: Beam intensity around 0.3 Tp
Results: ‘Correction’ functionS
igm
a_fi
t/sig
ma_i
np
ut
Intensity / ’Saturation intensity’
~ 0.3 Tp
’Saturation intensity’ ~ 0.3 Tp
0.3 Tp 30 Tp
We can use these ‘functions’ to correct the data
x y
~ 30 Tp
454 484
TARGET
BEAM
414
Beam size vs beam intensity (after correction)
Dots: from beam monitors dataLines: from beam optics calculations
Summary
Analysis of the MERIT beam monitors data has been completed
Two approaches: cross-checked
Measurements vs. calculations: controversy remains
http://hepunx.rl.ac.uk/uknf/wp3/shocksims/mermar/
More details: