Simulation of the Performance
of Lumical Using Mokka
Halina Abramowicz, Ronen Ingbir,
Sergey Kananov, Aharon Levy, Iftach Sadeh
Tel Aviv University
Collaboration
High precision design
Tel Aviv University
May 29th 2007
FCAL Collaboration Meeting – May 2007
Simulation and Analysis Tools
• Geant4 (v4.8.1.p02)
• Mokka (v06-03-p01) Model:
LDC 00-03Rp
Super-driver: LumiCalX
• Marlin (v00-09-06) / root (v5.08)
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FCAL Collaboration Meeting – May 2007
Detector Design
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FCAL Collaboration Meeting – May 2007
Detector Signal
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FCAL Collaboration Meeting – May 2007
Energy Resolution
Leakage through the outer cylinders depends on the minimal
polar angle min  , for a fixed maximal polar angle.
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FCAL Collaboration Meeting – May 2007
Energy Resolution
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FCAL Collaboration Meeting – May 2007
Inner Radius
For an inner radius of LumiCal - Rmin  80 mm
Energy  50,500 GeV  θmin  38.5,42.5 mrad
42.5 mrad  16.5 mm

accept
Rmin
 80  16.5  96.5mm
 Bhabha  42.5mrad  = 17.5 Hz
For Rmin  100 mm
accept
Rmin
 100  16.5  116.5mm
accept
 θmin
 51.3 mrad
 Bhabha  51.3mrad  = 11.3 Hz
55%
EVENTS MORE
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FCAL Collaboration Meeting – May 2007
Number Of Rings
 30 Rings
40 Rings 
 100 Rings
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Leakage Through The Back Rings
Leakage through the back rings for a 30-ring detector
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FCAL Collaboration Meeting – May 2007

rec
Reconstruction  MIN  
 ×W

=
W
Hit
Hit
Hit
Tel Aviv University
, WHit

 EHit  
 MAX  Const + Log 
 , 0 

 ETotal  

FCAL Collaboration Meeting – May 2007

Reconstruction   ~ 10
Tel Aviv University
6
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Detector Design
Peak-Shower Design
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FCAL Collaboration Meeting – May 2007

Reconstruction

Errors for Delta and For Sigma ~ 107

The units of Delta and of Sigma are [rad]
Uniform Detector
Peak Shower Detector
Energy
[GeV]
Log
weight
constant
10 
10 
100
4.6
-5.55
250
5.2
500
5.4
Number of
channels
Tel Aviv University
Delta
-6
Sigma
Log weight constant
10 
4.6
-6.21
4.59
2.4
5.2
1.76
3.23
2.2
5.4
2.2
2.5
High
granulation
4.56
2.4
2.16
3.26
2.07
2.5
~ 300,000
Sigma
10 
Low
granulation
-5
Delta
-6
-5
~ 170,000 = 56% of 300,000
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Digitization
For either a 10-Bit or an 8-Bit ADC
1024 Channels
1024 Channels
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FCAL Collaboration Meeting – May 2007
Digitization
1. 500 GeV electrons for 8-Bit
& 10-Bit schemes.
2. Energy MPV of a MIP in
0.3 mm thick silicon is 93.8 KeV.
3. The maximal number of MIPs in a single cell is 3,010.
4. 95% of the signal is below 10,575 fC = 2,586 MIPs.
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FCAL Collaboration Meeting – May 2007
Digitization
No change with regard to the non-digitized case
(The same goes for 10-Bits…)
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FCAL Collaboration Meeting – May 2007
Digitization
Below 400GeV, all of the signal is contained under the
95% cut (for 500GeV) of ~2,600 MIPs.
8-Bits
10-Bits
Signal in high gain range
Signal in high gain range
100
94%
98.5%
250
92.8%
97.7%
500
92%
97.1%
High gain range / step
[ 0.82 , 209.4 ] fC /
0.82 fC = 0.2 MIPs
[ 0.82 , 837.5] fC /
0.82 fC = 0.2 MIPs
Low gain range / step
[ 209.4 , 10575 ] fC /
40.5 fC = 9.9 MIPs
[ 837.5 , 10575 ] fC /
9.5 fC = 2.3 MIPs
Energy
Ratio of
lowUniversity
to high gain
Tel Aviv
49.5
11.5
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Alignment By Muons
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
θ
RIGHT
θLEFT
Δθ  θRIGHT - θLEFT
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
Axis of rotation is:
 at the center
at the begining 
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FCAL Collaboration Meeting – May 2007
Alignment By Muons
For expected statistics

events 
~5,000


year 

the accuracy will
be worse by a factor of ~10.
Displacement
Accuracy
Statistics needed
[events]
One ring displaced in comparison to
the rest of the detector
20 μm
50,000
Movement along Z
1 μm
30,000
Movement along Y,X
1 μm
50,000
Rotation around Y,X
0.1 mrad
6,000
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FCAL Collaboration Meeting – May 2007
Summary
1. Peak-Shower design:
30 rings, 48 sectors, 104 cylinders (inner 15 rings) /
13 cylinders (4 & 11 outer rings)
2. Inner / outer radius: Rmin  80mm , Rmax  350mm
 Angular polar cell size: θCELL  1.15 [mrad]
3. Number of electronics channels: 17  104
4. Energy resolution: ΔE =  0.203 ± 0.002   0.0024 ± 0.0006 
E
E
5. Digitization:
10-Bits with a high gain to low gain ratio of 11.5, for
a 95% acceptance of events
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FCAL Collaboration Meeting – May 2007
Summary
Systematic error on Luminosity
Energy
[GeV]
min [rad]
Events per year
(active for 31 year)
100
39.5  103
250
500
Bias in polar
angle -  [rad]
 L 2 

L
min
216.13  106
6.21 10 6
3.14  104
41.5  103
183.74  106
1.76  10 6
0.85  104
42.5  103
183.64  106
2.2  10 6
1.04  10 4

Events
6
500GeV  = 118.79  10 
 IF Rmin  100mm  
year


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FCAL Collaboration Meeting – May 2007