1. Detailed Models for Timing, Efficiency and Crosstalk in Resistive Plate Chambers
Werner Riegler, Christian Lippmann
CERN
Introduction
Detector physics parameters
Efficiency and charge spectra
Time resolution
Analytic cross-talk model
Coimbra, Nov. 2001
Werner Riegler

2. Geometries under Study
Trigger RPC
Timing RPC
R. Cardarelli, R. Santonico,
P. Fonte, V. Peskov
2mm gas gap
2mm Bakelite,   1010 cm
C2F4H2/Isobutane/SF6 97/2.5/0.5
HV: 10kV, E: 50kV/cm
0.3mm gas gap
3mm glass,   2x1012 cm
2mm aluminum
C2F4H2/Isobutane/SF6 85/5/10
HV: 3kV, E: 100kV/cm
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Werner Riegler

3. Simulation Input RPC material: FLUKA
Primary ionization: HEED (Igor Smirnov)
Townsend, attachment coefficient: IMONTE (Steve Biagi)
Diffusion, drift velocity: MAGBOLTZ 2 (Steve Biagi)
Avalanche fluctuations: Werner Legler (1960)
Frontend electronics + noise: analytic
Data from:
P. Fonte, V. Peskov, High-Resolution TOF with RPCs, LIP/00-04
P. Fonte et. al, High resolution RPCs for large TOF systems, NIMA 449 (2000)
P. Fonte, Development of Large Area and Position sensitive Timing RPCs, VIC 2001
G. Aielli et. al., Performance of a large-size RPC …, NIM A456(2000) 77-81
G. Aielli, Advanced studies on RPCs, Doctorate Thesis
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Werner Riegler

4. Observations
Wire chambers can be simulated very accurately (GARFIELD).
RPCs are much ‘simpler’ than wire chambers but the detector effects and the simulation turned out to be quite complicated.
Even to understand the orders of magnitude took a long time.
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Werner Riegler

5. Secondaries in RPC: FLUKA
electrons, photons
hadron showers
Probability that the Pion is accompanied by at least one charged particle is 4.92%
H. Vincke
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Werner Riegler

6. Primary Ionization: HEED
10. 5 clusters/mm at 7GeV
  95m
nav  2.4 electrons/cluster
long tail !
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Werner Riegler

7. Gas Parameters: MAGBOLTZ, IMONTE
Townsend
Attachment
Effective Townsend coefficients:
Trigger RPC 10/mm
Timing RPC 100/mm
Drift velocity:
Trigger RPC 130 m/ns, T 15ns
Timing RPC 220 m/ns, T 1.4ns
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Werner Riegler

8. Avalanche Fluctuations
W. Legler, 1960: Die Statistik der Elektronenlawinen in elektronegativen Gasen bei hohen Feldstaerken und bei grosser Gasverstaerkung
Assumption: ionization probability independent of the last collision
Avalanches started by a single electron
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Werner Riegler

9. Efficiency Results 0.3mmTiming RPC 2mm Trigger RPC data
points show data
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Werner Riegler

10. Efficiency Results 0.3mmTiming RPC 2mm Trigger RPC Attachment x 0.65
Simulated efficiencies are compatible with data
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11. Expected Charges
0.3mmTiming RPC 3kV
Simulated Measured
Qtot = 4.6 ·107pC 5 pC
Qind= 3.8 ·105pC 0.5 pC
2mm Trigger RPC 10kV
Simulated Measured
Qtot = 2.2 ·103pC 40 pC
Qind = 1.0 ·102pC 2 pC
One can show mathematically that with previous assumptions there cannot be a peak in the charge distribution (for the parameters and models descibed so far).
Measurements show very pronounced peak -> Saturation effects
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Werner Riegler

12. High Field 1: Collision Distance
W. Legler, 1960
After a collision, electron has to gain
energy in order to reach
ionization energy Uion(e.g eV).
1/ is the average distance between
ionizing collisions.
x0 =E/Uion is the average distance for
an electron to reach the ionization energy.
x0 << 1/ : Model shown before
x0 >> 1/ : More complicated model
Avalanches started by a single electron at x=0
1/ = 6.8m
x0=0, 2.5 m
Turns out to make no difference for RPCs !
Position fluctuation of first cluster completely smears out this effect.
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Werner Riegler

13. High Field 2: Space Charge
Exponential avalanche growth is stopped by space charge effects
In this simulation this is taken into account by simply cutting
the avalanche (M. Abbrescia, Progress in the simulation of RPCs …, CMS CR 1998/021).
Detailed Model: Presentation by Christian Lippmann
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Werner Riegler

14. Simulated Charge Spectra
0.3mm Timing RPC, 3kV
2mm Trigger RPC, 10kV
Nsat = 1.6 ·107 electrons
Nsat = 2.5 ·107 electrons
Shapes are not too far from measurements
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Werner Riegler

15. Timing with very fast amplifiers
We expect:
Time resolution depends only on effective Townsend coefficient and drift-velocity.
Dependence on threshold is weak
Trigger RPC:  1ns (130 m/ns, 10/mm)
Timing RPC:  58ps (220 m/ns, 100/mm)
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Werner Riegler

16. Trigger RPC Timing MC Monte Carlo shows as expected:
Time RMS has very weak dependence on threshold
Time RMS depends only on the effective Townsend coefficient
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Werner Riegler

17. Trigger RPC - Time Resolution
preamp tp=1.3ns
100fC threshold
saturate at 2.5 ·107 electrons
everything else from
MAGBOLTZ, IMONTE, HEED
Experimental: 1ns
needs further investigation
Coimbra, Nov. 2001
Werner Riegler

18. Time Resolution - Timing RPC
Single Gap, 2.8kV, 1GHz Amplifier, 20fC threshold, 1.6 ·107 electrons saturation,
all other parameters from MAGBOLTZ, IMONTE, HEED
52 ps after correction - matches well with measurements
(analytic formula gives 62 ps)
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Werner Riegler

19. Quad Gap
Quad Gap, 5.6kV, 1GHz amplifier, 20fC threshold, 1.6·107 electrons saturation (single)
99.2% efficiency matches
well with experiment
37 ps after correction,
would naively expect 52/4=26 ps
experiment shows 47ps
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Werner Riegler

20. Crosstalk and Termination
CERN-EP/
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Werner Riegler

21. Conclusions
We have applied standard detector physics simulations to RPCs and find good agreement with measurements for efficiency and time resolution.
Charge spectra can only be explained by very large space charge effect (see Christian Lippmann, next presentation).
We do not need ‘strange’ detector effects to explain measurements.
A matrix formalism allowing termination and crosstalk calculations for RPCs with long strips can be found in CERN-EP/
Coimbra, Nov. 2001
Werner Riegler