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

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 Coimbra, Nov. 2001 Werner Riegler

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) 295-301 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 Coimbra, Nov. 2001 Werner Riegler

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. Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

Primary Ionization: HEED 10. 5 clusters/mm at 7GeV   95m nav  2.4 electrons/cluster long tail ! Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

Efficiency Results 0.3mmTiming RPC 2mm Trigger RPC data points show data Coimbra, Nov. 2001 Werner Riegler

Efficiency Results 0.3mmTiming RPC 2mm Trigger RPC Attachment x 0.65 Simulated efficiencies are compatible with data Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

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. 15-25eV). 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. Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

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) Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

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

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) Coimbra, Nov. 2001 Werner Riegler

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 Coimbra, Nov. 2001 Werner Riegler

Crosstalk and Termination CERN-EP/2000-014. Coimbra, Nov. 2001 Werner Riegler

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/2000-014. Coimbra, Nov. 2001 Werner Riegler