RPC Simulation Vincent Français 3 février 2016 Vincent Français (LPC) RPC Simulation 3 février 2016 1 / 15
Gas and Geometry 1 Simulation 2 Avalanche multiplication model Diffusion Results 3 Signal and charge induction Threshold crossing time and detector efficiency Conclusion 4 Vincent Français (LPC) RPC Simulation 3 février 2016 2 / 15
Gas and Geometry 1 Simulation 2 Avalanche multiplication model Diffusion Results 3 Signal and charge induction Threshold crossing time and detector efficiency Conclusion 4 Vincent Français (LPC) RPC Simulation 3 février 2016 3 / 15
Calice RPC geometry Gap width : 0 . 12 cm Anode width : 0 . 07 cm Cathode width : 0 . 11 cm Resistivity : 10 12 − 10 14 Ω · cm ( ǫ r ∼ 7 ) HV : 6 . 9 kV ( E = 57 . 5 kV/cm ) Vincent Français (LPC) RPC Simulation 3 février 2016 4 / 15
Calice gas mixture 300 Townsend Attachment 250 Effective 200 α , η [ cm − 1 ] 1. TFE C 2 H 2 F 4 93% 150 2. CO 2 5% 100 3. SF 6 2% 50 0 0 20000 40000 60000 80000 100000 120000 E [ V.cm − 1 ] → At 57 . 5 kV/cm, the Townsend coefficients are α = 209 . 5 and η = 60 . 8 Vincent Français (LPC) RPC Simulation 3 février 2016 5 / 15
Gas and Geometry 1 Simulation 2 Avalanche multiplication model Diffusion Results 3 Signal and charge induction Threshold crossing time and detector efficiency Conclusion 4 Vincent Français (LPC) RPC Simulation 3 février 2016 6 / 15
The simulation Gas transport parameters Longitudinal diffusion fully computed with Magboltz computed, Transverse is (9.01) approximated using a radial charge distribution Primary ionisation simulated Space Charge Effect taken with HEED (1.01) into account Electron freed by ionisation Charges induction on anode drift and multiply according to computed using Ramo’s the Riegler Model theorem Vincent Français (LPC) RPC Simulation 3 février 2016 7 / 15
Avalanche development model (Riegler) average numbers of e − and positive ions : n ( x ) = e ( α − η ) x ¯ α � e ( α − η ) x − 1 � p ( x ) = ¯ α − η stochastic multiplication and attachment for one e − s < k ¯ n ( x ) − 1 0 , n ( x ) − k ¯ � � n = � � (¯ n ( x ) − k )(1 − s ) s > k ¯ n ( x ) − 1 1 1 + floor ln , · n ( x )(1 − k ) ¯ � � n ( x ) − k ¯ 1 − k ln 1 − n ( x ) − k ¯ with s a random number ∈ [0 , 1) , k = η/α here x is the drifted distance Vincent Français (LPC) RPC Simulation 3 février 2016 8 / 15
Diffusion Thermal diffusion motion superposed by drift motion ⇒ anisotropic diffusion � � − ( z − z 0 ) 2 1 ϕ L = √ exp 2 σ 2 2 πσ L L � � − ( r − r 0 ) 2 ϕ T = 1 exp σ 2 2 σ 2 T T 0 . 012 0 . 010 D L , D T [ √ cm ] diffusion characterized by their diffusion coefficient D L and 0 . 008 D T and drifted distance l 0 . 006 √ σ L,T = D L,T l Longitudinal 0 . 004 Transverse 0 20000 40000 60000 80000 100000 120000 E [ V.cm − 1 ] Vincent Français (LPC) RPC Simulation 3 février 2016 9 / 15
Diffusion - computation ⇒ Longitudinal : new z -coordinate is computed by drawing from a √ Gaussian ( ϕ L ) with µ = z and σ = D L ∆ z ⇒ Transversal : we consider the charges to be contained in a disk √ with a Gaussian radial distribution ( ϕ T ) with σ = D T l where l is the drifted distance Vincent Français (LPC) RPC Simulation 3 février 2016 10 / 15
Gas and Geometry 1 Simulation 2 Avalanche multiplication model Diffusion Results 3 Signal and charge induction Threshold crossing time and detector efficiency Conclusion 4 Vincent Français (LPC) RPC Simulation 3 février 2016 11 / 15
Signal and charge induction 10 − 1 0 . 08 0 . 07 10 − 2 Induced current [ pC/ns ] 10 − 3 Induced current [ mA ] 0 . 06 10 − 4 0 . 05 10 − 5 0 . 04 0 . 03 10 − 6 10 − 7 0 . 02 10 − 8 0 . 01 0 . 00 10 − 9 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Time [ A.U ] Time [ A.U ] Vincent Français (LPC) RPC Simulation 3 février 2016 12 / 15
Threshold crossing time and detector efficiency 120 Efficiency for 5 GeV/c muons 100 µ = 8 . 22 ± 0 . 05 ns Gaussian fit σ = 0 . 53 ± 0 . 02 ns data 100 80 80 Efficiency [%] 60 60 40 40 20 20 0 0 250 300 350 400 450 500 550 6 . 4 6 . 6 6 . 8 7 . 0 7 . 2 7 . 4 7 . 6 7 . 8 Crossing threshold time [0 . 019 ns ] HV [ kV ] Vincent Français (LPC) RPC Simulation 3 février 2016 13 / 15
Gas and Geometry 1 Simulation 2 Avalanche multiplication model Diffusion Results 3 Signal and charge induction Threshold crossing time and detector efficiency Conclusion 4 Vincent Français (LPC) RPC Simulation 3 février 2016 14 / 15
Conclusion 1.5D simulation, transverse diffusion is approximated Space Charge Effect taken into account Gives coherent results and behavior, still needs to be carefully compared to experimental data Biggest bottleneck : Pseudo-Random numbers generation Using GPU RNG generator (Nvidia Curand or Thrust) could give a very significant speed-up at the price of an increase in code complexity Vincent Français (LPC) RPC Simulation 3 février 2016 15 / 15
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