RPC Simulation Vincent Franais 3 fvrier 2016 Vincent Franais (LPC) - - PowerPoint PPT Presentation

RPC Simulation

Vincent Français 3 février 2016

Vincent Français (LPC) RPC Simulation 3 février 2016 1 / 15

1

Gas and Geometry

2

Simulation Avalanche multiplication model Diffusion

3

Results Signal and charge induction Threshold crossing time and detector efficiency

4

Conclusion

Vincent Français (LPC) RPC Simulation 3 février 2016 2 / 15

1

Gas and Geometry

2

Simulation Avalanche multiplication model Diffusion

3

Results Signal and charge induction Threshold crossing time and detector efficiency

4

Conclusion

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 : 1012 − 1014 Ω · cm (ǫr ∼ 7) HV : 6.9 kV (E = 57.5 kV/cm)

Vincent Français (LPC) RPC Simulation 3 février 2016 4 / 15

Calice gas mixture

• 1. TFE C2H2F4

93%

• 2. CO2

5%

• 3. SF6

2%

20000 40000 60000 80000 100000 120000

E [V.cm−1]

50 100 150 200 250 300

α , η [cm−1]

Townsend Attachment Effective

→ 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

1

Gas and Geometry

2

Simulation Avalanche multiplication model Diffusion

3

Results Signal and charge induction Threshold crossing time and detector efficiency

4

Conclusion

Vincent Français (LPC) RPC Simulation 3 février 2016 6 / 15

The simulation

Gas transport parameters computed with Magboltz (9.01) Primary ionisation simulated with HEED (1.01) Electron freed by ionisation drift and multiply according to the Riegler Model Longitudinal diffusion fully computed, Transverse is approximated using a radial charge distribution Space Charge Effect taken into account Charges induction on anode computed using Ramo’s 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 ¯ p(x) = α α − η

• e(α−η)x − 1
• stochastic multiplication and attachment for one e−

n =      0, s < k ¯

n(x)−1 ¯ n(x)−k

1 + floor

• ln
• (¯

n(x)−k)(1−s) ¯ n(x)(1−k)

• ·

1 ln

• 1−

1−k ¯ n(x)−k

• ,

s > k ¯

n(x)−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 ϕL = 1 √ 2πσL exp

• −(z − z0)2

2σ2

L

• ϕT = 1

σ2

T

exp

• −(r − r0)2

2σ2

T

• 20000

40000 60000 80000 100000 120000

E [V.cm−1]

0.004 0.006 0.008 0.010 0.012

DL , DT [√cm ]

Longitudinal Transverse

diffusion characterized by their diffusion coefficient DL and DT and drifted distance l σL,T = DL,T √ l

Vincent Français (LPC) RPC Simulation 3 février 2016 9 / 15

Diffusion - computation

⇒ Longitudinal : new z-coordinate is computed by drawing from a Gaussian (ϕL) with µ = z and σ = DL √ ∆z ⇒ Transversal : we consider the charges to be contained in a disk with a Gaussian radial distribution (ϕT ) with σ = DT √ l where l is the drifted distance

Vincent Français (LPC) RPC Simulation 3 février 2016 10 / 15

1

Gas and Geometry

2

Simulation Avalanche multiplication model Diffusion

3

Results Signal and charge induction Threshold crossing time and detector efficiency

4

Conclusion

Vincent Français (LPC) RPC Simulation 3 février 2016 11 / 15

Signal and charge induction

100 200 300 400 500 600

Time [A.U]

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Induced current [mA]

100 200 300 400 500 600

Time [A.U]

10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1

Induced current [pC/ns]

Vincent Français (LPC) RPC Simulation 3 février 2016 12 / 15

Threshold crossing time and detector efficiency

250 300 350 400 450 500 550

Crossing threshold time [0.019 ns]

20 40 60 80 100 120 µ = 8.22 ± 0.05 ns σ = 0.53 ± 0.02 ns

Gaussian fit data

6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8

HV [kV ]

20 40 60 80 100

Efficiency [%]

Efficiency for 5 GeV/c muons Vincent Français (LPC) RPC Simulation 3 février 2016 13 / 15

1

Gas and Geometry

2

Simulation Avalanche multiplication model Diffusion

3

Results Signal and charge induction Threshold crossing time and detector efficiency

4

Conclusion

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