PTFE Reflectance Measurements, Modeling and Simulation for Xenon Detectors

Transcription

1 PTFE Reflectance Measurements, Modeling and Simulation for Xenon Detectors Claudio F. P. Silva University of Coimbra LIP Laboratory Chicago, 11 June 2011 TIPP 2011 PTFE reflectance measurements, modeling and simulation for Xenon detectors p.1/31

2 The PTFE in Xenon Detectors PTFE (polytetrafluoroethylene) is a common choice for the inner walls of liquid/gaseous xenon experiments Dark Matter Detectors LUX XENON100 Panda-X Double-beta decay NEXT (gaseous xenon) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.2/31

3 Why the use of PTFE PTFE has a high reflectance in the visible spectra ( 99%). A large reflectance essencial to optimize the light collection. (LUX collaboration) Xenon emitts in the VUV region ( nm). Below 250 nm the reflectance of the PTFE is not well known. Hem. Reflectance 0.8 Spectralon PTFE Wavelength (nm) (Kadkhoda et al, SPIE, 3578, 544) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.3/31

4 Objectives The measurement of the reflectance distributions of various fluoropolymers samples for the xenon scintillation light. The modeling of the processes involved and the application to Geant4 simulations. Prediction of the reflectance distribution for the liquid xenon/ptfe interface. PTFE reflectance measurements, modeling and simulation for Xenon detectors p.4/31

5 The PTFE/Teflon R The simplest fluoropolymer ( (CF 2 ) n ) CF is the strongest bond in organic chemistry (good chemical resistance) High temperature resistance -200 C to 260 C Helicoidal structure (temperature dependent) Composed by a crystalline and amorphous phase (usually with different optical properties) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.5/31

6 PTFE - What we should be careful PTFE degradation under intense VUV radiation F F F C C C C F F F PTFE absorbs contaminants (hydrocarbonets) Vacuum-baking at about 90 C for a period of about 48 h recomended It should be left in a sealed container. Plastic containers are not recomended. PTFE reflectance measurements, modeling and simulation for Xenon detectors p.6/31

7 ϕ What do We Mean by Reflection? θ i θ r ϕ i r Bidirectional reflectance distribution function ρ (θ i,φ i ;θ r,φ r ) = di r (θ i,φ i,θ r,φ r ) dφ i (θ i,φ i ) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.7/31

8 What do We Mean by Reflection? Bidirectional Directional-Hemispherical Bi-Hemispherical Biconical Conical-Hemispherical H V Detector θ i θ r n Sample PTFE reflectance measurements, modeling and simulation for Xenon detectors p.8/31

9 The Angle Resolution System The Angle Resolution System (ARS) is placed inside an air tight chamber. The light of 175 nm is emitted by a xenon proportional counter. PTFE reflectance measurements, modeling and simulation for Xenon detectors p.9/31

10 The Angle Resolution System Light source 220 mm 80 mm Surface sample m m 91 mm θ i θ r Xenon light source scintillation Black cover iris diaphragms photo detector (photomultiplier) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.10/31

11 Reflectance Components Specular: Incident light Reflected light specular spike specular lobe Refracted light Rough surface Diffuse: Incident light diffuse light Internal reflection Internal scattering absorption PTFE reflectance measurements, modeling and simulation for Xenon detectors p.11/31

12 Reflectance Components Light Source Photo Sensor incident ray θ n θ Specular Spike Backscatterer Lobe diffuse lobe Specular Lobe reflecting surface ρ = ρ l + ρ s + ρ d + ρ b ρ l specular lobe ρ s specular spike ρ d diffuse lobe ρ b backscatterer lobe PTFE reflectance measurements, modeling and simulation for Xenon detectors p.12/31

13 The Specular Reflection ρ = F (θ i )χ 1 χ 1δ (i r) + (1 χ 1 χ 1)F (θ ) P α (α)g(θ i,θ r ) 4 cos θ i F - the Fresnel equations, dependent of n and κ χ 1 - the characteristic function of the probability distribution of heights P 1 (z) P α (α) - the probability distribution of the slopes α G (θ i,θ r ) - shadowing-masking attenuation coefficient i θ i θ i n α n θ r θ r V φ r PTFE reflectance measurements, modeling and simulation for Xenon detectors p.13/31

14 The Specular Lobe The following distributions P α were considered Cook-Torrance - Gaussian Like ( 1 P CT (α,m) = πm 2 cos 4 α exp Trowbridge-Reitz P TR (α,γ) = Bivariate-Cauchy P BC (α,γ) = γ 2 π(γ 2 cos 2 α+sin 2 α) 2 γ 2 +γ π(γ 2 cos 2 α+sin 2 α) 3 2 ) tan2 α m 2 PTFE reflectance measurements, modeling and simulation for Xenon detectors p.14/31

15 The Specular Reflection ρ = F (θ i )χ 1 χ 1δ (i r) + (1 χ 1 χ 1)F (θ ) P α (α)g(θ i,θ r ) 4 cos θ i F - the Fresnel equations, dependent of n and κ χ 1 - the characteristic function of the probability distribution of heights P 1 (z) P α (α) - the probability distribution of the slopes α G (θ i,θ r ) - shadowing-masking attenuation coefficient No Interference Shadowed Masked PTFE reflectance measurements, modeling and simulation for Xenon detectors p.15/31

16 PTFE Reflectance Distributions Dir.-Conical Reflectance (sr 1 ) Skived PTFE nm θ i = Dir.-Conical Reflectance (sr 1 ) Molded PTFE nm θ i = Viewing Angle θ r (deg) Viewing Angle θ r (deg) We observe three different components Diffuse Lobe Specular Lobe Specular Spike PTFE reflectance measurements, modeling and simulation for Xenon detectors p.16/31

17 The Specular Lobe The bivariate-cauchy has the best description γ is constant with θ i and decreases with λ. Dir.-Conical Reflectance (sr 1 ) Skived PTFE 175 nm 0 10 P (α) Cook-Torrance Trowbridge-Reitz Viewing Angle θ r (deg) Dir.-Conical Reflectance (sr 1 ) 10 1 Molded PTFE 470 nm P (α) Trowbridge-Reitz Bivariate Cauchy Viewing Angle θ r (deg) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.17/31

18 The Specular Spike ρc/(ρc + ρl) The intensity of the specular spike (ρ c / (ρ c + ρ l )) changes with the roughness, wavelength of the light and angle of incidence exp ( K cos θ i ) P 1 gaussian 0.05 P 1 exponential ETFE PTFE cos θ i cos θ i The usual distributions p 1 do not describe the data. Λ = exp ( K cos θ i ) is an empirical function. EL ET PTFE reflectance measurements, modeling and simulation for Xenon detectors p.18/31

19 The Fits A global fit is applied to results with only three or four parameters. For the different samples we obtain λ = 175 nm n a d γ K refractive albedo sp. lobe spike index width intensity Skived PTFE 1.49± ± ± PTFE (not polished) 1.51± ± ± Extruded ( ) PTFE 1.50± ± ± ±0.3 Extruded ( ) PTFE 1.46± ± ± ±0.5 Molded PTFE 1.45± ± ± ±0.2 PTFE reflectance measurements, modeling and simulation for Xenon detectors p.19/31

20 The Hemispherical Reflectances Directional-Hemispherical Direc.-Hemis. Ref PTFE Polished 175 nm Total Reflectance Diffuse Lobe Specular Spike 0.2 Specular Lobe Angle of Incidence θ i (deg) Bi-Hemispherical Reflectance Diffuse. S. Lobe S. Spike Total Skived PTFE 0.488± ± ±0.007 Molded Polished 0.625± ± ± ±0.04 PTFE reflectance measurements, modeling and simulation for Xenon detectors p.20/31

21 Geant 4 - Current The current descriptions (Unified and Glisur) do not agree in many ways with our measurements Diffuse lobe proportional to the reflected light The intensity of the specular spike is independent of the angle of incidence It is restricted to gaussian statistics The shadowing and masking are not fully considered PTFE reflectance measurements, modeling and simulation for Xenon detectors p.21/31

22 Geant 4 - New This model of reflection was included in the Geant4 as new method of the class G4BoundaryProcess. Inverse cumulative functions are used to generate the direction of both the diffuse reflected and specularly reflected light. Reflectance (sr 1 ) Angle of reflection θ r (deg) Angle of reflection θ r (deg) PTFE reflectance measurements, modeling and simulation for Xenon detectors p.22/31

23 Reflection in a Liquid Interface The reflectance obtained in the gas/ptfe is between 60-80%. There are strong indications that the reflectance in the liquid xenon is much higher (>80%). The liquid xenon has a higher index of refraction (n 1.69) comparatively to the air or vacuum PTFE reflectance measurements, modeling and simulation for Xenon detectors p.23/31

24 Reflection in a Liquid Interface Gas/Vacuum LXe Gas/Vacuum LXe absorption Fresnel Reflectance n(ptfe)=1.5 n(lxe)=1.69 gas-to-ptfe liquid-to-ptfe Angle of incidence θ i (deg) Angle of incidence θ i (deg) n(ptfe)=1.5 n(lxe)=1.69 PTFE-to-gas PTFE-to-liquid PTFE reflectance measurements, modeling and simulation for Xenon detectors p.24/31

25 Reflection in a Liquid Interface Gas/Vacuum LXe Gas/Vacuum LXe absorption In the liquid: The internal reflection probability is smaller. Less light returns to the bulk to be internally scattered where it can be eventually absorbed. The multiple-diffuse albedo a d will be larger. PTFE reflectance measurements, modeling and simulation for Xenon detectors p.25/31

26 Reflection in a Liquid Interface R(θi),2π Gas or Vaccum PTFE Polished 175 nm Total Reflectance Diffuse Lobe Specular Spike 0.2 Specular Lobe Angle of Incidence θ i (deg) R(θi),2π Liquid/PTFE Total Reflecance Diffuse Lobe Specular Lobe Specular Spike Angle of Incidence θ i (deg) Diffuse Lobe Specular Lobe Specular Spike Total Ref Gas Liq. Gas Liq. Gas Liq. Gas Liq. Skived PTFE Molded PTFE PTFE reflectance measurements, modeling and simulation for Xenon detectors p.26/31

27 Conclusion We developped an angle resolution system to measure the reflectance distribution in vacuum. The reflectance distribution of the PTFE is composed by three contributions (diffuse lobe, specular lobe and specular spike). Four free parameters reproduces fairly well the details of the measured reflectance distributions. A new simulation of the reflectance processes was included in Geant-4 The reflectance distributions were estimated to a Liquid-PTFE interface. PTFE reflectance measurements, modeling and simulation for Xenon detectors p.27/31

28 Thank you! PTFE reflectance measurements, modeling and simulation for Xenon detectors p.28/31

29 Surface Statistics h (x, y) the height function z = h (x,y) h (x,y) =0 P 2 (z,z ), bivariate distribution of heights h (µm) P 2 (z,z 1 ) = exp 2π[1 C(τ,T)]σh x (µm) } { z2 2C(τ,T)zz +z 2 2σh 2[1 C(τ,T)] C (r, T) correlation function C = 1 h (x σh 2 1,y 1 ),h(x 2,y 2 ) i θ i θ i n α n θ r θ r V P α (α,σ α ) - slope distribution φ r PTFE reflectance measurements, modeling and simulation for Xenon detectors p.29/31

30 The Specular Reflection in a Rough Surface A complex diffraction problem ρ = R2 cos 2 θ cosθ i λ 2 0 χ 2 (τ) J 0 (k z τ) τdτ χ 2 is the characteristic function of P 2 For a bivariate gaussian distribution ρ = E2 0 R2 cos 2 θ { χ λ 2 1 χ 1 J 0 (k z τ) τdτ 0 k 2n } z + σ2n h [C (τ,t)] n J 0 (k z τ) τdτ n! n=1 0 PTFE reflectance measurements, modeling and simulation for Xenon detectors p.30/31

31 The Diffuse Component Incident light diffuse light Internal reflection Internal scattering absorption ρ d = a d π cosθ rυ (θ i,θ r,φ) [1 F (θ i, )] [1 F (θ r )] The light is scattered isotropically in the bulk. The Fresnel factors account with the two refractions of the light, Air-to-PTFE and PTFE-to-Air. a d is the multiple-diffuse albedo of the surface. Oren-Nayar factor Υ accounts for the roughness of the surface. PTFE reflectance measurements, modeling and simulation for Xenon detectors p.31/31