Parameterisation of reflected light arrival times Patrick Green - - PowerPoint PPT Presentation

Parameterisation of reflected light arrival times

Patrick Green The University of Manchester

19/11/2018 1

Introduction

• As previously shown by Diego, the Landau +

Exponential parameterisation of VUV arrival times is very effective.

• With the inclusion of TPB coated reflective foils

an equivalent parameterisation for the reflected light is required.

• Aim: to use the distribution from the VUV

parameterisation to predict the reflected light distribution.

• The fastest path taken by the reflected light can

be calculated, then the arrival time distribution can be approximated by smearing the VUV distribution along this path.

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Diego Garcia-Gamez

Fastest arrival time

• Hotspot is the point on the

cathode most strongly illuminated by the scintillation.

• Image is reflection about cathode

plane weighed by refractive indices of each component in LAr.

• Intercept of line between image

and detector with the cathode plane gives the reflection point of the fastest path.

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𝑒 𝑒 ∗ 𝑜𝑤𝑗𝑡 𝑜𝑤𝑣𝑤

Scintillation point Arapuca Cathode Reflection point Hotspot Image Visible path VUV path

𝜄 𝛽

Fastest arrival time

• Time taken by VUV part of path

given by Landau + Exponential parameterisation.

• Time taken by visible part of path

calculated by the distance divided by the velocity since Rayleigh scattering negligible.

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𝑒 𝑒 ∗ 𝑜𝑤𝑗𝑡 𝑜𝑤𝑣𝑤

Scintillation point Arapuca Cathode Reflection point Hotspot Image Visible path VUV path

𝜄 𝛽

Fastest arrival time

• Fastest arrival time matches

full optical simulation to within 1-2ns.

• However, distribution of

arrival times inaccurate.

• Detected photons arrive

from area around the fastest path reflection point.

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Full simulation Parameterisation

d = 160cm, θ = 0°, α = 0°

Distribution of arrival times

• Distribution approximated by

smearing the arrival times found from the fastest path:

𝑢𝑡 = 𝑢 + 𝑢 − 𝑢𝑔 ∗ [exp −𝜐 ∗ ln 𝑦 − 1] where 𝑦 = 𝑠𝑏𝑜𝑒[0.5, 1 − 𝜀].

• 𝜐 and 𝜀 parameterised in terms of 𝑒

and 𝜄 using simple minimisation method.

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𝑒 𝑒 ∗ 𝑜𝑤𝑗𝑡 𝑜𝑤𝑣𝑤

Scintillation point Arapuca Cathode Reflection point Hotspot Image Visible path VUV path

𝜄 𝛽

Distribution of arrival times

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• 𝜐 and 𝜀 found using a simple minimisation method.

𝜐 fit 𝜀 fit

Smearing: d = 160cm, θ = 0°, α = 0°

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Un-smeared Smeared

Full simulation Parameterisation Full simulation Parameterisation

Un-smeared Smeared

Parameterisation Full simulation Full simulation Parameterisation

Smearing: d = 160cm, θ = 13.9°, α = 49.3°

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Smearing: d = 160cm, θ = 26.3°, α = 66.7°

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Un-smeared Smeared

Parameterisation Full simulation Full simulation Parameterisation

Smeared distributions: d = 60cm

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θ = 0°, α = 0° θ = 28.9°, α = 57.2°

Parameterisation Full simulation Full simulation Parameterisation

Smeared distributions: d = 260cm

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Parameterisation Full simulation Full simulation Parameterisation

θ = 0°, α = 0° θ = 24.1, α = 77.9°

Summary

• Can calculate the earliest reflected light arrival time to within 1-2ns

by calculating the fastest path accounting for the differing refractive indices of VUV and visible light in LAr.

• The distribution of the arrival times can then be approximated by

smearing the times calculated along fastest path with an exponential distribution.

• Approximation works well, although some discrepancy at large
• angles. However, these cases are minority of detected photons.
• The next stage is implementation into LArSoft.

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Back-up

Distribution of arrival times

• Used a simple minimisation

technique obtain values of 𝜐 and 𝜀.

• Parameterisation of 𝜐:

𝜐 = 12.30 − 0.114 𝑒 + 4.54 × 10−4 𝑒2 − 6.20 × 10−7 𝑒3

• Parameterisation of 𝜀:

𝜀 = 3.17 × 10−3 + 5.20 × 10−6 𝑒 + 2.21 × 10−8 𝑒2 ∗ 𝜄

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𝑒 𝑒 ∗ 𝑜𝑤𝑗𝑡 𝑜𝑤𝑣𝑤

Scintillation point Arapuca Cathode Reflection point Hotspot Image Visible path VUV path

𝜄 𝛽