Semi-Analytic Approach to Light Simulation Diego Garcia-Gamez & Andrzej Szelc The University of Manchester 1
Introduction Optical simulation in LAr detectors is very hard: huge time • and memory consuming This issue is even worse in large detectors like DUNE (SP & • DP) Different approaches to overcome this problem: Optical • library, hybrid library, extended library We propose here a new approach: analytical/parametric • solution: - Very good results already demonstrated for the time estimation (ns level) - We include now the estimation of the number of photons 2
Geometric approach • For “practical” reasons we will assume our light detector as circular disks: a symmetric shap e will make easier to generalize our results • Given a dEdx in a point (x, y, z) we want to predict the number of hits in our optical detector (x i , y i , z i ) • Isotropic scintillation emission makes the problem “almost” geometric Solid angle of a disk • “Almost” because we have Rayleigh scattering 3
Simulations In our studies we assume: Scintillation points with 5x10 7 photons • • 8” diameter disks as optical detectors Optical Detectors • Argon absorption length of 20 meters • No photon reflections in the walls (VUV light is highly absorbed in most materials ) • Three different active volume sizes: DUNE-SP like (3.6m x 12m x 14m) DUNE-DP like (12m x 12m x 8m) SBN like (2m x 4m x 10m) • Three different Rayleigh Scattering lengths (i.e. spectrums centered at): LAr ~ 60 cm ~ 120 cm ~ 180 cm 4
If we assume no Rayleigh Scattering • As expected, when switching off the Rayleigh scattering (or for larger wavelengths like visible) the situation is pure geometry hit )/N Poisson fluctuation hit 0.3 - N rec 0.2 (N 0.1 0 -0.1 -0.2 -0.3 0 200 400 600 800 1000 1200 1400 5 distance [cm]
Rayleigh Scattering in our simulations Rayleigh scattering length @ 90K as a function of wavelength from arXiv:1502.04213 (the one in LArSoft) 450 Rayleigh Length [cm] Mean 63.74 Mean 63.74 400 4 Std Dev Std Dev 20.23 20.23 10 350 300 3 10 250 200 Scatter-lengths plugged in our 150 2 10 simulations LAr scintillation emission: 100 Mean 128.0 50 Std Dev 3.2 10 0 0 20 40 60 80 100 120 140 160 180 200 100 150 200 250 300 350 400 450 [nm] Rayleigh Length [cm] λ 6
Including Rayleigh Scattering vs distance ß Situation a lot more complex in the More than 5 orders of magnitude range! realistic case when Rayleigh Scattering is included (λ RS ~ 60cm in this example) < λ RS ~ 60cm > DP-size < λ RS ~ 60cm > DP-size Relation N hits /Ω is more complex than a simple dependency on the distance à At a fixed distance, fluctuations are too big (unmanageably)! à More degrees of freedom needed! 7
Including Rayleigh Scattering vs distance and θ θ = angle between the scintillation point and the normal to the optical detector /cos(θ) surface < λ RS ~ 60cm > DP-size < λ RS ~ 60cm > DP-size Relation N hits /Ω/cos(θ) reduces significantly the uncertainties, but still quite large à strong dependency on the relative position between scintillation point and the optical detector surface 8
Including Rayleigh Scattering vs distance and θ D. Garcia-Gamez Modeled with Gaisser-Hillas function Preliminary < λ RS ~ 60cm > DP-size 9
Correcting Ω by RS(distance, θ): Dual-Phase with λ RS ~ 60cm /cos(θ) < λ RS ~ 60cm > DP-size Preliminary 10
Correcting Ω by RS(distance, θ): Dual-Phase with λ RS ~ 60cm /cos(θ) < λ RS ~ 60cm > DP-size Preliminary No bias and Reweighting by better than the number of entries/opdet 10% resolution, and better for larger λ RS 11
Correcting Ω by RS(distance, θ): Single-Phase with λ RS ~ 60cm < λ RS ~ 60cm > SP-size Preliminary 12
Correcting Ω by RS(distance, θ): Single-Phase with λ RS ~ 60cm < λ RS ~ 60cm > SP-size Preliminary No bias and Reweighting by better than the number of entries/opdet 10% resolution, and better for larger λ RS 13
Reminder: Library performance Correlation between geant4 and SBND optical library: (5cm x 5cm x 5cm voxels & 4x10 5 photons generated in each voxel) ~15% underestimation of the Notice in SBND the PMTs are 8” photon number with a 23% global diameter à voxels half size of PMT resolution window 9000 Entries Entries 51239 51239 8000 Mean Mean 0.1649 0.1649 − − 7000 Std Dev 0.2322 Std Dev 0.2322 6000 5000 4000 3000 2000 1000 0 − 4 − 3 − 2 − 1 0 1 2 3 4 14 (Photons - Photons )/Photons geant4 library geant4
RS(distance, θ) vs λ RS and detector size Single-Phase: < λ RS = 60 cm > < λ RS = 120 cm > < λ RS = 180 cm > Preliminary Preliminary Preliminary Dual-Phase: < λ RS = 60 cm > < λ RS = 120 cm > < λ RS = 180 cm > Preliminary Preliminary Preliminary 15
RS(distance, θ) vs λ RS and detector size Maximum Gaisser-Hillas Preliminary N Gaisser-Hillas Preliminary Single-Phase Single-Phase Maximum Gaisser-Hillas N Gaisser-Hillas Dual-phase Dual-phase Preliminary Preliminary 16
Photon Arrival Times • We are also working in an update/ extension of the time parametrization to larger detectors like DUNE 17
Arrival time distributions [reminder] • We have developed a parametrization to account for this in SBND à we have validated it with the other two Short Baseline detectors: MicroBooNE and ICARUS - It was designed as an addition to the fast optical mode We have parameterized the time distributions à resulted only from direct transport + Rayleigh scattering 160 photons (direct component) A Landau + Exponential function describes well 140 the arrival time distributions of the direct/VUV 120 light at any distance from the photocathode 100 Parameterization ready in LArSoft (next weeks): 80 par0 = Landau normalization Fit result 60 par1 = Landau MPV 40 par2 = Landau width par3 = Expo cte 20 par4 = Expo tau 0 20 40 60 80 100 120 140 time [ns] 18
Updating the arrival time distributions For the update we have generated 10 8 optical photons per scintillation point (dEdx ~ 4.2 GeV) to have the shape of the signals at very large distances distance = 341 cm distance = 119 cm Landau + Exponential Landau + Exponential Landau Landau 19
“Landau + Exponential” vs “Landau” • For distance < 300 cm Landau + Exponential model clearly describes better the signals than a single Landau • At distances > 300 cm both models work similarly 20
Updating the arrival time distributions • Extension to large distances (> 600 cm) soon: files with simulations at large distances ready • Study dependencies with different values of Rayleigh Scattering under way Landau + Exponential Landau Preliminary Preliminary 21
Conclusions • We have developed an analytical way to predict the scintillation light signals in LAr detectors: - A recipe for both number of photons and arrival time distributions • We have studied and parametrized the main dependencies of the signals: - Distance, angle, λ RS and detector size - Better performance than current tools • We want to have an operative module for doing this in LArSoft by the end of the summer • A technical paper is in preparation to explain all the details 22
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