Light Concentrators for Spherical Detectors:Tiling and Timing
Brian NaranjoUCLA Dept. of Physics & Astronomy
Advances in Neutrino Technology 2014University of California, Los Angeles
2014 September 24
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Introduction and NuDot motivation
Want spherical geometryOptimal volume-to-surface ratioMinimal angular variations in detection efficiencyExcellent structural properties
Want maximal photocathode coverageChallenging reconstructionReduced light yield
Want heterogeneous mix of photocathode shapes and sizes8 inch PMTs for collection of slow scintillation light2 inch PMTs (low TTS) for collection of fast Cerenkov lightIncremental LAPPD upgrade as they become available
Have developed some new code to satisfy these requirements:First, generate quasi-uniform heterogeneous tilings on the sphere.Second, construct a set of light concentrators that fits into the spherical tiling.
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Goldberg polyhedra
Can tile flat plane with hexagons. To tile sphere, need an occasional pentagon.Goldberg polyhedron1 G(m,n)
Path between neighboring pentagons: m steps, turn left 60◦, n steps.Example shown is G(2, 1)2, which is the mirror image of G(1, 2).
1M. Goldberg, “A class of multi-symmetric polyhedra,” Tohoku Math. J. 43, 104 (1937)2http://en.wikipedia.org/wiki/Goldberg_polyhedron
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Goldberg Polyhedra - Examples
G(3, 0) - MiniCLEAN Dark Matter Experiment
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Goldberg polyhedra - examples
G(1, 1) - Adidas Telstar
Let’s arrange 8” PMTs on the polygons and 2” PMTs on the vertices. . .
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Goldberg polyhedra - which one do we want?
polyhedron pentagons hexagons vertices
G(1, 1) 12 20 60
G(2, 0) 12 30 80
G(2, 1) 12 60 140
G(3, 0) 12 80 180
G(2, 2) 12 110 240
. . .
Pick G(2, 0) to match NuDot budget/scale of about 42 8” PMTs and 80 2” PMTs.
Easiest to implement special case G(m, 0).
More fun to implement G(m,n) for arbitrary m and n.
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Goldberg polyhedra - G(2, 1) construction
Twenty shaded triangles fold up into a dodecahedron.Blue regions correspond to 8” PMTs. Orange regions correspond to 2” PMTs.Computational Geometry Algorithms Library (CGAL) doing most of the heavy lifting.
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Goldberg polyhedra - G(2, 1) construction
Project dodecahedron onto the sphere.Pentagons formed at the dodecahedron’s 12 vertices.Code can handle arbitrary tilings satisfying symmetry – Geodesic domes!
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Light concentrators
Etendue theorem - optical analog of Liouville’s theoremCompound parabolic concentrator3 (CPC) achieves maximum theoretical lightconcentration A/A′ = 1/ sin2 θi.To accomodate irregular aperture, use simple linear scaling of CPC. Seems to workfine, but there could still be a better way.Tends to concentrate reflected light around the rim. Want to avoid getting too closeto edge of photocathode, where the performance degrades4.
3R. Winston, “Light Collection within the Framework of Geometrical Optics,” JOSA 60, 245 (1970)4J. Brack et al., NIM A 712, 162 (2013)
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Light concentrators
Light concentrators made of electroformed nickel with a thin reflective layer ofprotected aluminum.
Commercial shops:http://www.phoenixelectroforms.com and http://optiforms.com
CNC-machine stainless mandrel
Polish to scratch-dig 80-50 or better
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G(2, 0) tiling for NuDot
42 8” PMTs
80 2” PMTs
Radius of scintillatorsphere is 400 mm
Inner radius of lightcollection sphere is450 mm
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G(2, 0) tiling for NuDot
42 8” PMTs
80 2” PMTs
Radius of scintillatorsphere is 400 mm
Inner radius of lightcollection sphere is450 mm
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Monte Carlo
Using RATPAC (RAT-Plus Addition Codes) simulation/analysis framework forGeant4.
Added back-end code to RATPAC for importing meshed concentrator surfaces viaCADmesh.5
PMT and concentrator geometry, in terms of xyz coordinates and Euler angles, iswritten to a JSON database.
Use RAT’s detailed photomultiplier model.
5C. Poole et al., IEEE Trans. Nucl. Sci. 99, 1 (2012)12 / 17
Monte Carlo - hexagonal light concentrator
0 50 100 150 200 250 300∆d/c (ps)
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Direct hit
One reflection
Photon source at center of scintillator volume.Beeline distance from photon source to photocathode = 654 mm.Histogrammed in terms of vacuum optical path. Multiply by refractive index.Assuming no reflections from PMT glass and perfect specular reflections offconcentrator.
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Monte Carlo - hexagonal light concentrator
0 500 1000 1500 2000∆d/c (ps)
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One reflection
Two reflections Three reflections
Go far off to the edge of the scintillator volume (r= 400 mm)Photocathode is completely obscured, so all detected photons undergo at least onereflection.Light concentrator is kicking out some of the photons.
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Monte Carlo - hexagonal light concentrator
0 100 200 300 400 500 600 700r (mm)
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r =0 corresponds to a photon source at the center of the scintillation volume.
r = 400 mm corresponds to the previous slide.
Look at two different extremes in light concentrator axial orientation. Don’t see muchdifference in acceptance. Good!
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Monte Carlo - small round light concentrator
-2 0 2 4 6 8 10 12 14 16∆d/c (ps)
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75 mm round cone. Little bit bigger than ones we are now considering
Figure on left: photon source is at center of scintillator volume
Figure on right: photon source is at edge of scintillator volume
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Conclusion and what’s next
Now have a flexible general purpose code for constructing spherical detectorgeometries.
Next step is extensive simulation to finalize NuDot geometry.
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