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Aging tests for dielectric-coated aluminum to be used in the Sudbury Neutrino Observatory McGarry, Louis J. 1993

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AGING TESTS FOR DIELECTRIC-COATED ALUMINUM TO BEUSED IN THE SUDBURY NEUTRINO OBSERVATORYLouis John McGarryB. Sc. (Physics) University of California, Davis, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1993© Louis John McGarryIn presenting this thesis in partial fulfilment of the requirements for an advanced degreeat the University of British Columbia, I agree that the Library shall make it freelyavailable for reference and study. I further agree that permission for extensive copyingof this thesis for scholarly purposes may be granted by the head of my department orby his or her representatives. It is understood that copying or publication of this thesisfor financial gain shall not be allowed without my written permission.Department ofThe University of British Columbia1956 Main MallVancouver, CanadaDate:/TisAbstractThe Sudbury Neutrino Observatory is a heavy water erenkov detector designedto detect solar neutrinos. Its main objective is to confirm or negate the solar neutrinoproblem. To achieve maximum counting rates and, thus, minimum statistical uncer-tainties, collection of erenkov light must be maximized. Our group at UBC, workingwith collaborators at Oxford, have designed and tested an optical concentrator thatcouples with a photomultiplier tube to achieve an effective gain in light collection bynearly a factor of 2.We have designed a procedure for measuring the reflectivity of flat mirror immersedin water within the incident angular range of 15° to 750 to facilitate the reflectivitymeasurement of dielectric-coated aluminum (DCA) mirror—the reflective component inthe the concentrators. DCA is a standard product used in lighting fixtures to enhancethe total reflected light. We determined that our application would best be served witha dielectric coating that was 10% thinner than standard. Our DCA was manufacturedwith the thinner coating. To ensure that the mirror will not significantly deterioratewithin the 10 year expected life span of the detector, equipment was designed and con-structed that accelerates the aging of the mirror, allowing 10 year-equivalent aging tooccur in 70 lab-days. The reflectivity of aged mirror was then measured to verify thatno significant loss occured.11Table of ContentsAbstract^ iiList of Figures^ viAcknowledgements^ vii1 Introduction 11.1 Solar Neutrino Problem ^ 11.1.1^Solar Models 21.2 Previous Experiments ^ 31.2.1^Homestake 41.2.2^KAMIOKANDE II ^ 51.2.3^SAGE and GALLEX 61.3 SNO 62 Concentrator Theory 102.1 Introduction^ 102.2 Concentrator Theory ^ 102.2.1^The Calculation 112.2.2^The 2-Dimensional Concentrator ^ 122.2.3^The 3-Dimensional Concentrator 152.2.4^The Profile ^ 163 Concentrator Material Candidates and Requirements 181113.13.2Introduction^Reflector Candidates ^18193.2.1^TIRF ^ 193.2.2^Anodized Aluminum ^ 193.2.3^Glass ^ 203.2.4^DCA 203.3 DCA Design^ 203.3.1^DCA Optics^ 223.4 Retainer Plastic Candidates ^ 224 Concentrator Manufacture 244.1 Introduction^ 244.2 DCA Manufacture ^ 244.3 DCA Petal Production 254.4 Plastic Retainer^ 264.5 Concentrator Assembly ^ 264.6 Photomultiplier Support Structure ^ 265 Test Methods and Results 285.1 Introduction^ 285.2 Absolute Reflectivity Measurement ^ 285.2.1^Reflectometer ^ 295.2.2^Determination of Absolute Reflectivities ^ 305.3 Determination of Optimal DCA Coating Thickness 325.4 Aging Tests ^ 335.4.1^Test conditions ^ 355.4.2^Equipment 36iv5.4.3 Tests Results ^  376 Conclusion^ 44Bibliography 46List of Figures1.1 The proton-proton cycle.  ^31.2 The solar neutrino spectra.  ^41.3 The SNO detector^  72.4 Optical coordinate space. ^  112.5 Two-dimensional concentrator.  132.6 Edge-ray Principle for two-dimensional concentrator^  142.7 Edge-ray Principle for two-dimensional concentrator with spherical ab-^sorber    152.8 Concentrator profile^  173.9 DCA layers^  214.10 Concentrator assembly ^  264.11 PSUP ^  275.12 Reflectometer. ^  295.13 Merit factor for standard DCA^  345.14 DCA accelerated aging device.  365.15 Combined data set, R1S1 and R1S2 . ^  395.16 Relative reflectivity of sample 234-806  415.17 Relative reflectivity of sample 151-177^  42viAcknowledgementsI would like to thank Dr. Christopher Waltham for providing the opportunity forme to pursue my interests in neutrino physics and for supervising this work. I alsowish to thank Dr. Salvador Gil for his help, understanding and encouragement andIvor Yhap and Jack Bosma for their insight and help in designing and constructing theequipment used for this work.VIIto my wife, Margoandparents, Larry and BonnieVI"Chapter 1Introduction1.1 Solar Neutrino ProblemAccording to accepted theory of solar nuclear energy production, there is a large fluxof solar neutrinos incident upon the earth. Since the early 1970's there has existed alarge discrepancy between the measured number of solar neutrinos and those predictedby theory. All completed measurements report the experimental/theoretical ratio forthese fluxes to fall within the range of 1:4 to 2:3. This discrepancy is known as theSolar Neutrino Problem, SNP.Due to the small neutrino cross-sections, the above experiments have relatively smalldata sets resulting in reasonably large statistical uncertainties. The Sudbury NeutrinoObservatory, a 1000 tonne heavy-water Cerenkov detector, will collect data at a ratenearly 20 times that of previous experiments, allowing a significant reduction in sta-tistical uncertainties. In order to reduce the total number of photomultiplier tubes(PMTs) without compromising detector efficiency, each PMT is surrounded by a lightconcentrator made from dielectric-coated aluminum sheet (DCA) that reflects the lightinto the PMT.A majority of the material in this chapter is presented in more detail in a text byBahcall [1] and the SNO proposal [2].1Chapter I. Introduction^ 21.1.1 Solar ModelsThe most widely accepted models for solar energy production are collectively knownas the Standard Solar Model, SSM. The model assumes that the Sun began as a zero-age main sequence star and then makes specific assumptions about its evolution. Theresult is a star with all of the measured properties of our Sun, except that of the neu-trino flux.The standardness of these models refers to a common set of assumptions about thephysics and input parameters. Nonstandard models modify particular assumptions,often to account for the measured neutrino flux and often at the expense of agreementwith other measured quantities.Specifically, the assumptions are:1. The Sun is a spherically symmetric plasma in hydrostatic equilibrium due to gravi-tational forces opposing a radiative and particle pressure gradient.2. Energy is generated by nuclear reactions.3. Energy is transported to the surface by convection and radiation.4. At each point within the sun the pressure, density and temperature are related byan equation of state similar to that for an ideal gas.5. Specific values for a large number of input parameters including radiative opacity,initial elemental abundances, nuclear cross-sections and reaction rates, etc..The pertinent predictions are:1. More than 98% of the Sun's energy is generated in the proton-proton cycle, figure1.1.2. Specific neutrino flux values due to pp and pep reactions. The pp and pep fluxes areChapter 1. Introduction^ 3Figure 1.1: The proton-proton cycle.largely dependent upon solar luminosity and nuclear cross-sections, both of which havebeen independently measured.3. Production rates of 'Be and 8B depend critically on core temperature. Thus, theirassociated neutrino flux is also very temperature dependent.4. 8B is produced in the most central region of the Sun.1.2 Previous ExperimentsTo date there are four solar neutrino experiments that have produced measurements;Homestake in South Dakota, KAMIOKANDE II in Japan, SAGE in the former SovietUnion and GALLEX in Italy. Each looks at a specific part of the neutrino spectrum,Chapter 1. Introduction^ 4Figure 1.2: The solar neutrino spectra.figure 1.2, and none measures more than 2/3 of the neutrino flux that is predicted bythe SSM.1.2.1 HomestakeThe Homestake experiment has been reporting data since 1971. It is based uponthe reactionv. + ^e- + ^ (1.1)where the radioactive argon is flushed out of the chlorine and then counted. It candetect only ye with energy greater than 0.814MeV. This experiment is sensitive toChapter 1. Introduction^ 5fluxes from 8B, 7Be, pep and hep reactions. The measured interaction rate, as mea-sured in Solar Neutrino Units of 1SNU = linteractionl second110'targetparticles, is[3] (2.2 ± 0.2)SNU, 1a error compared to the results of the solar computer model withthe best input parameters of approximately 8SNU.1.2.2 KAMIOKANDE IIKAMIOKANDE II is a light water .C. erenkov detector. .erenkov light is producedwhen the velocity, v, of a charged particle in a dielectric meduim of refractive indexn exceeds that of light in that medium, c, where c„ = c/n [4]. The light waves forma characteristic conical pattern with the half-angle, 0, as measured from the particle'spath given by case = (n x 0)-1 where # is defined by # = v/c and has a spectral distri-bution that is proportional to 1/A2. The light cone is detectable by the 'hit' pattern onthe PMTs from which the cone vertex (location of reaction) and particle momentumcan be determined.In KAMIOKANDE lithe *erenkov light is generated by scattered relativistic elec-trons produced in the reactionye + C —> ve + C' (1.2)where the source of the electrons is the light water. With an energy detection thresholdof 7.5MeV, this experiment is sensitive only to neutrinos from the 8.I3 and hep reactions.The current results for the 8B flux are [3] [0.48±0.05(10±0.06(syst)]0(8B)Average where0(8B)Average is the best-estimate theoretical prediction given in the paper by Bahcalland Bethe.Chapter 1. Introduction^ 61.2.3 SAGE and GALLEXThe Soviet American Gallium Experiment and GALLEX are based upon the reac-tionIle +71 Ga —> e- +71 Ge (1.3)where the germanium is chemically separated from the gallium. With an energy thresh-old of 0.2332MeV, these experiments are sensitive to the neutrino flux from the pp andpep reactions. Since the predicted pp flux is orders of magnitude greater than the otherneutrino fluxes, these experiments will measure 55% of their flux from the pp and pepreactions. The current results of SAGE measure [3] (58±174 ± 14(syst))SNU and forGALLEX (83 ± 19(1a) ± 8(syst))S NU. The best-estimate theoretical prediction is132SNU which differs from the SAGE measurement by 3.5a and from GALLEX by2a. These results provide modest evidence for the existence of the SNP.1.3 SNOSNO is a heavy water Cerenkov detector that will be located in the INCO nickelmine near Sudbury, Ontario, Canada. It is being built in a cylindrical cavern 2070meters underground to provide adequate shielding from background cosmic radiation.The cavern will have a diameter of 22 meters and a height of 32 meters. Inside willbe constructed a spherical acrylic vessel with a diameter of 12 meters containing 1000tonnes of D20. Surrounding the acrylic vessel will be 9,600 PMTs completely immersedin 7,000 tonnes of ultra-pure light water so as to quench background radiations fromthe surrounding rock and the PMTs themselves. See figure 1.3.The main advantage of SNO over other 'Cerenkov detectors is its sensitivity notonly to electron neutrinos, but to all neutrino flavors through their interaction with theChapter 1. Introduction 7Figure 1.3: The SNO detector.Chapter 1. Introduction^ 8deuteron nucleus, (d). These reactions areI^ye - - I - dII 1, + e-III vz + dIV 7e+ dV Ve+Pp + p + e-vs + e-p + n + yrn + n + e+Ti + e+Reaction I is detected by the Cerenkov light from the relativistic electron. It iscurrently expected that the electron energy detection threshold will be 5MeV. The Q-value for this reaction is -1.44MeV. Thus, only electron neutrinos with energy greaterthan 6.44MeV will be detected.Reaction II also detects Cerenkov light from the scattered electron. Due to the5MeV threshold there exists the probability that at low energies an electron neutrinowith energy greater than 6MeV will produce an electron with energy less than 6MeV.Thus, at low energies the effective cross-section will be reduced and at higher energiesit should remain relatively unaffected. One should note that the cross section for theelectron-neutrino interaction is 6-7 times larger than that for the other neutrino flavors.Reaction III has a Q-value of -2.2MeV and will be detected as a result of the neu-tron being captured on a free chlorine molecule . The chlorine will most likely be in anaqueous solution of NaC1 in the D20. The capture will be followed by a gamma raycascade (total energy ,=:,-' 8MeV) which will be detected by the photomultiplier tubes.The cascade energy is independent of neutron energy, making this reaction sensitiveto the entire neutrino flux above 2.2MeV. With 25 tonnes of NaCl in 1000 tonnes ofD20, the neutron capture efficiency will be 83%.Chapter 1. Introduction^ 9Reaction IV is detected by seeing the positron erenkov light followed by the gam-mas from the capture of the two neutrons by the chlorine. The Q-value for this reactionis -4.03MeV. Thus, sensitivity is limited to neutrinos above 9.03MeV with a doubleneutron capture efficiency of (83%)2.Reaction V will occur only in the light water surrounding the acrylic vessel. Apositron of energy ER — 1.8MeV will produce Cerenkov light and the neutron would becaptured in the hydrogen resulting in a gamma-ray of energy 2.2MeV. The neutroncapture would be invisible since it is below the detector threshold of 5MeV, but thereaction can be identified by the reconstruction of the Cerenkov cone showing the originto have been in the light water.Both reactions IV and V detect anti-neutrinos which are thought not to be producedin the sun. But anti-neutrinos are produced in supernovae. Thus, these reactions pro-vide an opportunity to measure the anti-neutrino flux from a supernova, should theflux of such an event be incident upon the earth during the operational period of SNO.Chapter 2Concentrator Theory2.1 IntroductionAn optical concentrator is a device that accepts light through an entry aperture andconcentrates that light through an exit aperture. It can be shown that requiring theconcentrator to image the input light constrains the collector design such that optimalconcentration cannot be attained. In SNO we detect O' erenkov light which does notrequire imaging. We have specified the profile of a non-imaging concentrator that whencoupled to a PMT will maximize Cerenkov light collection.The complete theoretical treatment of optical concentrators can be found in thetext by Welford and Winston [5] where much of the theoretical development presentedin this chapter can be found in more detail. The specific application to SNO can befound in the M.Sc. thesis by Ouellette [6].2.2 Concentrator TheoryThe theoretical maximum concentration of an optical system can be determinedusing the principle of 'conservation of phase space', or `Liouville's Theorem'. As withall physical devices, the theoretical optimum cannot be realistically achieved, but onceknown it aids in the optimization of the physical design.10Chapter 2. Concentrator Theory^ 11Figure 2.4: Optical coordinate space.2.2.1 The CalculationBefore specifying the Lagrange invariant for the optical system it is best to specifythe optical coordinate space, figure 2.4. Consider an incoming light ray traveling ina medium with refractive index n and specify the coordinate system by origin 0 andaxes x, y, z. A ray passes through a point P = (x, y, z) and in a direction specifiedby the direction cosines (L, M, N). This ray enters the optical device and emergesinto a medium with refractive index n' with a coordinate system specified origin 01and coordinate axes x', y',z'. In this exit medium the ray passes through the pointP' = (x', y', z') and in a direction specified by the direction cosines (L', M', N').One can define increments of position by dx and dy and of direction by dL anddA1 . The product of these differentials with the square of the refractive index is anChapter 2. Concentrator Theory^ 12invariant throughout the entire optical system,n2dxdydLdM = n'2dx'dy'dVd.W. (2.4), To find the theoretical concentration of any optical system one has only to equatethe invariant of the input medium with that of the output medium, specify the integra-tion boundary conditions at the interface with the optical device and then integrate.The above process can be complicated by the presence of a lens at the input apertureand/or a lens or non-flat absorber at the exit aperture. The actual optical system thatwill be used in SNO is a cylindrically symmetric collector open at the input apertureand with a near-spherical absorber, the PMT, at the exit aperture.2.2.2 The 2-Dimensional ConcentratorTo temporarily avoid complications presented by skew rays and the convex absorber,consider only rays that are incident in a plane which includes the concentrator axis andassume there to be no absorber. This is the case of a 2-dimensional concentrator withopen exit aperture. The expressions derived under these conditions will later be mod-ified to compensate for these restrictions.Align the concentrator's symmetry axis along the z-axis and specify the input aper-ture by the radius a and exit aperture by radius a', figure 2.5. For an arbitrary incidentangle limit 0 and exit angle limit 0', integration of the Lagrange Invariant from the axisto these limits yieldsI I f n2dxdydLdM = n2(ra2)(rsin20) = n'2(ra'2)(rsin20').^(2.5)One can define a concentration ratio, C, as the ratio of the areas of the incidentChapter 2. Concentrator Theory 13(2.6)aperture to the exit aperture,^ira2^n'ain81= (--al^nsinec =The maximum possible value for 9' is w/2, yielding the theoretical maximum con-centration ratio,Ianar =^ (2.7)nain9In applying these ideas to a physical concentrator one may maximize the con-centration ratio with respect only to a single acceptance angle, C. This angle can bedefined by the z-axis and a ray that enters at the edge of the entry aperture and exitsat the opposite edge of the exit aperture. This ray is refered as an extreme ray. Welfordand Winston show that if all rays that enter the concentrator at the extreme angle, 8„Chapter 2. Concentrator Theory^ 14Figure 2.6: Edge-ray Principle for two-dimensional concentrator.are upon the first reflection directed to the opposite edge of the exit aperture, then8,„ equals 7r/2, figure 2.6. This is the condition for maximal concentration and forphysical concentrators is known as the Edge-ray Principle, ERP.It is easily shown that for each point of reflection on the profile of such a con-centrator a ray at the extreme angle, 6, defines the boundary between rays that willreflect through the exit aperture and those that will strike the opposite side of theconcentrator. Thus, all rays that enter the concentrator at 6 < Oi will pass throughthe exit aperture. Rays that enter at 8 > Oi will reflect to the opposite side of theconcentrator and exit through the entry aperture.This condition is not changed if the exit aperture is directly coupled to a flat ab-sorber. But if the absorber is spherical with a half-angle, Oc, the ERP must be modified.Due to the curvature of the absorber, the opposite edge of the exit aperture is not ac-cessible to all rays that enter at the edge of the entry aperture. In such a case, theChapter 2. Concentrator Theory^ 15Figure 2.7: Edge-ray Principle for two-dimensional concentrator with spherical ab-sorber.extreme ray is defined to be that ray which enters at the edge of the input aperture andjust grazes the surface of the absorber. The ERP is then modified such that all raysthat enter the concentrator at 6, are upon reflection directed so as to just graze thesurface of the absorber, figure 2.7. Thus, all rays that enter the concentrator at 8 <are reflected onto the absorber and all rays that enter at 8> 8; exit back through theinput aperture.2.2.3 The 3-Dimensional ConcentratorThe 3-dimensional concentrator is generated by revolving the 2-dimensional profileabout the concentrator axis. Correspondingly, the previous 2-dimensional expressionsare modified to apply in 3-dimensions.sin2(0,/2)C •pro = 4j^sin2 Ocsin2 90D) (2.10)Chapter 2. Concentrator Theory^ 16The SNO concentrators will have open input apertures such that n = n'. To accountfor skew rays, etc., Moorhead and Tanner [7] show that the concentrator acceptanceangle is modified such thatsin(0,/2) . 4sin9i0D) =^sznai(2D)0,/2(2.8)where 9i(2D) is the 2-dimensional concentrator acceptance angle. The geometric con-centration factor, the area of the input aperture to that of the spherical absorber,isC_ .^szn200D)The concentration factor can be expressed as the ratio of the entry and exit apertureareas and is found to be1(2.9)The PMT that will be used in SNO is the Hamamatsu 1408 with photocath-ode radius of 9.5 cm. When combined with the concentrator, the final characteristicsare a photocathode effective angular acceptance of 0, = 54.5° and acceptance angle943D) = 55.3° (90D) = 58.6°). These values yield C = 1.479 and Cpr,i = 1.875.2.2.4 The ProfileThe final profile is fixed with the given values for the acceptance angle, 9i, the inputand exit aperture radii, a and a' and application of the ERP. The final profile is givenby a set of tabulated height values and is shown in figure 2.8 [6].N2-93 1E1 rule". —*{1---  I on wow. tonsue • alms I w•wir, atm i•..•■■-•■111 *INSWIM 11111/1.11.1/WIER PROF ILEsaw nem am 1 1^/ I IMP NUMENO tr cum21 FLATSCOORONIATES AREINNER SURFACEX —"nu— i^ 1011101 RIN OEM&SECTOR. UN CENTRELINEne or CURVE1=11111M WIENMinUNIVERSITY OF !IRMO PNYSICS LABORATORYRANO IVI,^VW. PliY Xnee Ns—isi ilia—... No it—.3, ... 43fat N..—V/NM7 yr---14t—111l7T----ImoI a at In 71.n it,...._IaLt 13:..___I•at liiM—mar—R110---—441i—ii: .4——ruiliair----—1117 fill It----1, ilr—iffor------ii.) irias46.4 i------1,111-----'*lit''.--k•IFILAS--....-it-3-.......-....----.-.--21.4----..—! i.e=P?4P——.44,4 ilk.,OW (Wu--44:420---JIIBL----14:1,—:=7——iiii—rlotr-----iime—TRir--TiLar—bliiOw vim--iiiiir----Thil--131A—sow 1)144SW In 14114 ale.1tat iro 4 I..-.--fiii-----1-T. n_!'4i US!___45____PA.R_Rtg______orovePLASTIC RETAINER I I12-93-58Chapter 3Concentrator Material Candidates and Requirements3.1 IntroductionThe materials chosen to construct the concentrator assembly must satisfy require-ments from the following categories; optical, radioactive, mechanical, biological andfinancial. Of these, optical, radioactive and biological are related to detector perfor-mance, mechanical to detector operating lifetime and financial to funding constraints.The basic optical requirement is to be specular and highly reflective in the wave-length range of 280nm to 600nm.Radioactivity, in the form of decays from trace amounts of 232Th and 238U and theirdaughters, can interfere with neutrino signal detection. As is the case with all detectorcomponents, this problem is being controlled by stringently limiting the amount ofthorium and uranium in the construction materials used in the concentrator assembly.The mechanical requirements are the ability to survive in ultra-pure water for aminimum of 10 years and not to distort under the various internal and external stressesto which the assembly will be exposed.Bacterial growth has occured in other water detectors such that significant scatter-ing of light occurs. To suppress the bacterial growth, the plastics chosen have beentested against other candidates to insure minimal availability of nutrients.The concentrator assembly is expected to add only $50 to a PMT channel cost of$1000.18Chapter 3. Concentrator Material Candidates and Requirements^193.2 Reflector CandidatesBasically, four reflector material candidates were considered; Total Internal Reflec-tion Film (TIRF), anodized aluminum, evaporated aluminum on glass (back surface)and dielectric-coated aluminum (DCA) on anodized aluminum (front surface). Eachhas its attractive qualities but only the DCA was shown to satisfy all of the necessaryrequirements.3.2.1 TIRFTIRF is a clear polycarbonate sheet material with 45° ridges on one side that fa-cilitate the internal reflections. Being a plastic, it is virtually free of radioactive traceelements. It was shown not to work efficiently in water [8] and was subsequently re-jected.3.2.2 Anodized AluminumThe anodized aluminum was to be spun into a cone of the correct shape. Theinherent advantage in this option is that the manufacturing is relatively quick and in-expensive. Unfortunately, the reflectivity of prototypes was marginal at approximately75% specular and 6% diffuse. It was also found that in ultra-pure water the aluminumquickly deteriorated, smutting the reflective surface. Thus, it was rejected.Chapter 3. Concentrator Material Candidates and Requirements^203.2.3 GlassAlso considered was a design in which aluminum was evaporated onto the backsurface of appropriately shaped low-radioactivity glass. The reflectivity was very high,approximately 90%. Various methods to protectively seal the aluminum were tried,but none was demonstrated to be effective.3.2.4 DCAThe only material that was demonstrated to satisfy all of the requisite criteria is thedielectric-coated aluminum, DCA. The material consists of an anodized aluminum sub-strate, a specular aluminum overcoat and a series of dielectric layers that enhance over-all reflection. This material is used in the lighting industry as a reflector in flourescentlighting fixtures to increase the total reflected light. It so happens that the dielectriccoatings also provide excellent protection from the chemical reactivity with ultra-purewater.3.3 DCA DesignThe DCA begins with a 0.3mm thick aluminum sheet substrate with a 2000nmlayer of anodized Al203. The Al203 is then polished, providing a smooth, stable, hardfoundation upon which to apply the other coatings.The four upper coatings perform a protective and/or optical function, figure 3.9.First is applied 29nm of Si02. The Si02 serves two functions; it inhibits oxygen mi-gration from the Al203 to the highly reflective Al layer and has excellent adhesioncharacteristics upon which to apply the aluminum layer.Chapter 3. Concentrator Material Candidates and Requirements^21Figure 3.9: DCA layers.Chapter 3. Concentrator Material Candidates and Requirements^22The basic reflecting surface consists of 56nm of Al. Upon this is an 82nm layer ofMgF2 with a low-refractive index of P.: 1.433 and a quarter-wave thickness atP...-' 460nm.Over this is applied a 65nm thick layer of TiO2 mixed with a small amount of Pr203.This layer has high-refractive index of :::-.,. 1.96, also with a quarter-wave thickness at460nm. These two layers form a high-low optical stack that enhance the reflection atthe interface.The uppermost layer of Ti02/Pr203 provides the added advantage, andin the case of SNO the most important advantage, of being a very effective chemicalbarrier, preventing corrosion by the ultra-pure light water.To prevent the aluminum substrate from corroding, the four upper layers are alsoapplied to the back side of the aluminum substrate.3.3.1 DCA OpticsThe optical theory of thin films can be found in many optics texts [9]. An unpro-tected aluminum surface that is exposed to air will form an Al203 layer. The oxide layerhas a low refractive index which results in a higher probability for transmission of lightat the interface. The DCA effectively replaces the oxide layer with the high-low stack ofTi02/Pr203 and MgF2. With the chosen layer thicknesses this effectively increases con-structive interference and thus, reflection, in the region of interest, AP.,- 300nm — 600nmat an incident angle of Pe. 60°.3.4 Retainer Plastic CandidatesOf possible plastic candidates available for the retainer, acrylonitrile butadienestyrene (ABS) was chosen by the engineers as appropriate for this use. EspeciallyChapter 3. Concentrator Material Candidates and Requirements^23attractive was its relatively low cost.It was postulated that organic carbon and ions may leach from the ABS, providingnutrients for bacterial growth. Free-floating bacteria could scatter the •Cerenkov light,inhibiting the reconstruction of the vertex and measurement of the particle momentum.In a collaborative effort with biologists at UBC, it was shown that the ABS does notprovide any significant stimulus to the growth of bacteria in water [10].Chapter 4Concentrator Manufacture4.1 IntroductionThe complete assembly will consist of a hexagonal ABS retainer in which will bepressed 20 rectangular petals cut from a flat sheet of DCA. Ray tracing has shown thatthe use of 20 petals has nearly the same optical response as a circular cone [8].4.2 DCA ManufactureThe substrate is purchased from the German company Alanod who manufacturesthe substrate and also applies the anodizing. The upper four coatings are applied bythe Santa Rosa, CA company Optical Coatings Laboratories, Inc. (OCLI).OCLI applies the coatings using an electron-beam evaporation process in a multi-chamber apparatus. Each chamber is a self-contained evaporation unit which appliesa single optical layer. The chambers are connected in-line with the substrate rollingthrough the apparatus on a conveyor system.Prior to evaporating, the anodized aluminum is plasma etched, a process that re-moves a majority of the surface contaminates and a few angstroms of Al203.A total of 1750 sheets of 1000mm X 750mm will be coated. To date, 1520 havebeen coated in 2 separate production runs of 820 sheets in August, 1992 and 700 inNovember, 1992.24Chapter 4. Concentrator Manufacture^ 25Quality control during production was implemented according to the following spec-ifications:1. Total photopic reflectance (weighted for the human eye and including both specularand diffuse components), as measured on a Diano TR-2, greater than 93%.2. Total specular reflectance, as measured on a Perkin-Elmer Lambda-9 spectropho-tometer, greater than 80% at 380nm and at normal incidence.3. The same as (2) but greater than 84% at 700nm.In addition to the above, and to remove some of the normalization difficulties in-herent in (2) and (3), the wavelength at which the specular reflectance crossed the 85%point was kept between 340nm and 400nm.Additional tests:1. Visual inspection (for scratches, etc.).2. Nitto tape test (for adhesion of coating).3. Rub test.The DCA sheets from both production runs satisfactorily met the above criteria.One should note that at larger incident angles the drop-off occurs at cze, 300nm.4.3 DCA Petal ProductionThe DCA sheets will be machined by CNC into approximately 3cm by 9cm rectan-gular petals. To prevent corrosion the bare edges will be sealed by evaporating 0.4pmof TiO onto the bare edge.Chapter 4. Concentrator Manufacture^ 26Figure 4.10: Concentrator assembly4.4 Plastic RetainerThe retainer will be injection molded from high-grade ABS plastic.4.5 Concentrator AssemblyThe completed petals will be inserted into the retainer, held in place by compression.See figure Photomultiplier Support StructureThe PMTs will be attached to the concentrator assemblies and then the assemblieswill be attached to a stainless steel frame creating a reflector panel. The reflectorChapter 4. Concentrator Manufacture^ 27Figure 4.11: PSUPpanels will then be attached to each other forming a geodesic structure. The entirePMT support structure (PSUP) is shown in figure 4.11. The PSUP will be completelyimmersed in light water and will surround the acrylic vessel.Chapter 5Test Methods and Results5.1 IntroductionWe have devised a technique to measure the absolute reflectivity of a flat mirrorimmersed in water or air. Using this technique, we were able to determine the optimalthickness of the DCA coating for use in SNO, of which OCLI had an ability to adjust.To ensure that the mirror will not significantly deteriorate within the 10 year expectedlife span of the detector, equipment was designed and constructed that accelerates theaging of the mirror, allowing 10 year-equivalent aging to occur in 70 lab-days. Usingequipment constructed for the optimal Ti0 2/Pr203 layer determination, the reflectivityof aged mirror was measured to verify that no significant loss occurred.5.2 Absolute Reflectivity MeasurementThe technique to measure absolute specular reflectivity of flat mirror immersed inwater or air works within an incident angular range of 15° to 75°. The wavelengthrange studied was from 200nm to 900nm. The technique is based upon a low costvariable-angle reflectometer and a commercial spectrophotometer.28Chapter 5. Test Methods and Results^ 29Figure 5.12: Reflectometer.5.2.1 ReflectometerThe reflectometer used in this work consists of a water-tight, aluminum box thatfits into the sample receptacle of a Perkin-Elmer Lambda 3B ITV/VIS double beamspectrophotometer. The reflectometer intercepts only one of the beams. It has twowindows, as illustrated in figure 5.12, for light entry and exit, made of 1.5mm thickfused silica. The incident beam is reflected by a 900 mirror prism, which has a frontsurface aluminum coating. The beam then strikes a rotatable reflectance accessory,that contains two mirrors forming a 90° angle. The intersection of the two mirrorscoincides with the axis of rotation of this accessory and is parallel to the edge of the90° prism.The rotating accessory is formed by a fixed mirror (front surface aluminum) andChapter 5. Test Methods and Results^ 30the test or sample mirror. This last mirror is supported by three rest points, which canbe adjusted for alignment. The alignment of the internal mirrors is accomplished us-ing a laser beam. Conceptually, this reflectometer is similar to commercially availablemodels that operate in air.In front of the entrance window, and mounted on the spectrophotometer itself, weplaced an ultraviolet (UV) dichroic polarizer. This polarizer can be rotated continu-ously.5.2.2 Determination of Absolute ReflectivitiesWe have purchased absolute reflectance standards with known reflectivity as a func-tion of wavelength calibrated at an incident angle of 8°. To avoid possible damage oralteration in the reflectivity of these primary reference standards due to immersionin water, we prepared secondary standard mirrors for immersion by evaporating Al(99.99% pure) onto a glass substrate. In order to determine the absolute reflectivityof these secondary reflectance standard mirrors, Raste.r,(A), at each wavelength, A, theywere calibrated against the primary reflectance standards. For this we used an inte-grating sphere reflectometer with incident angle of 8° attached to a Beckman UV5270spectrophotometer.To use these standards at other angles, a computer model was constructed basedupon the matrix method of thin films [9]. The secondary standard was also studiedusing ellipsometric techniques. Due to environmental conditions at the time of coating,such as temperature, humidity, contaminants, etc., voids and impurities formed withthe result that the refractive indices deviated from the standard textbook values. Theellipsometry allowed the determination of the complex refractive index of the aluminumChapter 5. Test Methods and Results^ 31as well as the refractive index and thickness of the natural Al203 layer. These were nec-essary input parameters for the model. The results of the model were then comparedwith the independent measurement of reflectivities using the primary standard at 8°.The two approaches agree within 1%, except at A < 300rtm, where the agreement isonly within 5%. Thus, the model of reflectivity for the secondary standard allowed usreliably to extend the values of reflectivities to other incident angles within the samewavelength range for which the ellipsometric studies were conducted.The reflectivity in water for the secondary standard, Risveact"(A, 0), was obtained ina similar manner. With the notation RTaemdzi , , ,0 0, pol) we will denote the absolute re-flectivity of the sample, at the angle of incidence 0, wavelength A and polarization statepol=s or p. Medium stands for either Water or Air. Similarly, RRTsnaemdire (A, 0,pol)(RRLecdium(A, 0,pol)) represents the relative reflectivity measured with the spectropho-tometer.The protocol used to extract the absolute reflectivity for a given sample consistedof measuring the relative reflectivities, RR'snaemdi7,1:(A, 0,pol), of the sample and the sec-ondary standard, RR'sn.:cdium(A, 0, pol), under exactly the same geometry and polariza-tion state (pol=s,p). The absolute reflectivity, RTati;y: (A, 0,pol), of the sample wasthen calculated asRR medium (A , 0 , pol)Rrstre/(A 0, Poi) = Rnsleecdium (A , 0, Pol) x R^Rrsneeglium(A, 0,pol) •(5.11)It is interesting to note that without using a reference standard with well knownreflective properties, it is not possible to extract reliable information with this type ofreflectometer. Usually the reflectivities of the 90° prism and the fixed mirror are notknown at all angles. Therefore, the relative reflectivities will depend on the propertiesChapter 5. Test Methods and Results^ 32of all the mirrors involved. The advantage of using the protocol proposed here is thatby using the above expression the properties of the fixed mirror and the prism cancelout.5.3 Determination of Optimal DCA Coating ThicknessSince OCLI has the ability to adjust slightly the thickness of the DCA coating, itseemed reasonable to determine if there is an advantage to having a slightly thinneror thicker coating. This section summarizes our work relating to this subject. A morecomplete discussion of the following material can be found in [11] and [12].Using the reflectometer immersed in de-ionized water and attached to the Perkin-Elmer spectrophotometer, we measured the reflectivity of OCLI's standard DCA rel-ative to the secondary standards at 45°, 600 and 75°. The choice of these angles wasmotivated by the results of Monte Carlo simulation of the angular distribution probabil-ity of the Cerenkov photons of the reflectors [13]. This distribution takes into accountthe actual geometry of the SNO detector, the shape of the reflectors and peaks at 60°with a FWHM that is contained within the range of 45° to 750 •To determine the optimum coating thickness, we define the following merit factorfunctionMFF(A, clacro ) = Ref lectivity(A) W (A, clacryi ).^(5.12)and the merit factor parameter (MFP)00MFP = I Ref lectivity()) * W(A, dacryiJThe weighting function W(A, &wry' ) is defined by)dA.^(5.13)\^rr, Y1W(A5 dacryl )^EPMT(A) *^* lacr^uacrylA' ),(5.14)Chapter 5. Test Methods and Results^ 33where epmT(A) is the photomultiplier tubes quantum efficiency. The factor 1/A2 de-scribes the spectral distribution of the eren.kov light. The quantity Tacryl(Al dacryl )describes the optical transmission of the acrylic in water and depends upon the typeof acrylic and the thickness of the acrylic vessel, dacro, as followsTacry/(A, daffy/ ) = eXP(—Aacryl(A) * dacryl (5. 15)The transparency of acrylic, Aocro(A), for the specific type to be used in the SNOdetector, was measured by SNO collaborators at Chalk River [14]. The acrylic thicknessused in our calculation was d,o= 10 cm, in accordance with the design thickness ofthe acrylic vessel in the SNO detector.To evaluate the overall performance of a given sample the MFP are averaged atdifferent angles using the weighting factor W(A) dacry/ ). Typical results are shown infigure 5.13 with the first row being the averaged result. From this figure 5.13 it is clearthat the best choice for the DCA coating thickness is 10% thinner than the nominalvalue. Considering the thickness tolerance of the coating process is of the order ±10%,a reasonable choice for the DCA coating thickness is —10% of the nominal.5.4 Aging TestsDue to the inaccessability of the detector components, all components must be ableto survive in their environment for the full 10 year operating period of SNO. Withonly a few years available to design and test components, it was imperative to devisea method to accelerate the component aging process. Since the concentrators will beimmersed in ultra-pure light water, chemical interaction with the water is the only sig-nificant factor. Using the common technique of increasing the chemical reaction rateby elevating the temperature, we have been able to simulate 10 years of aging in SNOChapter 5. Test Methods and Results^ 34Acrylic Thickness= 10 Cm (28-Apr-92)Using Measured Reflectivities in WATERFigure 5.13: Merit factor for standard DCA.Chapter 5. Test Methods and Results^ 35in only 70 days in the lab.5.4.1 Test conditionsIn designing the aging procedure it was attempted to simulate the actual SNOenvironment as accurately as possible. To simulate the concentrator, the DCA sampleswere placed two at a time, slightly bent and butted together under compression in anABS holder as they will be in production models. In the detector there will be an esti-mated water flow of lem/hr due to the purification cycle. The water flow is simulatedby very slowly rotating the samples in a bucket of water at the appropriate speed. Tokeep water purity levels high, de-ionized water was used and was changed often. Theion content was also monitored frequently with a conductivity meter. Stainless steelhardware and acrylic parts were used to keep the water pure.The expected operating temperature of SNO is 8C. By heating the immersion waterto 65C the aging process was accelerated such that 70 days in the lab was equivalent to10 years in SNO. This is expected due to a typical increase in chemical reaction ratesby a factor of 2 to 3 for each 10C increase in temperature. Periodic replacement of thewater necessitated cooling and reheating of the samples. This introduced differentialstresses at the bond interfaces which also contributed to the aging process. Assumingthe worst case, the factor of 2 was used in determining the number of required lab daysof aging. A faster aging rate could have been achieved with temperatures above 70C,but this may have resulted in the softening of the acrylic components.Chapter 5. Test Methods and Results^ 36Figure 5.14: DCA accelerated aging device.5.4.2 EquipmentThe aging device consists of a bucket to hold the water and immerse the samples,and a motor/gearbox to drive the rotation, figure 5.14.The bucket is a standard 5 gallon plastic bucket that originally held food prod-ucts. Since food containers must satisfy very strict government leaching criteria, theuse of a food container is ideal. Prior to this procedure the bucket was extensively usedfor similar heating procedures in which it is expected that any residual contaminantswere leached out of the plastic.To the lid is bolted a 0.5" thick acrylic support plate through which are drilledChapter 5. Test Methods and Results^ 37holes for the thermometer, immersion heater and acrylic shaft collar/bearing assembly.Through the collar/bearing assembly is a 0.75" diameter acrylic shaft upon which ismounted two 0.5" thick acrylic plates for attaching the ABS sample holders. Up to 5holders can be attached to each plate. To minimize heat loss and maintain uniformwater temperature the bucket is tightly wrapped with insulation.Driving the shaft is a belt/pulley combination attached to the motor/gearbox. Thegearbox has 24 speed settings, the slowest of which, when combined with the appropri-ate pulley diameters and acrylic plate diameters, results in the desired lcm/hr speedof the samples in the water.5.4.3 Tests ResultsI have completed aging and testing 10 samples from the first OCLI DCA produc-tion run; 6 samples designated by R1S1 from the initial aging procedure and 4 samplesdesignated by R152 which began aging 1 month later. The relatively small reflectivitychanges in 8 of the 10 samples indicates a successful coating run. The failures that areobserved can be mostly explained and avoided if precautions are taken during concen-trator production.For R1S1 the maximum conductivity was approximately 4.0pS/cm with an esti-mated average of 2.3pS/cm and for R152 the maximum conductivity was approxi-mately 2.3pS/cm with an estimated average of 1.6pS/cm.The reflectivity measurements were made in water at an incident angle of 60° overthe wavelength range of 200nm to 900nm. The aged and unaged samples that wereused for reflectivity measurements were received from OCLI as separate samples withmatching identification numbers, cut from the production sheet by OCLI as specifiedin the coating contract.Chapter 5. Test Methods and Results^ 38The results are• 8 samples show average relative reflectivity loss of 1.2% with standard deviationof 2.3%.• 2 samples visibly failed on the front side.• No visual failures of the coating on the back side.Two sets of reflectivity measurements, Data Set 1 and 2, were conducted on11151 to verify consistency of results. The RMS of the difference of the data sets is1.8% which is taken as the level of reproducibility of the spectrophotometer.The ratio of reflectivities measured in 1120 at 600 of aged to unaged was calculatedat 500nm. This wavelength was chosen due to the small change in reflectivity at thiswavelength.SampleR1S1(sidel — side2)RelativeRe f lectivityDataSet1(%)RelativeRe f lectivityDataSet2(%)596 — 5 100.4 100.7269 — 67 100.4 99.262 — 14 102.1 102.2494 — 107 97.6 96.7838 — 201 98.4 97.4234 — 806 92.3, 55.0 86.7,47.3Chapter 5. Test Methods and Results^ 39Histogram of Relative ReflectivitiesData Sets: <R1 S1 >, R1 S2Figure 5.15: Combined data set, R1S1 and R1S2.Sample^RelativeReflectivityR1S2^DataSell(sidel — side2)^(%) ^722 — 65 98.2^596 — 5^94.3151 — 177 96.8838 — 201^100.4A histogram of the combined data set of R1S1 and R1S2 is shown in figure 5.15.Excluding the visibly failed samples, 234-806 from R1S1 and 151-177 from R1S2,the average loss in reflectivity is 1.2% with a standard deviation of 2.3%. The mean andChapter 5. Test Methods and Results^ 40standard deviation were calculated from a data set consisting of the average reflectivityof R1S1 samples from data sets 1 and 2 along with the reflectivity values of the R1S2samples. The coating specifications state that aging should not change the reflectivityby more than 2%.Due to an error in labelling it is suspected that the sample labeled 62-14 has onlybeen aged for 4.3 years-equivalent, 838-201 for 6.1 years-equivalent and 151-177 for14.3 years-equivalent.The R1S1 failed sample is labeled 234-806. On the aged sample there is a dark8mm wide strip along the entire length of one edge. The relative reflectivities on andoff-of the strip are 47% and 87%, respectively. The ratio of aged to unaged reflectivitiesfor the entire wavelength range along with that of a sample that did not fail is plottedin figure 5.16.First, one should note the oscillation in the 234-806 lines. This is typical of coat-ing failure where the reflective aluminum layer has oxidized. The oscillation appearsboth on and off of the strip, indicating that the entire surface of the sample has failed.The fact that the graph of the good sample shows no oscillations indicates that ourmeasurement technique is sensitive to such coating failures.Secondly, this strip is similar in dimension to those visibly apparent on some unagedsamples. These strips are caused by the overlap of the sheet and frame during the coat-ing process, leaving an uncoated strip along the sheet edge. Due to the configurationof the frame, such strips should only occur on the sides of the sheet and should notoccur on the leading or trailing ends. The failed sample shows this strip on the leadingedge. It is possible that the corresponding sheet was incorrectly positioned in the frameduring the coating procedure. Since the strip is not visible on the unaged sample, sucha defect may not be visible on other sheets. To avoid similar failures that may occurto petals in the concentrators I propose that a lOmm to 15mm strip along the entireChapter 5. Test Methods and Results^ 41Relative Reflectivity - Aged to UnagedR1 S1 , Data Set 1Figure 5.16: Relative reflectivity of sample 234-806.-...Alit _ .. AL ■tirii%.m......--^-•••41116.,v, pi ' V ‘o, iiiir Vir . • Wir1.40.40.2Chapter 5. Test Methods and Results^ 42Relative Reflectivity - Aged to UnagedR1S2, Data Set 1, Sample 151-177200^300^400^500^600^700^800^900Wavelength— No Stripes^— Stripes^-- Stripes, RotatedFigure 5.17: Relative reflectivity of sample 151-177.edge of all sheets be discarded.The R1S2 failed sample is 151-177. The aged sample developed 0.5mm wide dark,regular, horizontal strips emanating inward from both side edges on the upper-half ofthe sample. I see no obvious cause of the failure but suspect either improper prepara-tion before coating or possible malfunction of the coating apparatus.The reflectivity value at 500nm listed above is for a section of the sample that doesnot show the failure. This value has not been included in the determination of the meanreflectivity and standard deviation. Reflectivity data from the striped region containsoscillations and reduced reflectivity, confirming the failure of the coating. The resultsare shown in figure 5.17.A yellow sheen is observed when white light is viewed at an incident angle ofapproximately 85° off the back side of unaged DCA. When the coating fails this sheenChapter 5. Test Methods and Results^ 43becomes pink due to a shift in the absorbed wavelength. The yellow sheen was observedon the back side of all samples, aged and unaged, indicating that the coating has notfailed on the back side.To protect the front surface of all samples during storage, I cover them with a pro-tective plastic film that is identical to that used by OCLI. Upon repeated removal ofthis film from four of the samples, 269-67, 62-14, 234-806 and 494-107, sections of thedielectric-coating stuck to the film. These sections are approximately 2mm wide andvary in length from 2mm to 25mm in length.Since samples 269-67 and 494-107 were unaged while 62-14 and 234-806 were aged,the destruction of the coatings adhesion is not a result of the aging procedure. I suspectthe cause is related to a score line approximately 2mm from the sample edge. Thereare many such lines on various samples and were probably made during the shearingprocess at OCLI. The close proximity of the score line to the bare edge may allowthe water to penetrate easily the coating from two opposite directions, facilitating thedestruction of the coating's adhesion.To avoid this problem, special care should be taken during the petal machiningprocess so that similar score lines do not occur.A large, white spot approximately 1.4cm in diameter appeared on the back of sam-ples 62-14, 722-65, 596-5 and 151-177 where each was in contact with the ABS holder.The cause of the mark may be leaching from the ABS holder. Since it is localized onthe back of the DCA, I suspect that this poses no threat to long-term light collection.Chapter 6ConclusionThe solar neutrino problem has existed since the early 1970's. All relevant experi-ments report a significant deficit in the expected neutrino flux, although their data setsare relatively small and statistical uncertainties relatively large. These experimentsare Homestake in South Dakota, KAMIOKANDE II in Japan, SAGE in the formerSoviet Union and GALLEX in Italy. With an event rate 20 times that of any previousexperiment, SNO will collect a large data set resulting in relatively small statisticaluncertainties and determine whether or not the expected solar neutrino flux is correct.SNO, a 1000 tonne heavy water Cerenkov detector will use 9,600 photomultipliertubes. To increase the effective area of each tube, a concentrator will be attached suchthat the light collection capability is nearly doubled at an increased assembly cost ofonly 5%.Applying `Liouville's Theorem' to the optical concentrator allows one to define theconcentration ratio, C, the ratio of the areas of the incident aperture to the exit aper-ture. The concentration ratio is maximized for rays entering at some particular inputangle by applying the Edge-ray Principle. The final profile is determined using angularand dimensional parameters of the chosen photomultiplier tubes and maximum inputaperture size.In choosing materials for the concentrator assembly, various physical and financialcriteria had to be met. Of these, the most important is the ability to survive in ultra-pure water for a minimum of 10 years. The final choice for the reflective surface was to44Chapter 6. Conclusion^ 45use dielectric-coated aluminum, a standard material used in lighting fixtures to enhanceoverall reflection. The DCA is manufactured in large sheets and will be cut into smallstrips and placed into the ABS retainer forming a cone.It was necessary for us to measure the absolute reflectivity of the DCA immersed inwater within an incident angular range of 15° to 75° and wavelength range of 200nmto 900nm. For this purpose we built a reflectometer to be used in water and developeda computer model that allowed us to extend the absolute reflectivity of standards cal-ibrated at only a single angle.We determined that the optimal DCA coating thickness is 10% less than the nomi-nal. This was implemented on the DCA that will be used in SNO. To ensure that thisDCA would survive for the full 10 year life span of the detector, special equipment wasbuilt that simulates the environmental conditions in which the DCA will be exposedbut which also elevates the temperature such that the chemical reaction rate betweenthe DCA and the water will be accelerated making it possible to simulate 10 years ofaging in approximately 70 lab days.10 samples of the DCA that will be used in SNO were aged and their reflectivitycompared to virgin samples. Relatively small reflectivity changes occured in 8 of thesamples with an average loss of 1.2% and standard deviation of 2.3%. Two samplescompletely failed, but the causes are understood and can be eliminated during concen-trator production.With only 40% of the total Cerenkov light hitting the concentrators and of that,only 87% being reflected into the PMTs, a 1.2% loss in reflectivity translates into lessthan 1% loss in collection of total light.Bibliography[1] J. Bahcall, Neutrino Astrophysics, Cambridge University Press, 1989.[2] SNO Collaboration, Sudbury Neutrino Observatory Proposal, 1987.[3] J. Bahcall and H. Bethe, Phys. Rev. D (1992), preprint.[4] E. Fenyves and 0. Haiman, The Physical Principles of Nuclear RadiationMeasurements, Academic Press, 1969.[5] W. Welford and R. Winston, Optics of Non-Imaging Concentrators: Lightand Solar Energy, Academic, 1978.[6] G. Ouellette, M.Sc.thesis, University of British Columbia, 1992, unpublished.[7] M. E. Moorhead and N. W. Tanner, The Concentration of Light onto Near-spherical Photomultipliers, Nucl. Instrum. Methods, to be published.[8] G. Ouellette et al., Nonimaging light concentration using total internal re-flection films, Applied Optics, Vol 31, No 13, 1 May 92.[9] K. Moller, Optics, University Science Books, 1988.[10] C. Waltham et al., Light Scattering and Absorption due to Bacterial Activityin Water, Applied Optics, 1993, submitted for publication.[11] S. Gil et al., Determination of Absolute Specular Reflectivities in LiquidMedium with Variable Angle of Incidence, Applied Optics, 1993, to be sub-mitted for publication.46


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