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Doctoral Thesis
Detector performance and background studies for the ArDM experiment
Author(s): Kaufmann, Lilian Dominique
Publication Date: 2008
Permanent Link: https://doi.org/10.3929/ethz-a-005709651
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ETH Library DISS. ETH NO. 17806
Detector Performance and Background Studies for the ArDM Experiment
A dissertation submitted to ETH ZURICH for the degree of Doctor of Sciences presented by Lilian Dominique Kaufmann Dipl. Phys. ETH born 10.01.1980 citizen of Wilihof, LU Switzerland
accepted on the recommendation of Prof. Dr. Andr´eRubbia, examiner Prof. Dr. Ralph Eichler, co-examiner
2008
Abstract
The detection of dark matter is an important issue of today’s astroparticle physics. Dark matter pre- sumably consists of a sea of particles of an unknown kind, common candidates being weakly interacting massive particles (wimps), in particular the supersymmetric neutralino. The ArDM project aims at mea- suring interactions of wimps with a liquid argon target. This thesis presents the cosmological and particle physics properties of dark matter, assuming it to be of supersymmetric nature. The ArDM detector response to a wimp interacting with liquid argon and entailing scintillation light and ionization charge signals is outlined. Characteristics of light and charge signals due to wimps are described and compared with signals produced by background radiation. The propagation and collection of scintillation light and ionization charge within the ArDM detector is studied with simulations and conclusions regarding the detector design are drawn. A detailed description of the development, construction and testing of a high voltage generation device which provides a high electric drift field for the collection of free ionization electrons is given. It repre- sents one of the three technical keypoints of the ArDM detector, the other two being the charge and light readout. The main sources of background radiation relevant to the ArDM experiment, namely gamma, electron and neutron sources, the number of background events to be expected due to these different types as well as possibilities for background rejection are studied extensively.
Zusammenfassung
Der Nachweis von dunkler Materie ist ein wichtiges Ziel der aktuellen Astroteilchenphysik. Dunkle Materie besteht m¨oglicherweise aus einem See von Teilchen, deren Natur nicht bekannt ist. H¨aufig genannte Kandidaten sind die sogenannten wimps, unter ihnen im Speziellen das supersymmetrische Neutralino. Das ArDM-Projekt hat das Ziel, die Wechselwirkung von wimps mit einem Fl¨ussigargon- Target zu messen. Diese Dissertation pr¨asentiert die kosmologischen und teilchenphysikalischen Eigenschaften von dunkler Materie unter der Annahme, dass diese von supersymmetrischer Natur ist. Die ArDM-Detektorantwort auf eine Wechselwirkung eines wimps mit Fl¨ussigargon, welche Szintillationslicht und Ionisationsladung produziert, wird erl¨autert. Die Charakteristika der Licht- und Ladungssignale, die von wimps ausgel¨ost werden, werden beschrieben und mit Signalen der Hintergrundstrahlung verglichen. Die Propagation und das Auslesen von Szintillationslicht und Ionisationsladung im ArDM-Detektor wird mit Hilfe von Simulationen studiert und Schlussfolgerungen bez¨uglich dem Design des Detektors werden gezogen. Die Entwicklung, Konstruktion und das Testen eines Ger¨ats zur Produktion von Hochspannung, welches ein hohes elektrisches Driftfeld f¨ur das Sammeln von freier Ionisationsladung generiert, wird beschrieben. Dieses Ger¨at bildet einen der drei technischen Schl¨usselkomponenten des ArDM-Detektors. Die anderen zwei technischen Schl¨usselkomponenten bilden die Auslese von Ladungs- und Lichtsignalen. Die wichtigsten Quellen von Hintergrundstrahlung, welche f¨urs ArDM-Experiment relevant sind, n¨amlich Gamma-, Elektron- und Neutronquellen, die zu erwartende Anzahl Ereignisse induziert durch diese Typen von Quellen, sowie M¨oglichkeiten zur Unterscheidung der Hintergrundstrahlung vom wimp-Signal werden ausf¨uhrlich beschrieben. Contents
1 Introduction 13 1.1 Darkmatter...... 13 1.2 Supersymmetry...... 16 1.3 Experiments...... 16 1.4 TheArDMproject ...... 17 1.5 Organisationofthethesis ...... 17
I Dark Matter 19
2 Dark Matter and Cosmology 20 2.1 Relicdensity ...... 20 2.2 Cosmological abundance of WIMPs ...... 21 2.2.1 Boltzmannequation ...... 21 2.3 Candidatesfordarkmatter ...... 22 2.4 Halomodels...... 23 2.4.1 Suggestions for the distribution of dark matter ...... 23 2.4.2 Localneutralinoflux...... 24
3 Supersymmetry 25 3.1 Motivationforsupersymmetry ...... 25 3.1.1 Hierarchyproblem ...... 25 3.2 Supersymmetrybreaking...... 26 3.3 MinimalSupersymmetricStandardModel ...... 27 3.3.1 Particle content of the MSSM ...... 27 3.3.2 R-parity...... 28 3.3.3 Simplifyingassumptions ...... 29 3.4 Mass eigenstates and the neutralino ...... 31 3.4.1 Mixing of interaction eigenstates ...... 31 3.4.2 Neutralinos and their mass matrix ...... 32
4 Detecting Dark Matter 35 4.1 Directdetection...... 35 4.2 WIMP-targetcrosssection ...... 36 4.2.1 Spin-independent cross section ...... 36 4.2.2 Spin-dependent cross section ...... 38 4.3 Detectionrate...... 38 4.4 Modulation of the WIMP signal...... 39 4.5 Experimentalconstraints...... 39 4.5.1 Accelerator constraints ...... 39 CONTENTS 7
4.5.2 Regions excluded by dark matter experiments ...... 41 4.6 Different detector materials ...... 41
II The ArDM experiment 45
5 The ArDM detector 46 5.1 DesignoftheArDMdetector ...... 46 5.1.1 Chargereadout...... 48 5.1.2 Lightreadout...... 48 5.1.3 Combining light and charge signals ...... 49 5.2 Setupofthedetector...... 50 5.3 Eventimaging ...... 50 5.3.1 3Deventpositioning ...... 50 5.3.2 Signalshapes ...... 52
6 Light and charge production in liquid argon 54 6.1 Scintillation mechanism ...... 54 6.2 WIMP orneutronevents...... 54 6.3 Electronandgammaevents ...... 56 6.4 Simulation of light and charge produced for WIMP/neutron and electron/gamma events ...... 57 6.4.1 Diffusionofelectrons...... 58 6.4.2 Results ...... 59 6.5 Scintillation light pulse shape ...... 59
7 Light collection in the ArDM detector 62 7.1 Argon scintillation light ...... 62 7.2 Photomultipliertubes ...... 62 7.3 Wavelength shifter and reflector ...... 63 7.4 Collectionefficiency ...... 63 7.4.1 Positioning of the wavelength shifter ...... 63 7.4.2 Angular distribution of incident photons ...... 65 7.4.3 Overall collection efficiency ...... 68
8 High Voltage Supply 69 8.1 Greinachercircuit ...... 69 8.2 The Greinacher chain of the ArDM detector ...... 70 8.3 Theoretical models for the voltage distribution on a Greinacher circuit ...... 72 8.3.1 Model with peak-to-peak voltage attenuation ...... 73 8.3.2 Model with effective capacitance due to load resistance...... 74 8.3.3 Fit of Cd ...... 75 8.3.4 Comparisonofthetwomodels ...... 75 8.4 Approaches for measuring the Greinacher circuit voltage in liquid argon . . . . . 76 8.4.1 Measurement with resistance ...... 76 8.4.2 Measurement with capacitance ...... 79 8.4.3 Comparison of resistive and capacitive couplings ...... 79 8.5 Measurements of the Greinacher output ...... 81 8.5.1 Voltage measurement with field mills ...... 81 8.5.2 Testsinairandnitrogen...... 81 8 CONTENTS
8.6 Characterization of the Greinacher circuit with a 10-stagemodel ...... 83 8.6.1 Measurementsinair ...... 83 8.6.2 Measurementsinvacuum ...... 87 8.6.3 Measurements in liquid argon ...... 87 8.7 Connectiontothefieldshaperrings ...... 92
9 An alternative application of the ArDM detector 95 9.1 Search for 0νββ decay ...... 95 9.1.1 Neutrinoless double beta decay ...... 95 9.1.2 Candidateelements ...... 96 9.1.3 Measuring 0νββ inliquidargon...... 96 9.1.4 A multiple-source concept ...... 97 9.1.5 Measurement of the movement of µm size grains in liquid argon ...... 100 9.1.6 Scintillation light attenuation ...... 101 9.1.7 ConclusionandOutlook ...... 103
III Background studies for ArDM 105
10 Background radiation overview 106
11 Gamma and 39Ar electron background 108 11.1 Gammas from radioactivity in detector components ...... 108 11.1.1 Gamma interactions in the detector ...... 110 11.2 Expected gamma background above ground ...... 116 11.3 39Arelectronbackground ...... 118 11.3.1 Natural atmospheric argon ...... 118 11.3.2 Decay of 39Ar...... 118 11.3.3 Relevant electron interactions ...... 119 11.3.4 39Ardepletedargon ...... 120 11.4 Gamma and electron background rejection ...... 121 11.4.1 Light over charge ratio ...... 121 11.4.2 Scintillation light pulse shape ...... 121
12 Neutrons 125 12.1Radioactivity ...... 125 12.1.1 (α,n)reactions ...... 125 12.1.2 Spontaneousfission...... 127 12.2 Neutrons from radioactivity in detector components ...... 127 12.2.1 Neutronspectra ...... 128 12.3 Neutrons from radioactivity in rock and concrete ...... 128 12.3.1 Setup and contamination of the underground laboratory...... 129 12.3.2 Simulation of neutron attenuation by a hydrocarbon shield ...... 131 12.3.3 Attenuation of neutron energy spectra by hydrocarbon...... 133 12.3.4 Comparison of hydrocarbon and water ...... 133 12.4 Detectorresponsetoneutrons ...... 133 12.4.1 Multiplescattering ...... 136 12.4.2 WIMP-likeevents...... 137 12.5 Neutron background rejection ...... 140 13 Summary and Outlook 143 13.1 StatusoftheArDMdetector ...... 143 13.1.1 Scintillation light and ionization charge readout ...... 143 13.1.2 Highvoltagesupply ...... 144 13.2 BackgroundsourcesforArDM ...... 144 13.2.1 Electron and gamma background ...... 144 13.2.2 Neutronbackground ...... 145 13.3FutureofArDM ...... 145 List of Figures
1.1 Rotation curve of the galaxy NGC 6503 ...... 14 1.2 Mass contours after collision of two galaxy clusters ...... 14 1.3 Locationoftheplasmas ...... 15
3.1 CorrectionstotheHiggsmass ...... 25 3.2 Unification of the sparticle masses in msugra ...... 30 3.3 Neutralino properties in msugra ...... 34
4.1 Scalar quark-neutralino coupling ...... 37 4.2 Axialquark-neutralinocoupling ...... 38 4.3 Differential rate per recoil energy ...... 40 4.4 Experimentalconstraints...... 42 4.5 Total rates for different threshold recoil energies ...... 43
5.1 SetupoftheArDMdetector...... 47 5.2 PrototypeLEM...... 48 5.3 PMTarray ...... 49 5.4 ArDMouterandinnerdetector ...... 51 5.5 A neutron multiple scattering and electron event ...... 52 5.6 SimulatedPMTandLEMsignals...... 53
6.1 Light and charge versus energy for wimp/neutron and electron/γ events . . . . 57 6.2 Light versus Charge for wimp and 39Arevents...... 60 6.3 Simulated scintillation light pulse shape ...... 61
7.1 Reflector with wavelength shifter ...... 64 7.2 Simulated detector geometry ...... 65 7.3 Photon collection at different positions in detector ...... 66 7.4 IncidentanglesonPMTs...... 67
8.1 Greinachercircuitscheme ...... 70 8.2 Components of the Greinacher circuit ...... 71 8.3 CAD drawing of two Greinacher stages ...... 71 8.4 Greinacher circuit of the ArDM detector ...... 72 8.5 Voltage at different stages ...... 75 8.6 Differenceofmodels ...... 76 8.7 Setup with resistive and capacitive couplings ...... 77 8.8 Calculated voltage attenuation with one load resistance RL ...... 78 8.9 Calculated ouput voltage versus load resistance ...... 78 8.10 Threeresistors ...... 79 8.11 Capacitive coupling with sphere ...... 80 8.12 Voltage amplitude attenuation ...... 80 LIST OF FIGURES 11
8.13 Field mills used for measuring the Greinacher voltage output ...... 82 8.14 10-stage Greinacher circuit ...... 83 8.15 Setupfortestsinair ...... 84 8.16 Output voltage versus input peak-to-peak voltage ...... 85 8.17 Output voltage versus number of stages ...... 86 8.18 Setup for measurements in liquid argon ...... 88 8.19 Measurements of the Greinacher circuit in liquid argon ...... 89 8.20 Low voltage measurements of the Greinacher circuit in liquid argon ...... 90 8.21 Currentandvoltagesignals ...... 91 8.22 GenericdiodeU-I-curve ...... 92
9.1 Depositedenergyspectrum ...... 98 9.2 Dependenceofspeedonradius ...... 99 9.3 Setupformeasurement...... 100 9.4 Downwardsvelocity...... 101 9.5 Concentrationdependence ...... 102 9.6 Electricfielddependence...... 102
10.1 Vertical muon intensity versus depth ...... 107
11.1 Uranium and thorium γs...... 111 11.2 Cross sections of γ processes...... 111 11.3 γ interaction points for γsfrompillars ...... 113 11.4 γ interaction points for γsfromthedewar ...... 114 11.5 Radial dependence of dewar γ interactions ...... 115 11.6 Depositedenergyspectra...... 116 11.7 Measured γ energyspectrum ...... 117 39 11.8 β− spectrum of Ar ...... 119 11.9 Light and charge versus energy for wimp/neutron and electron/γ events . . . . 122 11.10 Light versus charge for wimp and 39Arevents ...... 123 11.11 Chargeoverlightratio ...... 124
12.1 Uraniumandthoriumalphas ...... 126 12.2 Spontaneous fission neutron energy spectrum ...... 129 12.3 Neutronenergyspectra...... 130 12.4 Elemental composition of rock and concrete ...... 131 12.5 Percentage of neutrons reaching the cavern ...... 132 12.6 Emission spectrum of neutrons from rock and concrete ...... 132 12.7 Attenuation of neutrons from rock and concrete by CH2 ...... 134 12.8 Attenuation of neutrons by water and hydrocarbon ...... 134 12.9 Argon recoil spectrum caused by neutrons from detector components ...... 135 12.10 Neutron multiple scattering ...... 136 12.11 Percentage of multiple neutron recoils with a higher threshold of 30 keV. . . . . 138 12.12 Percentage of multiple neutron recoils with a higher threshold of 60 keV. . . . . 139 12.13 Percentage of single neutron induced recoils with a threshold of 30 keV . . . . . 141 12.14 Percentage of single neutron induced recoils with a threshold of 60 keV . . . . . 142 List of Tables
2.1 Classification of cosmological models...... 20
3.1 The Standard Model fermions and scalars and their supersymmetric partners within the mssm...... 27 3.2 The Standard Model bosons and their supersymmetric partners within the mssm. 28 3.3 Interaction and mass eigenstates of the mssm...... 31
4.1 Dark matter direct detection experiments...... 36
6.1 Drift velocities of electrons for different electric fieldstrengths...... 58
7.1 Effects that limit the light collection efficiency...... 68
8.1 Load resistances and resulting output voltages at the end of the Greinacher circuit, calculated with the model described in section 8.3.2...... 77 8.2 Voltage output in air of the Greinacher circuit at different stages...... 82 8.3 Connection of Greinacher chain stages to field shaping rings...... 94
9.1 Properties of some 0νββ candidates...... 96
11.1 Uranium and thorium decay chain count rates in tru per 1 ppb of source. . . . 108 11.2 Uranium and thorium contaminations of materials...... 109 11.3 Masses of detector components...... 109 11.4 γ emissionnumbers...... 110 11.5 Gammas emitted per second and the percentage which enters the active volume. 112 11.6 Percentage and absolute numbers of γs inside the WIMP-like energy deposit range(5keV–100keV)...... 115
12.1 Total neutron emission numbers per year obtained with two different approaches.128 12.2 Emitted neutron numbers from rock and concrete and neutrons reaching the cavern and different thicknesses of shielding...... 133 12.3 Percentage of neutrons emitted from different detector components and scatter- ing more than once above the indicated upper and lower thresholds...... 137 12.4 Percentage of neutrons causing wimp-like events, assuming the indicated upper andlowerthresholds...... 140 Introduction 1
1.1 Dark matter
Some of the oldest questions of mankind concern the nature of our universe. Where does it come from and what is it made of? What governs the development and movement of stars, planets, light? The last question was believed to be solved when Einstein’s theory of general relativity had been published and experimentally confirmed in the early 20th century. General relativity describes the structure of spacetime as well as the behaviour of matter and light contained therein. The rotation of galaxies and the angular velocity of their stars can be computed within it. However, a problem arose when predictions for the angular velocity of stars in galaxies were compared with experimentally measured values—the behaviour of stars did not agree with theoretical cal- culations. There are basically two consequences that can be drawn from this fact: Either the law of gravity is not properly described by general relativity—or the universe contains additional mass that we cannot see—dark matter [1]. It is considered today as rather unlikely that the law of gravity described by general relativity is wrong. It is difficult to find an alternative theory which can explain the rotation of galaxies as well as the vast amount of measurements of gravitational effects at very small and very large scales at the same time. Therefore, this thesis focuses on the second possibility—the existence of dark matter. Dark matter is called dark because it has no electromagnetic interactions. Consequently, it neither absorbs nor emits photons—and remains invisible. Its presence has however gravita- tional influence on visible matter. This is the fact which may explain the behaviour of stars in galaxies. They are gravitationally influenced not only by each other, but also by dark matter. Furthermore, depending on the nature of dark matter, it might also have weak interactions with ordinary matter. The effect dark matter on the angular velocity of stars in galaxies is illustrated in fig. 1.1. The disk of ordinary matter mainly contributes to the velocity of stars at small radii. At large radii, the dark matter halo keeps the velocity at a nearly constant level. Another proof for the existence of dark matter was provided by the observation of two collid- ing galaxy clusters [2]. Apart from ordinary visible matter which constitutes about 1–2% of the mass, these clusters contain about 5–15% plasma and presumably a large amount of dark matter. When two galaxy clusters collide, the galaxies and their dark matter halos behave like collisionless gases, whereas the plasmas feel some friction which decelerates their movement and are therefore spatially separated from the visible matter and dark matter parts. Via weak gravitational lensing it is possible to determine how the mass of the clusters is distributed. It turns out that most of the mass is located in the regions of visible matter, whereas the plasmas are closer to each other and off the mass centers. Fig. 1.2 displays the mass contours of the two clusters after the collision. In fig. 1.3, the plasmas are shown, clearly away from the mass centers. Since the mass of the plasmas is much larger than the mass of the visible parts, this observation can only be explained with an additional mass component—dark matter. 14 Introduction
Figure 1.1: Rotation curve of the galaxy NGC 6503. The total rotation curve corresponds to the upper line with measured values. The expected effects of the dark matter halo, the ordinary matter disk and gas are displayed separately [4].
Figure 1.2: Mass contours after collision of two galaxy clusters. The mass contours of the two clusters were determined with weak gravi- tational lensing [2]. 1.1 Dark matter 15
Figure 1.3: Location of the plasmas. The plasmas of the two colliding galaxy clusters are displayed. They are clearly off the mass centers, indicating the presence of dark matter [2].
So far very little is known about the nature of dark matter. It is not clear what it is made of and only little can be said about its distribution in the universe. Presumably, dark matter is not uniformely distributed, but localized at the same places as visible matter. This implies that galaxies not only consist of a disk made of visible matter, but also contain a dark matter halo. The dark matter halo is assumed to be much bigger in diameter than the visible disk. Therefore, the two components do not rotate at the same speed but may have a relative motion. The shape of the dark matter halo is difficult to determine, since its effect on visible matter can only tell us something about the inner part of the halo. Furthermore, dark matter might be clustered, or may even entirely consist of large, compact objects rather than an evenly distributed sea of particles [3, 4]. Altogether, dark matter is estimated to provide approximately one third of the matter and energy contained in the universe. Visible matter only accounts for a few percent. The biggest contribution to the content of the universe is provided by so-called “dark energy”—a so far rather obscure form of energy which causes the universe to accelerate its expansion, whereas matter is expected to decelerate the expansion because of the attractive nature of gravity. This thesis focuses on the approximately 23% [5] of the content of the universe provided by dark matter and its detection. As stated above, it is not known what dark matter is made of. Today, it seems likely that it can be imagined as a sea of yet undiscovered particles moving around freely, except for weak and gravitational interactions with visible matter and with each other. The nature of these particles is not precisely known. However, some of their general features must be the following: Since they have eluded detection so far, their interaction strengths have to be at most weak. The entire sea of particles should provide enough mass to account for the missing mass in galaxies. Furthermore, they need to be stable compared to the age of the universe, otherwise they would have disappeared by decaying into other particles long ago. Any particle with these properties is generically called Weakly Interacting Massive Particle (wimp). There are some promising candidates for wimps proposed by several theories. Some of these theories have even been developed independently of the dark matter problem. This is the case for the theory which provides the most promising candidate—supersymmetry, introducing the lightest supersymmetric particle (lsp) which is usually assumed to be the neutralino [3, 4]. 16 Introduction
1.2 Supersymmetry
Supersymmetry was invented by field theorists in 1970. During the seventies, it was also applied to nonrelativistic quantum mechanics, and supersymmetry breaking was studied. The aim of supersymmetry is the connection of the two worlds of bosons and fermions, which have so far been separated. In order to do so, a symmetry between bosons and fermions, i. e. between integer spin and half integer spin particles is postulated. The result of introducing this new symmetry is a large number of new particles as well as the appearance of many unknown parameters. The presence of approximately 124 parameters in general supersymmetric theories makes it difficult to derive unique phenomenological statements—another choice of parameters may produce very different results. It is therefore common to introduce simplifying patterns which relate some of the parameters. In this way, the number of free parameters can be reduced to as few as five. However, the resulting model will not be as general as the original model and not necessarily valid. One candidate for dark matter appears as a by-product of supersymmetric theories. It is commonly assumed that supersymmetric theories conserve a new quantum number—called R- parity—which is positive for Standard Model particles and negative for their supersymmetric partners. The lightest supersymmetric particle (lsp) is stable, since its decay into supersym- metric particles is kinematically excluded, whereas its decay into Standard Model particles is forbidden by the conservation of R-parity. In many models the lsp is neutral and has a mass of approximately 100 GeV—compatible with the requirements of a wimp. It is assumed throughout this thesis that the lsp is the neutralino—a linear combination of the supersymmetric partners of the Standard Model gauge fields B, W 3 and the Higgs bosons1. In this way, the lsp connects two realms of physics: particle physics with supersymmetric theo- ries, where it originates from—and astrophysics, searching for an explanation for the matter content of our universe.
1.3 Experiments
A lot of experimental efforts are currently undertaken in order to detect dark matter. Most of them aim at its detection in the form of neutralinos. Although there are other candidates for the dark matter particle (see section 2.3), the neutralino is regarded today as the most likely explanation. Basically, there are two approaches to prove its existence: direct and indirect detection. The goal of direct detection is to measure the interaction of the neutralino with ordinary matter. If a wimp hits a target and scatters off from it, a certain amount of energy is deposited therein. Currently developed very sensitive detectors are designed to measure this deposited energy. There are three different signals into which the deposited energy is converted. A certain fraction is transferred to the target medium in the form of phonons or heat, another fraction goes into ionization of the target atoms and is thereby converted into free charge, and a third fraction causes excitation of the target atoms and finally produces scintillation light when the excited atom deexcites. Indirect detection does not measure the wimp itself, but a product of its annihilation with another wimp. Since the neutralino is a Majorana particle, it can annihilate with a second neutralino that might cross its way. The products of the annihilation (e. g., neutrinos, photons or cosmic rays) could be measured in detectors.
1In supersymmetric theories two Higgs doublets are needed instead of one as in the Standard Model (see section 3.3). 1.4 The ArDM project 17
It is possible to predict the probability of such interactions if an underlying model describing the dark matter particle is provided. It depends on this probability or cross section whether an experiment aiming at detecting the neutralino is promising or not. For experiments based on the supersymmetric neutralino, the range of possible cross sections is very large since the parameters of supersymmetric models are only very weakly constrained. Therefore it is impossible to predict how large a target needs to be or how long a data taking time would be necessary to certainly detect the neutralino. Most experiments therefore envisage an enlargement of the target volume if the current setup does not reach a high enough sensitivity. In case of a negative signal upper limits can be derived for the wimp-target cross section. Some experiments have already measured and published such limits (see fig. 4.4).
1.4 The ArDM project
The ArDM (Argon Dark Matter) project is one experiment which aims at detecting dark matter in the form of neutralinos or similar particles. It is a direct detection experiment designed to measure the impact of wimps on a dedicated target. In the case of ArDM the chosen target material is the noble element argon in its liquid state. Noble elements in general are proven to be efficient targets for rare event searches like dark matter or neutrino searches. The signals produced by a wimp in liquid argon and measured by the ArDM detector are twofold: the detector is constructed to simultaneously measure scintillation light and ionization charge which are both emitted after an interaction of particles in liquid argon. Measuring these two signals simultaneously gives the possibility to characterize the interacting particle according to its typical produced scintillation light and ionization charge amounts, and therefore provides an important means of background rejection. The quest for scintillation and ionization signals determines the technical design of the detector, its most important parts being the light readout with photomultiplier tubes, the charge readout with large electron multipliers and the generation of the electric drift field which is needed to drift free electrons towards the charge readout region. The ArDM detector has a comparably large size. A stainless steel dewar of a height of almost 2 meters contains one ton of liquid argon. Since the boiling point of argon is at 87 K at 1 bar, the inner parts of the dewar are cooled down and kept at this temperature. It remains to be tested if the one ton target is enough to measure a wimp signal. If not, all technical parts are relatively easily scalable, such that larger versions of the ArDM detector concept are realistic.
1.5 Organisation of the thesis
This thesis is split into three parts. The first part describes the phenomenon of dark matter. The first chapter therein is dedicated to cosmological observations related to dark matter as well as candidates for the dark matter particle and suggestions for its distribution. The next two chapters describe the supersymmetric model which provides the neutralino—the most popular dark matter candidate—and the implications of this model on interaction cross sections and rates. Issues related to dark matter detection like experimental constraints and detector material properties are discussed as well. The second part is dedicated to the ArDM experiment. The technical details of the detector as well as the characteristics of scintillation light and ionization charge signals are described. One key part—the high voltage generation—is presented in detail in a separate chapter. Finally, 18 Introduction some alternative applications of the detector are investigated. The third part of the thesis is devoted to the study of background radiation. As for every rare event search, background radiation is an important issue which has to be taken into account when designing the ArDM detector. Three kinds of background radiation are presented in detail, namely γ, neutron and internal 39Ar radiation. Furthermore, the possibilities for background rejection are outlined. Part I
Dark Matter Dark Matter and Cosmology 2
This chapter introduces the most important cosmological quantities relevant to dark matter de- tection. Cosmological observations provide some information on how many wimps pass through a detector, and at what speed they move relative to the earth. Furthermore, some conclusions concerning the properties of a wimp can be drawn from the age of the universe. The most important dark matter candidate particles and their cosmological characteristics are outlined.
2.1 Relic density
The average density of matter or energy contained in the universe determines its evolution. Since matter attracts itself gravitationally, a high matter density would cause the universe to slow down its expansion and finally collapse. If, on the other hand, the density is relatively small, the gravitational effects will not be strong enough to stop the expansion and the universe will grow forever. The value of the relic density which is exactly inbetween these two cases is called the critical density ρc. The normalized value Ω is then defined by
ρ Ω= , ρc where ρ is the actual average density (a homogeneous density is assumed here). The value of Ω determines the geometry of the universe as indicated in table 2.1. The numbers for the relic density are often given for Ωh2 instead of Ω, where h is defined by 1 1 1 1 h = H /100 km s− Mpc− and the present Hubble constant is given by H = 73 3 kms− Mpc− 0 0 ± [4]. Theoretical arguments and astronomical observations reveal that the total value of Ω is most likely around 1 [6]. It is however unclear which partition of Ω is provided by which form of matter or energy. Probably the biggest part does not consist of matter, but of gravitationally self-repulsive “dark energy”. The share contributed to Ω by dark energy is denoted by ΩΛ, and probably lies within the range of 0.6–0.7 [5]. This would imply that the matter part ΩM is equal to 0.3–0.4. The contribution of ordinary (or baryonic) matter is known to be small, i. e., around 2 ΩBh = 0.0224. Therefore, dark matter must be mostly non-baryonic.
Density Ω Universe ρ < ρc Ω < 1 open ρ = ρc Ω = 1 flat ρ > ρc Ω > 1 closed
Table 2.1: Classification of cosmological models. 2.2 Cosmological abundance of WIMPs 21
2.2 Cosmological abundance of WIMPs
Any existing stable particle should have a significant cosmological abundance today. The ex- planation for this statement is the following: such particles were in thermal equilibrium in the early universe. They remain in thermal equilibrium as long as the temperature of the universe exceeds the mass of the particles. Annihilations as well as creations of these particles occur and maintain the equilibrium. As soon as the temperature drops below the particle masses the interactions “freeze out” and a relic cosmological abundance is established. If several particles with nearly degenerate mass exist, they may annihilate each other. This process is called coannihilation.
2.2.1 Boltzmann equation
The relic abundance of any particle can be calculated by solving differential equations for its number density n in the universe. The time evolution of the number density without including coannihilations is described by the Boltzmann equation [3]
dn = 3Hn σ v n2 (n )2 . (2.1) dt − − h A i − eq It describes Dirac particles as well as Majorana particles which are self-annihilating. The first term on the right hand side with the time dependent Hubble expansion rate H accounts for the expansion of the universe and the consequent density decrease. The last two terms describe the depletion and creation of the particles in question. σ v is the thermal average of the h A i total annihilation cross section times the relative velocity, and neq is the relic particle number density at thermal equilibrium. In the non-relativistic limit and in the Maxwell-Boltzmann approximation neq is equal to
3/2 mT m/T n = g e− , eq 2π where m is the particle mass, T the temperature and g the internal degree of freedom. Since this expression for neq is valid in the non-relativistic limit, it is not appropriate to describe neutrinos. For the case that σ v is energy-independent Ωh2 is given by h A i mn 3 10 27cm3s 1 Ωh2 = · − − . ρ ≃ σ v c h A i The calculation including coannihilation is more involved and is described in detail e. g. in [4]. Therein, N particles relevant to coannihilations, with ascending masses mi and internal degrees of freedom gi are considered. In that case, eq. (2.1) becomes
dn = 3Hn σ v n2 (n )2 , (2.2) dt − − h eff i − eq where
i j neqneq σeff v = σijvij . h i h ineqneq Xij 22 Dark Matter and Cosmology
Here, σ = σ(X X X ) is the total annihilation rate for X X annihilations into a ij X i j → SM i j Standard Model particle. Furthermore, P
(p p )2 m2m2 i j − i j vij = q EiEj is the relative particle velocity, with pi and Ei being the four-momentum and energy of particle i. According to [7], σ v can be reformulated into the expression h eff i
2 0∞ dpeff peff Weff K1(√s/T ) σeff v = , h i 4 2 2 2 m1TR i gi/g1mi /m1 K2(mi/T ) P where Ki are modified Bessel functions of the second kind and of order i. Weff is given by
2 2 (s (mi mj) ) (s (mi + mj) ) gigj Weff = − − −2 2 Wij, s s(s 4m1) g1 Xij − where W = 4E E σ v , and s = m2 + m2 + 2E E 2 ~p ~p cosθ. These quantities mainly ij i j ij ij i j i j − | i|| j| depend on the particle masses, energies and momenta. The particle masses are determined by the underlying particle physics model. A particle is relevant for coannihilations with the relic particle if its mass does not differ by more than 10% from the relic particle mass, and if it shares a quantum number with it. ∼
2.3 Candidates for dark matter
After finding that the evidence for dark matter is compelling, it is natural to ask what it is made of. There are many candidates within the Standard Model as well as within new theories like supersymmetry or extra-dimensions. Some of them are presented in this section. Later on, we focus on the most popular supersymmetric candidate, the neutralino. When talking about dark matter candidates, some distinctions are usually made: First, it is common to discern between cold dark matter (cdm), which moved non-relativistically at the time of galaxy formation, and hot dark matter (hdm), which moved relativistically by that time. Second, there are baryonic and non-baryonic candidates, the latter seeming to be more likely. Heavy particle candidates for dark matter are generically called wimps (weakly interacting massive particles).
MACHOs
The most important baryonic candidates are so-called massive compact halo objects (machos). These include, for example, brown dwarfs, black-hole remnants, white dwarfs and neutron stars. Their presence can be revealed mainly by gravitational lensing effects. Current observations indicate that there are not enough machos to provide the whole amount of dark matter. 2.4 Halo models 23
Neutrinos
The main hot dark matter candidate is the Standard Model neutrino. Since some recent neutrino-oscillation experiments show that the neutrino of the Standard Model is not mass- less, it seems to be an ideal dark matter candidate. However, the limits on the neutrino masses have become quite low recently. In order to provide enough mass to account for the whole dark matter, the neutrinos would have to be packed very tightly inside galaxies, which makes con- tradictions with the Pauli principle unavoidable. In addition to that, there is a general problem with hot dark matter candidates: since they move at very high speed, they are not able to cluster, implying a different large scale structure than cold dark matter. Therefore, although neutrinos might contribute to dark matter, they cannot provide the whole amount of it.
Neutralinos
The lightest neutralino is the lightest supersymmetric particle in many supersymmetric models. It is stable if R-parity—a new quantum number of supersymmetric theories—is conserved. The neutralino is the most popular dark matter candidate.
Sneutrinos
The sneutrinos (supersymmetric partners of the neutrinos, see section 3.3.1) have a relic density which lies within the cosmologically expected range for almost all supersymmetric parameter choices and were therefore considered as dark matter candidates. However, their interaction with nucleons is so strong that an abundant presence of them is already experimentally excluded.
Gravitinos
Gravitinos appear in supersymmetric theories as superpartners of the graviton. In some su- persymmetry breaking scenarios, they are the lightest supersymmetric particles and therefore stable. In theoretical models they can cause problems for cosmology, a fact that can be circum- vented only in specific scenarios. Having gravitational interactions only they are very difficult to observe.
2.4 Halo models
An important quantity entering the calculation of dark matter direct detection rates is the local halo density ρ0, i. e. the density of dark matter at our position in the galaxy. If the distribution of dark matter in a galaxy was known, i. e. determined by a halo model, ρ0 could be calculated within it. However, such a distribution is not easy to measure nor predict, especially not in our own galaxy. There are several proposals for the shape of the dark matter distribution, but the final solution is not yet known.
2.4.1 Suggestions for the distribution of dark matter
Most of the halo models considered today can be parametrized in the following way [8]: 24 Dark Matter and Cosmology
ρ ρ(r) 0 , (β γ)/α ∝ (r/a)γ (1+(r/a)α) − where a is a scale radius, and ρ = 4.5 10 2(r /kpc) 2/3M pc 3 (M denotes the solar mass, 0 · − 0 − S − S 2 1030 kg). This density parametrization describes the sum of an exponential thin stellar disk · and a spherical dark matter halo with a flat core of radius r0. The different possible shapes of the halo density within this family correspond to different values of the parameters (α, β, γ). (α, β, γ) can be thought of as the radial dependence at r a, r a and r a, respectively. ≃ ≫ ≪ The spherical profile can be flattened in two directions to form a triaxial halo. Two important examples within this family are the isothermal profile with (α, β, γ) = (2, 2, 0) and the cuspy Navarro-Frenk-White (nfw) model with (α, β, γ) = (1, 3, 1) [8]. The local halo densities ρ0 following from these models and being in agreement with astronomical data lie roughly within a range of 0.2–0.5 GeV/cm3. It is not known if dark matter is provided entirely or only partly by neutralinos. Assuming that neutralinos substantially contribute to 3 dark matter, the local neutralino density ρχ is usually set equal to 0.3 GeV/cm . This number will enter the calculation of the neutralino detection rate later on in this thesis.
2.4.2 Local neutralino flux
The detection rate of neutralinos is proportional to their flux relative to the detector, which equals the local density times the velocity of the neutralinos. The latter is described by a velocity distribution which is usually assumed to be a Gaussian [3]
2 2 e v /v0 f(v)d3v = − d3v, 3/2 3 π v0 with a cutoff velocity if f(v) is integrated. The Gaussian is characterized by the average relative earth-halo speed v0 and the galactic escape velocity vcut, which are typically set to 220–230 km/s and 600 km/s, respectively1. With these numbers the flux of particles of a mass of 100 GeV at 9 2 1 the location of a detector on earth is roughly 10 m− s− .
1The dark matter halo is assumed to be at rest with respect to the rotating Milky Way Supersymmetry 3
After a brief introduction into the cosmology of dark matter in the last chapter we now focus on the theoretical description of the neutralino. As already stated, the neutralino is a product of supersymmetric theories. In order to understand its properties, the basics of supersymmetry are presented in this and the following chapters. Supersymmetry was originally invented without any thought of dark matter, but as a possible enlargement of the Standard Model by introducing an additional symmetry.
3.1 Motivation for supersymmetry
The Standard Model (sm) of particle physics is an exceptionally successful model. Its predictions agree very accurately with experimental results. However, there are some problems with the Standard Model which indicate that it needs to be embedded in a new, bigger theory. Although the sm works very well at the elecroweak scale, it fails to explain physics at higher energy scales like the gut scale, where radiative corrections are important. For example, these radiative corrections cause the Higgs mass to diverge—a fact that can only be circumvented by an inelegant fine-tuning of counterterms. This difficulty—which is called the hierarchy problem—is one of the main reasons for the attractiveness of a new, additional symmetry: supersymmetry (susy). Supersymmetry is a symmetry between fermions and bosons, i. e. between half integer and integer spin particles.
3.1.1 Hierarchy problem
The hierarchy problem concerns the self-energy of the Higgs boson in the Standard Model. Quantum corrections which are caused by fermion and scalar loops as shown in fig. 3.1 result in quadratically divergent contributions to the Higgs mass. The following Lagrangian describes a fermion, a Higgs boson and a charged scalar appearing in the diagrams of fig. 3.1 [9]
ψ φ
H H ψ H H Figure 3.1: Corrections to the Higgs mass. The fermion (left) and scalar (right) loops causing radiative corrections to the Higgs mass. 26 Supersymmetry
= ψ (iγµ∂ m ) ψ + ∂ φ 2 m2 φ 2 (3.1) L µ − ψ | µ | − φ| | 1 m 2 λ λ + (∂ H)2 H H2 φ φ 2H2 ψ ψψH +h.c. . 2 µ − 2 − 2 | | − 2 Here and in the following φ denotes any scalar field, ψ any fermion field, and H a Higgs boson. The calculation of the diagrams results in self-energies of the Higgs boson δMH = δMH,1 +δMH,2
λ2 Λ 1 δM 2 = ψ Λ2 + m2 6m2 log + . . . + (3.2) H,1 −8π2 H − ψ m O Λ2 ψ λ Λ 1 δM 2 = φ Λ2 2m2 log + . . . + . (3.3) H,2 8π2 − φ m O Λ2 φ Λ is a cutoff-parameter on which both corrections depend quadratically. They are therefore divergent for Λ —but with opposite sign. It is possible to solve this problem inside the → ∞ framework of the Standard Model, i. e. by adding counterterms to the mass corrections. However, these terms have to be fine-tuned up to arbitrary orders of perturbation theory. Although this is technically possible, it seems inelegant and unnatural. There is a more elegant way to avoid the quadratic divergences, namely, to set
2 λψ = λφ. (3.4)
2 2 In that case the corrections δMH,1 and δMH,2 cancel each other. To explain such a conspiracy between fermion and boson couplings, a symmetry between these two species of particles is required: supersymmetry. In unbroken supersymmetric models, each particle of the Standard Model receives a supersym- metric partner whose spin differs by 1/2 from the spin of the Standard Model particle, whereas all the other quantum numbers and the mass of the two partners are the same.
3.2 Supersymmetry breaking
Until today no supersymmetric particle has been directly detected. As mentioned above, a su- persymmetric partner for each Standard Model particle should exist which has the same mass. For example there should be a partner of the electron with a mass of 0.5 MeV, and even massless partners of the gluons and the photon. Since they have not been detected, supersymmetry must be a broken symmetry at low energy scales. Usually supersymmetry is assumed to be broken at the Grand Unification (gut) scale, where the running couplings of the electroweak and the strong interaction unify. In order to describe the symmetry breaking theoretically, a term has to be added to the super- symmetric Lagrangian
= + . (3.5) L LSUSY Lsoft The term describes a “soft” spontaneous breaking of supersymmetry. The subscript “soft” Lsoft means that only those expressions are allowed which do not spoil the solution of the hierarchy problem, i. e. which maintain the relation (3.4) between fermion and boson couplings. 3.3 Minimal Supersymmetric Standard Model 27
Names Spin 0 Spin 1/2
quarks, squarks (˜uL d˜L) (uL dL) ( 3 families) u˜ u × R R d˜R dR
leptons, sleptons (˜ν e˜L) (ν eL) ( 3 families) e˜ e × R R
0 ˜ 0 ˜ Higgs, higgsinos (H1 H1−) (H1 H1−) + 0 ˜ + ˜ 0 (H2 H2 ) (H2 H2 )
Table 3.1: The Standard Model fermions and scalars and their supersym- metric partners within the mssm.
3.3 Minimal Supersymmetric Standard Model
The Minimal Supersymmetric Standard Model (mssm) is minimal in the sense that it contains the minimum number of additional particles compared to the Standard Model. In the mssm framework each Standard Model particle obtains one supersymmetric partner whose spin differs by 1/2 unit.
3.3.1 Particle content of the MSSM
The supersymmetric partners of the Standard Model fermions are spin-0 particles, generically called “sfermions”. In the individual case an “s” is attached in front of the Standard Model name, e. g. “selectron” (shortly for supersymmetric electron), etc. Since the fermions have two chirality states, i. e. two degrees of freedom, each fermion receives two superpartners, one for the right-handed and one for the left-handed fermion. The subscripts L and R of the sfermions thus refer to the chirality of their Standard Model partners, whereas the sfermions themselves have no chirality. The Standard Model gauge bosons have supersymmetric partners with spin 1/2, generically called “gauginos”. Individually, the ending “ino” is attached to the name of the gauge boson to label its supersymmetric partner. In the case of the Standard Model Higgs boson it turns out that one Higgs doublet is not enough if the mssm is to remain theoretically consistent. Therefore, two Higgs doublets are postulated, whose supersymmetric spin-1/2 partners are called higgsinos. Usually the two Higgs doublets are denoted by H1 and H2. Both of them have two components, a charged one and a neutral one. The Standard model particles and their supersymmetric partners within the mssm are summa- rized in tables 3.11 and 3.2.
1Although right-handed neutrinos might exist, they are not listed here, since they are not relevant to the physics discussed in this thesis. 28 Supersymmetry
Names Spin 1/2 Spin 1
gluon, gluino g˜ g
0 0 W bosons, winos W˜ ± W˜ W ± W
B boson, bino B˜ B
Table 3.2: The Standard Model bosons and their supersymmetric partners within the mssm.
3.3.2 R-parity
In the Standard Model, the conservation of the total lepton number L and the baryon number B is usually assumed to hold separately2. In the framework of the mssm there is no theoreti- cal motivation why these quantum numbers should be conserved. The model would suffer no inconsistency if e. g. the proton decay—which may violate both lepton and baryon number— would be allowed. In that case the supersymmetric Lagrangian would contain a few additional terms describing the baryon and lepton number violating processes. However, the experimen- tal constraints on these processes are very strong: for example, the proton lifetime is limited to be above 1032 years. One could simply postulate B and L conservation in the mssm, but this would be a drawback since it is known that B and L are not exact symmetries (see the remark in the footnote). For this reason a new symmetry is introduced in the mssm which elim- inates the possible B and L violating terms in the Lagrangian without imposing their separate conservation—R-parity. It combines baryon and lepton number and might therefore be an exact symmetry, even in the context of Grand Unified Theories. The R-parity of a particle is given by
3(B L)+2S P = ( 1) − , R − where S is the spin of the particle. The R-parity of all particles of the Standard Model and of both Higgs doublets is +1, while all supersymmetric partners have R-parity 1. Therefore, the − conservation of R-parity has some important consequences:
The lightest supersymmetric particle—the “lsp”—is stable • All sparticles eventually decay into lsps • Sparticles can only be produced in pairs. •
From here on in this thesis the mssm is defined to conserve R-parity.
2In fact, already within the Standard Model, lepton and baryon number violation is proved to occur in non- perturbative electroweak effects. However, there is a cancellation between the diagrams describing these effects, such that they are experimentally negligible. 3.3 Minimal Supersymmetric Standard Model 29
3.3.3 Simplifying assumptions
The enlargement of the Standard Model to the mssm introduces a large number of new parame- ters. The mssm has 124 free parameters, most of them describing the masses and mixing of the particles. However, there are some experimental hints that an “organizing principle” governs the model parameters. There are for example severe experimental restrictions on flavour mixing or CP violation effects. Therefore, the following two phenomenologically motivated assumptions are usually made [12]:
The squark (indices U and D) and slepton (indices L and E) mass matrices are diagonal • in family space
2 2 2 2 2 2 2 2 MU = mU 1; MD = mD1; ML = mL1; ME = mE1.
The trilinear couplings are proportional to the Yukawa couplings Y •
aU = Au0 YU ; aD = Ad0 YD; aE = Ae0 YE. (3.6)
This set of assumptions is a specific example of what is often called the “soft-breaking uni- versality”. There are much stronger versions of these assumptions, of which two examples are presented in the next sections.
Phenomenological MSSM
In a general phenomenologically motivated mssm, sometimes abbreviated as pmssm, the follow- ing equations are assumed to hold [12]:
2 2 2 2 2 MU = MD = ML = ME = m01 (3.7) 5 2 5αem M1 = tan θW M2 = 2 M3 3 3αs cos θW AU = diag(0, 0, At); AD = diag(0, 0, Ab); AE = 0.
This example of a pmssm is defined by seven parameters: µ, M2, mA, tanβ, m0, At and Ab. mA is the mass of the CP-odd Higgs boson, M1, M2 and M3 are the gaugino mass parameters, µ is the higgsino mass term of the mssm Lagrangian and tanβ is the ratio of the Higgs boson vacuum expectation values
v tanβ = 2 . v1
The parameters of the pmssm are usually given at the weak scale. 30 Supersymmetry
Figure 3.2: Unification of the sparticle masses in msugra. The unification of the gaugino masses, which are equal to m1/2, and the unifica- tion of the sfermion masses, which are equal to m0 at the gut scale [8].
Minimal supergravity model mSUGRA
At the gut scale, the following universality relations are assumed
α1 = α2 = α3 = αU (3.8) 2 2 2 2 2 MU = MD = ML = ME = m01
M1 = M2 = M3 = m1/2
aU = A0 YU ; aD = A0 YD; aE = A0 YE
This leaves four continuous parameters and one discrete parameter: m0, m1/2, tanβ, A0 and signµ. These parameters are given at the gut scale. In order to determine the masses and couplings at lower scales, e. g. the weak scale, rges (renormalization group equations) are eva- luated. Therefore, a direct translation between msugra and the pmssm cannot easily be given. Fig. 3.2 illustrates the unification of the gaugino and sfermion masses at the gut scale and their evolution to lower scales.
Measurements of the muon anomalous magnetic moment aµ seem to favour a positive sign of µ [13]. The corrections to the value of aµ introduced by supersymmetry take over the sign of µ. Since they are positive—according to experimental measurements—µ also has to be. 3.4 Mass eigenstates and the neutralino 31
Interaction eigenstates Mass eigenstates
bino B˜ wino W˜3 neutralinos χ ˜ 0 1,2,3,4 higgsino H1 ˜ 0 higgsino H2 ˜ winos W ± ˜ higgsino H1− charginos χ ˜ + ± higgsino H2
squarksq ˜L,q ˜R q˜1,q ˜2
sleptons ˜lL, ˜lR ˜l1, l˜2
0 0 Higgs H1 , H2 h, H
Table 3.3: Interaction and mass eigenstates of the mssm.
3.4 Mass eigenstates and the neutralino
3.4.1 Mixing of interaction eigenstates
The fields presented in the last chapter and summarized in tables 3.1 and 3.2 are the interaction eigenstates of the mssm. As in the Standard Model, the interaction eigenstates are not necessarily equal to the mass eigenstates. A Standard Model example of this fact is the mixing of the gauge interaction B and W 0 bosons to the mass eigenstates γ and Z0. Similar mixings are assumed to occur to several particles of the mssm. Some possible mixings of mssm particles are the following:
Mixing of the gauginos and higgsinos • Mixing of the squarks • Mixing of the Higgs bosons •
The strength of the mixings is determined by the mass matrices, which can be read off from the mssm Lagrangian. In order to do so, all terms of the Lagrangian contributing to the particle masses in question are collected and rewritten in matrix notation in the basis of the interaction eigenstates. The interaction and mass eigenstates of the mssm are summarized in table 3.3. 32 Supersymmetry
3.4.2 Neutralinos and their mass matrix
A very important mixing regarding dark matter detection is the one of the gauginos and the mssm ˜ ˜ 3 ˜ 0 ˜ 0 higgsinos of the . The neutral gauginos B and W mix with the higgsinos H1 and H2 to four mass eigenstates which are called “neutralinos”. They are usually numbered from 0 to 3 or from 1 to 4 with ascending mass. The lightest neutralino is in many models the lightest supersymmetric particle (lsp) and therefore stable (assuming R-conservation). Since it is neutral, it interacts at most weakly with matter and is therefore an appropriate candidate to account for at least a part of the dark matter in the universe. There is also a mixing of the charged gauginos and higgsinos which combine to the “charginos”. Since they are only indirectly relevant to the discussion of dark matter detection they are not further described. ˜ ˜ 3 ˜ 0 ˜ 0 The neutralino mass matrix in the basis of the interaction eigenstates B, W , H1 and H2 is given by
′ ′ M 0 g v1 g v2 1 − √2 √2 0 M gv1 gv2 2 √2 √2 0 = ′ − . (3.9) χ1,2,3,4 g v1 gv1 M √ √ δ33 µ − ′ 2 2 − g v2 gv2 µ δ44 √2 − √2 − The entries M and M can be read off directly from the mssm soft Lagrangian. The entries µ 1 2 − are the higgsino mass terms given in the mssm Lagrangian, whereas the two off-diagonal 2 2 × matrices are the result of Higgs-higgsino-gaugino couplings. The one-loop corrections δ33 and δ44 are given by the following expressions [14]
3 δ = y2m sin(2θ )Re B (Q, b, ˜b ) B (Q, b, ˜b ) (3.10) 33 −16π2 b b ˜b 0 1 − 0 2 3 δ = y2m sin(2θ )Re B (Q,t, t˜ ) B (Q,t, t˜ ) . 44 −16π2 t t t˜ 0 1 − 0 2 B0 is a two-point function, given for example in [15]
1 1 B (p,m ,m )= dnq . 0 1 2 iπ2 (q2 + m2)((q + p)2 + m2) Z 1 2 Its first argument is the external momentum scale Q, the second and third arguments stand for the quark and squark masses. yb and yt are the Yukawa couplings of the b- and t-quarks:
gmb gmt yb = , yt = . (3.11) √2MW cosβ √2MW sinβ The Yukawa couplings are analogously defined for the lighter up- and down-type quarks. The mixing angles θq˜ of the squark interaction eigenstates are defined by
q˜1 =q ˜L cosθq˜ +q ˜R sinθq˜ (3.12) q˜ = q˜ sinθ +q ˜ cosθ 2 − L q˜ R q˜ 3.4 Mass eigenstates and the neutralino 33
The mass eigenstates—i. e. the composition of the neutralinos—is obtained by diagonalizing the mass matrix. The eigenvalues correspond to the masses of the four neutralinos, whereas the eigenvectors determine the linear combinations of the interaction eigenstates which are the physically observable particles. The obtained expressions are lengthy and complicated. It is therefore not straight-forward to determine the effects of the supersymmetric model parameters. The most important influence is exhibited by the gaugino masses M1 and M2, but µ and tanβ enter the expressions as well. 3 The four neutralinos χ1,2,3,4 written as linear combinations of the gauginos B˜, W˜ and the ˜ 0 ˜ 0 higgsinos H1 , H2 read
˜ ˜ 3 ˜ 0 ˜ 0 χi = Ni1B + Ni2W + Ni3H1 + Ni4H2 . (3.13)
The lightest eigenstate—the lsp—is often simply referred to as χ. The coefficients Nij are normalized such that
2 2 2 2 Ni1 + Ni2 + Ni3 + Ni4 = 1.
The first two terms indicate the gaugino fraction of the neutralino, usually written as
2 2 Zg = Ni1 + Ni2, whereas the higgsino fraction is determined by the two last terms
2 2 Zh = Ni3 + Ni4.
The magnitude of the gaugino and higgsino fractions are important to the strength of different couplings. Depending on the choice of the supersymmetric parameters their numerical values can be very different. If the one-loop corrections δ are neglected, the following general statements on the gaugino and higgsino fractions of the lsp—depending on the Z boson mass MZ and the fundamental supersymmetric parameters M2, M1, and µ can be made [16]
if M , M << M , µ χ is mostly a wino 2 Z 1 | | → if µ , M << M , M χ is mostly a higgsino | | Z 1 2 → if M , M << M , µ χ is mostly a bino. 1 Z 2 | | →
An example for typical gaugino fractions of the lsp in the framework of msugra is displayed in the left plot of fig. 3.3. The gaugino fraction is dominant in most areas of the scanned parameter space. Only for relatively small values of m0 and m1/2 there exist some higgsino dominated versions of neutralinos. The gaugino and higgsino fractions are also related to the mass of the neutralino. The right plot in fig. 3.3 displays the gaugino fraction Zg versus the neutralino mass mχ for a scan in the msugra parameter space. Most models produce a gaugino-like neutralino. A considerable higgsino fraction corresponds to rather lower masses of χ. The value for mχ favoured by dark matter searches lies within the region 50 GeV< mχ < 100 GeV. Inside this range almost all values for the gaugino fraction are possible—except for Z 0. The bulk of models however g ≃ produce a gaugino-like neutralino. 34 Supersymmetry
700 450
400 600 350 500 300
400 250 (GeV) (GeV) χ
1/2 300 200 m m 150 200 100 100 50
0 0 0 1000 2000 3000 0 0.2 0.4 0.6 0.8 1 m (GeV) Z 0 g
Figure 3.3: Neutralino properties in msugra. The left plot indicates regions with different gaugino and higgsino fractions of the neutralino dependent on the parameter choices. The parameters m0 and m1/2 are displayed. For tanβ the values 5, 25 and 50 have been caluculated. Furthermore, both signs of µ have been evaluated. The white areas correspond to regions with a gaugino fraction bigger than 0.95, gaugino fractions between 0.5 and 0.95 are displayed with points, between 0.05 and 0.5 with circles and below 0.05 with crosses. The right plot displays the neutralino mass versus the gaugino fraction. Values for negative signµ are indicated with crosses, the points correspond to positive signµ.
No qualitative difference between signµ = (crosses) and signµ = + (points) can be seen. − A general remark must be made here considering the density of the displayed points. It is not correct to regard the density of points as a gauge for the probability of the displayed quantities. Nature has chosen one specific value for the gaugino fraction of the lightest neutralino which can be any of the displayed points. Detecting Dark Matter 4
This chapter outlines how the underlying supersymmetric theory described in the last chapter determines the dark matter detection possibilities. The cross section for wimp-target interactions is directly derived from the theory. Together with the local halo density and flux described in chapter 2, the cross section determines the interaction rate. Furthermore, current experimental constraints, the annual modulation of a dark matter signal and some characteristics of different detector materials are outlined.
4.1 Direct detection
As described in section 1.1, dark matter is believed to consist of a sea of particles moving about in the universe, through the Milky Way, the earth and ourselves. When flying across ordinary matter, dark matter leaves almost no traces, since it is at most weakly interacting. However, it is possible that dark matter particles elastically scatter off ordinary matter with a very low probability, i. e., the cross section for this kind of interaction is very low. Nevertheless, every now and then it should be possible to detect some traces of such an impact. When crossing the atoms of ordinary matter, it is most likely that a dark matter particle or wimp scatters off the nucleus. Interaction with shell electrons is also possible, but is strongly suppressed, i. e. by about three orders of magnitude. The encounter of a wimp with a nucleus results in a movement of the latter. If such a recoiling nucleus is located in a dedicated medium, it deposits its kinetic recoil energy therein, typically in the form of phonon, scintillation light or ionization charge production. This process is further described in chapter 6. It is possible to measure these forms of energy deposition in dedicated detectors. Apart from the target material in which the interaction takes place, readout devices which are sensitive to one or several of the above mentioned interaction products are central parts of such a detector. The measurement of two different interaction products, e. g. scintillation light and ionization charge, has the advantage of providing powerful background rejection possibilities, since the relative amount of the products is typical for the interacting particle. Such rejection possibilities will be described in section 11.4. The above described method of measuring interactions of wimps with ordinary matter is referred to as direct detection, since the impact of a wimp itself is measured. Another possibility to reveal dark matter would instead consist of looking for wimp annihilation products. Since the neutralino is a Majorana particle, two neutralinos can annihilate each other if they meet. Annihilation products are electrons and positrons as well as hadrons and photons from further decays of these products. This second approach is called indirect detection. Several direct detection experiments are currently in preparation and running worldwide. Table 4.1 summarizes some currently relevant examples and their target materials. 36 Detecting Dark Matter
Experiment Location Detector material
CDMS USA Germanium+Silicon XENON Gran Sasso, Italy Liquid xenon ZEPLIN Boulby Mine, UK Liquid xenon ArDM CERN, Switzerland Liquid argon Warp Gran Sasso, Italy Liquid argon Edelweiss France Germanium CRESST Gran Sasso, Italy CaWO4
Table 4.1: Dark matter direct detection experiments.
4.2 WIMP-target cross section
The number of events seen in a direct detection experiment is determined by the wimp-target interaction cross section, the wimp flux which was described in chapter 2, the running time of the experiment and the size of the target. In this section, we focus on the cross section. The cross section is not known numerically, since it is determined by a model describing the wimp. The currently most common candidate for such a model is supersymmetry (see chapter 3), on which this thesis focuses. However, there are other ideas for what dark matter may consist of which should not be forgotten, some of them were described in section 2.3. Within the supersymmetric model there are two possible ways for a neutralino to interact with a nucleus, namely the spin-dependent and the spin-independent interaction. The former is only relevant to target materials with non-zero spin. Since argon has a spin of zero, only the spin- independent interaction is measurable with the ArDM detector. The calculation of the spin-dependent and spin-independent cross sections is rather involved. A detailed description can be found in [17] or [18]. Here only a short summary is given. The calculation starts with the supersymmetric interaction Lagrangian, from which supersymmet- ric Feynman rules for the neutralino-quark-interaction are derived. Further steps include the summing up of the quarks to nucleons, and nucleons to nuclei. Thereby, coherence effects have to be taken into account, which depend on the momentum transfer q2. Generally speaking, if q2 is non-negligible, form factors have to be introduced which reduce the strength of the coupling.
4.2.1 Spin-independent cross section
The possible tree-level spin-independent couplings of a neutralino to a quark are due to Higgs and squark exchange. The corresponding diagrams are displayed in fig. 4.1. In order to sum up the quarks contained in a nucleon, the so-called four fermion couplings G are introduced. The indices s and a refer to scalar (spin-independent) and axial (spin-dependent) coupling, p and n refer to proton and neutron, respectively. The cross section for spin-independent neutralino-nucleus interactions at low momentum transfer is then obtained by summing up the couplings to the nucleons, yielding [17, 19]
µ2 σSI = χi ZGp + (A Z)Gn 2, (4.1) χi π | s − s | 4.2 WIMP-target cross section 37
!! !! q~ H, h
q q
Figure 4.1: Scalar quark-neutralino coupling. The tree-level spin- independent coupling of neutralinos to quarks is due to Higgs and squark exchange [4].
where Z is the number of protons and A the number of nucleons of the target nucleus, the index i refers to different species of target nuclei and µχi = mχMi/(mχ + Mi) is the reduced p n neutralino-nucleus mass. In most cases, Gs G , i. e., the cross section is roughly proportional ≃ s to the number of nucleons squared. Therefore, for heavy nuclei, the spin-independent cross section is larger than the spin-dependent cross section. Expression (4.1) for the cross section has to be corrected if the momentum transfer is not negligible due to a “loss of coherence”. This is done by multiplying it by a form factor in which the dependence on q2 is absorbed. For the spin-independent form factor, different proposals are found in the literature.
Form factors
The form factor F (q) takes the nonzero momentum transfer effects into account. F (q) is defined as the normalized Fourier transform of a spherical nuclear ground state mass density distribution. Information on mass distributions can be obtained from pion elastic scattering. More precise measurements can be made of the charge distribution by elastic electron scattering, and it is usually assumed that charge and mass distributions are roughly proportional. Both the mass density and the charge density distributions ρ(r) are often approximated by a Gaussian with mean-square radius 3/5 R, where R 1.2 A1/3 fm. The resulting form factor ≃ is given by p
1 (qR)2 F1(q)= e− 10 .
However, the nuclear density is better described by a Woods-Saxon shape, whose Fourier trans- form has to be evaluated numerically. Nearly indistinguishable from the Woods-Saxon shape is the Helm form whose Fourier transform can be expressed analytically
3j1(qR0) 1 (qs)2 F2(q)= e− 2 . qR0 j is a spherical Bessel function of the first kind, R = √R2 5s2, and s=1 fm. 1 0 − 38 Detecting Dark Matter
!!
!! q~ Z
qq qq Figure 4.2: Axial quark-neutralino coupling. The tree-level spin-dependent coupling of neutralinos to quarks is due to Z and squark ex- change [4].
4.2.2 Spin-dependent cross section
The possible tree-level spin-dependent interactions of a neutralino with a quark are due to Z and squark exchange. The corresponding diagrams are displayed in fig. 4.2. The spin-dependent cross section at zero momentum transfer reads
4µ2 J + 1 σSD = χi S Gp + S Gn 2, (4.2) χi π J |h pi a h ni a | where J is the nuclear spin. As for the spin-independent coupling form factors have to be taken into account. The cross section times an arbitrary axial form factor reads
4µ2 σSD F SD(q) 2 = χi S (q). (4.3) χi | i | 2J + 1 A
The derivation of the axial form factors is rather involved. There is no general scheme how it has to be carried out, so the calculation is redone with appropriate models and assumptions for each element. For some nuclei simple models can be applied in order to estimate the spin content, at least in the case of zero momentum transfer. Details and examples for such models can be found in [17].
4.3 Detection rate
At this point all ingredients are ready to state the detection rate of neutralinos interacting with a certain detector material. Basically, the detection rate is proportional to the flux of the neutralinos times the probability of interaction, which is determined by the cross section σ and the form factor. The direct differential detection rate per recoil energy E for galactic neutralinos reads
2 dR ρχσχi Fi(qi) f(v,t) 3 = ci | 2 | d v. (4.4) dE 2m µ 2 v χ χi v> MiE/2µχi Xi Z q 4.4 Modulation of the WIMP signal 39
Here, a detector with several nuclear species i is described, Mi being the nuclear mass and ci the detector mass fraction in nuclear species i. µχi = mχMi/(mχ + Mi) is the reduced neutralino- nucleus mass. σχi denotes the total elastic scattering cross section of a wimp off a point-like 2 nucleus, while the nuclear form factor Fi(qi) takes nonzero q effects into account. Moreover, | | 3 ρχ is the local neutralino density and v the neutralino speed relative to the detector. f(v,t)d v is the neutralino velocity distribution, which is integrated over all neutralino speeds that can impart a recoil energy E to the nucleus. These last three parameters follow from cosmological assumptions as described in chapter 2. The total rate R is found by integrating eq. (4.4) over the recoil energy bin dE, assuming a detector threshold energy ET .
4.4 Modulation of the WIMP signal
Since the wimp halo is assumed to be at rest with respect to the rotating Milky Way, the sun and earth move at a certain relative speed through it. As a consequence of the movement of the earth around the sun, the speed of the earth relative to the wimp flux varies throughout the year. The velocity of the earth and the sun are aligned in June, whereas they are of opposite direction in December. Therefore, the relative flux of wimps with respect to the earth has a sinusoidal variation. The differential rate can consequently be expressed in the following way
dR(E ,t)= dR (E )+ dR (E )cos (ω(t t )) , R 0 R m R − 0 1 where ω = 2π/365 days− . The date when the direction of the movement of the earth and the nd sun coincide maximally is on June 2 . dR0 is the average differential scattering rate and dRm is the modulation amplitude. The relative size of dR0 and dRm depends on the target material, the neutralino mass and the recoil energy ER. It is typically of the order of a few percent. If this annual modulation was measured in a detector it would be a strong evidence that the registered interactions were produced by wimps. It depends on the recoil energy if the maximum amount of interactions occurs in June or in December. This fact is illustrated in fig. 4.3 for the element argon: If the recoil energy is below approximately 17 keV, the maximum of the differential rate per day, kg and keV occurs in December. If the recoil energy is above 17 keV, the situation is reversed. This fact provides another potentiality to distinguish a dark matter signal from background radiation. It is possible that some background sources also manifest a natural annual modulation like the wimp signal. However, it is highly unlikely that any background source also causes an inverted modulation curve if recoil energies below 17 keV are explored. Unfortunately the detection of such low recoil energies is experimentally very challenging.
4.5 Experimental constraints
Although the properties of the dark matter particle are poorly known, some constraints on the supersymmetric parameters as well as on cosmological properties can be derived from experi- mental results. Some of them are briefly outlined in the following sections.
4.5.1 Accelerator constraints
The results obtained in accelerator experiments place constraints on the supersymmetric pa- rameter space as well as on the properties of a dark matter candidate. Since the consequences 40 Detecting Dark Matter
−4 x 10 1.2
1
0.8
0.6
0.4 dR/dE per day,kg,keV Summer
Winter 0.2
0 0 10 20 30 40 50 60 70 80 90 100 E R
Figure 4.3: Differential rate per recoil energy. The differential rate per day, kg and keV is displayed for argon. The dashed line represents the summer rate, whereas the solid line corresponds to the winter rate. There is a crossing-over of the two lines at approximately 17 keV.
of accelerator measurements are highly model dependent, it is difficult to draw general conclu- sions. The usual way to make use of these results is to choose a model and check whether it is consistent with accelerator constraints. Some of the most important accelerator searches are briefly presented here (for a more complete discussion see [4]).
Invisible Z-width
If a dark matter candidate particle is sufficiently light, it can influence the invisible Z-width, since the Z boson may decay into it. There is however a substantial background to these events, namely Z νν¯ decays. →
Charged particle limits
+ In e e− colliders like lep, cross sections for direct pair production of charged particles are large, allowing for limits to be placed at approximately half of the center-of-mass energy of the collision. In this way, lep2 placed lower limits around 100 GeV on charginos and charged sleptons. However, these constraints can only indirectly influence dark matter via the unification of gaugino masses. Since this unification is assumed only in specific models like msugra, these limits are not valid in general supersymmetric models. If gaugino mass unification is assumed, the limits on the neutralino mass are about half of the limits on chargino masses, i. e. mχ & 50 GeV. 4.6 Different detector materials 41
Searches for coloured sparticles
The strongest limits on squarks and gluinos can be placed by hadron colliders such as Tevatron. Dark matter candidates may appear among the decay products of these particles. Typically, lower limits of around 200 GeV are obtained for squarks and gluino masses.
Higgs searches
Since radiative corrections to the Higgs mass are produced by superparticles, limits on the Higgs mass can be translated into limits on e. g. the top squark mass and other superparticle masses.
Decay b → sγ
The branching ratio for the fcnc (flavour changing neutral current) process b sγ is of → particular interest for physics beyond the Standard Model. In many scenarios, this process is greatly influenced by new physics like supersymmetry or universal extra dimensions. In supersymmetry, the constraints are stronger for µ< 0, but also relevant for µ> 0.
4.5.2 Regions excluded by dark matter experiments
In addition to the accelerator constraints, the results of dark matter detection experiments can be used to impose limits on the supersymmetric parameter space. As mentioned in section 2.3, dark matter candidates like the sneutrino can be ruled out by the (negative) results of dark matter searches. Some current and future limits on the nucleon cross section given by different experiments as well as theoretically motivated exclusion regions are shown in fig. 4.4, which was generated by using the webpage [20].
4.6 Different detector materials
Some points have to be taken into account when selecting the detector material for dark mat- ter direct detection. The spin-independent interaction is in most cases significantly stronger than the spin-dependent interaction, at least for heavy nuclei. In first approximation the spin- independent cross section is proportional to the square of the nucleon number. Therefore, heavy elements like argon, xenon or germanium are more suitable. However, there is an important effect of the form factor for large energy transfers, often referred to as “loss of coherence”. The influence of the form factor is illustrated in fig. 4.5. The total rates per day and kg detector material are displayed for different threshold energies and for the three elements argon (A = 40), xenon (A = 131) and germanium (A = 73). For low energy transfers the heavy elements pro- duce larger rates, whereas for large energy transfers the situation is vice versa. The crossing-over between argon and xenon occurs at approximately 37 keV. This plot is only an example for a specific set of model parameters and a lot of assumptions enter the results. The mass of the 8 neutralino is here equal to 107 GeV, the nucleon cross section is approximately 10− pb and the form factor is Woods-Saxon shaped. Since it is more difficult to detect interactions with low energy transfers, light elements have the advantage of a smaller influence of the form factor. 42 Detecting Dark Matter
-41 10 http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini
-42 10
-43 10 ] (normalised to nucleon)
2 -44 10
-45 10
-46 Cross-section [cm 10 080222055000 1 2 3 10 10 10 WIMP Mass [GeV/c2] DATA listed top to bottom on plot CDMS (Soudan) 2005 Si (7 keV threshold) CRESST 2004 10.7 kg-day CaWO4 Edelweiss I final limit, 62 kg-days Ge 2000+2002+2003 limit DAMA 2000 58k kg-days NaI Ann. Mod. 3sigma w/DAMA 1996 WARP 2.3L, 96.5 kg-days 55 keV threshold ZEPLIN II (Jan 2007) result CDMS (Soudan) 2004 + 2005 Ge (7 keV threshold) XENON10 2007 (Net 136 kg-d) CDMS Soudan 2007 projected SuperCDMS (Projected) 2-ST@Soudan SuperCDMS (Projected) 25kg (7-ST@Snolab) Ruiz de Austri/Trotta/Roszkowski 2007, CMSSM Markov Chain Monte Carlos (mu>0): 68% contour Ruiz de Austri/Trotta/Roszkowski 2007, CMSSM Markov Chain Monte Carlos (mu>0): 95% contour x x x Ellis et. al Theory region post-LEP benchmark points Baltz and Gondolo 2003 Baltz and Gondolo, 2004, Markov Chain Monte Carlos 080222055000
Figure 4.4: Experimental constraints. Current and future experimentally reachable cross sections, generated by using the webpage [20], are displayed, as well as the m σ region compatible with χ − N the dama result [21]. The cross section is indicated in cm2. 42 2 6 44 2 10− cm correspond to 10− pb, 10− cm correspond to 8 10− pb, etc. 4.6 Different detector materials 43
0 10
−5 10
−10 10 R (events/day/kg)
−15 10 0 50 100 150 200 250 300 350 E (keV) T
−2 10
Xenon
−3 10
Argon Germanium R (events/day/kg)
−4 10 0 10 20 30 40 50 60 70 80 90 E (keV) T
Figure 4.5: Total rates for different threshold recoil energies. The total rates dR R = ∞ in events per day per kg versus the threshold recoil ET dE energy E in keV are displayed for the three elements argon R T (A = 40), xenon (A = 131) and germanium (A = 73). The two different curves for each element correspond to the summer and winter values. The lower plot is a zoom of the upper plot with limited ranges of ET and R. The spin-dependent interaction of xenon and germanium is neglected.
Part II
The ArDM experiment The ArDM detector 5
The ArDM detector is an example for a dark matter direct detection experiment. Principles of detecting dark matter and especially of the direct detection method were described in chapter 4, where several target materials were presented as well. Noble liquids like neon, xenon and argon are proven to be well suited targets due to their high scintillation and ionization yields. When choosing between them, factors like coherence effects, discrimination possibilities and cost have to be taken into account. The target material of the ArDM detector is argon. The choice of natural argon instead of xenon—which is used in the majority of competing noble element experiments—for the initial ton-scale target can be motivated by three arguments:
The event rate in argon is less sensitive to the energy threshold than in xenon, due to form • factor effects (see fig. 4.5).
Argon is significantly less expensive than xenon, the experiment is therefore scalable at • moderate costs. Sizeable experience in the handling of massive liquid noble element de- tectors has been acquired in other projects [22, 23].
Recoil energy spectra are different in xenon and argon, providing a crosscheck if a potential • wimp-signal is measured.
The readout of the detector is designed to detect ionization charge and scintillation light pro- duced by interactions of particles with the liquid argon volume. This defines the main technical keypoints. Apart from the liquid argon volume which fills the major part of the detector vol- ume, a gas phase on top is necessary in order to create electron avalanches (see next section). Therefore, ArDM is a two-phase detector. This chapter presents the technical keypoints of the ArDM detector, especially the charge and light readout, and how they facilitate the event imaging of the detector.
5.1 Design of the ArDM detector
Fig. 5.1 illustrates the conceptual design of the ArDM one-ton prototype [24, 25, 26]. Its three technical keypoints are the charge readout on the top, the electric drift field and the light readout at the bottom of the detector. After an event in the fiducial volume has produced scintillation light and free ionization electrons, the electrons are pulled away from the interaction point and drifted upwards. The drift field is provided by a Greinacher or Cockcroft-Walton high-voltage circuit, designed to reach up to 4 kV/cm. The maximal drift length is approximately 120 cm. A detailed description of the electric field generation is given in chapter 8. When the electrons reach the level of the liquid argon surface, they are extracted into a gaseous argon volume on the top of the detector where the readout of the ionization charge takes place. 5.1 Design of the ArDM detector 47
Two-stage LEM for electron multiplication and readout to measure ionization charge 6 Greinacher chain: supplies the voltages to the field shaper rings and the cathode up to 500 kV
Field shaping rings
Cathode grid
Maximal? drift length 120 cm PMT below the cathode to detect the scintillation light
Figure 5.1: Setup of the ArDM detector. A CAD drawing of the ArDM detector is shown [27]. 48 The ArDM detector
Figure 5.2: Prototype LEM. A protoype LEM plate with 9 strips is shown. The diameter of this prototype is 25 cm, compared with approx- imately 80 cm and 512 strips per layer for the final version.
5.1.1 Charge readout wimp and neutron events typically produce between one and 30 free electrons (see chapter 6). In order to convert them into a detectable signal, the electrons need to be multiplied, even in a low-noise sensitive charge preamplifier1. In argon, such a charge amplification is achieved in the gas phase by using two LEM (Large Electron Multiplier) plates on top of each other for charge multiplication and readout [28]. A LEM consists of a Vetronite plate, coated on both sides with copper and perforated with holes. Inside these holes, the strength of the electric field present within the whole ficudial volume is considerably increased, such that electrons passing through the holes gain enough kinetic energy to produce secondary electron avalanches. The dimension of the LEM holes is 500 µm, and their distance 800 µm. The metal coatings of the upper LEM plate are stripped, one coating in the x-, the other in the y-direction. Therefore, the readout is segmented, defining the 3D-location of the event in space together with the prompt light signal (see section 5.3). A photograph of a prototype LEM with 9 strips is displayed in fig. 5.2.
5.1.2 Light readout
For the readout of the scintillation light, an array of 14 photomultiplier tubes is used, which is located at the bottom of the detector. The primary VUV scintillation light of argon at a wavelength of 128 nm needs to be shifted to visible light in order to match the sensitivity range of the photomultiplier tubes. This is achieved by a TPB (Tetra-Phenyl-Butadiene) compound
1The typical equivalent noise is approximately 1000 electrons 5.1 Design of the ArDM detector 49
Figure 5.3: PMT array. The layer of the ArDM detector containing the PMT array is displayed. An array of seven tubes was used for the first tests, 14 tubes are foreseen for the final version.
evaporated on a reflecting polymer, which absorbs UV light and reemits visible light, and there- fore acts as a wavelength shifter. More details on the light production, collection and readout are given in chapters 6 and 7. Fig. 5.3 shows the photomultiplier tube array with the transparent cathode above. This array was used for first tests of the ArDM detector.
5.1.3 Combining light and charge signals
The combination of charge and light readout provides a powerful background rejection possibi- lity. Since nuclear recoils due to wimp or neutron interactions have a much higher characteristic light over charge ratio than electron and gamma interactions, these types of events are in prin- ciple well distinguishable if the light over charge ratio can be measured precisely. This is a mandatory condition for the rejection of predominant background signals like the internal 39Ar signal. The 39Ar isotope is present in natural argon liquefied from the atmosphere [29], and pro- duces a background rate due to beta decay of approximately 1 kHz in one ton of liquid argon. The alternative possibility of using 39Ar-depleted argon extracted from underground natural gas is currently also studied. Since 39Ar is created in the atmosphere by secondary cosmic rays, argon which has been kept underground for a long time contains less 39Ar—provided there is no other way of producing the isotope by radiation present underground. The comparison of fast and slow light components can also be used to further discriminate be- tween nuclear recoils and background events. Due to different ionization densities the population of the two argon excimer states is different for nuclear recoil and electron/γ events, leading to characteristic contributions to the fast and slow scintillation light components. More details on the background rejection are given in section 11.4. 50 The ArDM detector
5.2 Setup of the detector
Fig. 5.1 displays a schematic view of the detector setup, wherein the detector parts which are described below are labelled. The entire size of the ArDM detector is comparably large—the liquid argon target has a mass of one ton, of which 850 kg act as sensitive fiducial volume. It is kept in a stainless steel dewar with a height of approximately 2 m and a diameter of 1.12 m. The liquid argon—which has a temperature of 87 K at 1 bar—is cooled, recirculated and purified by a dedicated recirculation system. All inner detector parts are mounted to the top flange, and can therefore easily be removed, cleaned and modified. The structure of the inner detector is supported by polyethylene pillars on which metal field shaping rings are mounted. They surround the electric field region that also defines the fiducial volume. The electric field region is terminated on the lower end by a cathode, consisting of a metal grid. Below the cathode, the photomultiplier tubes are mounted. Fig. 5.4 shows two photographs taken of the outer and inner detector.
5.3 Event imaging
The precise event imaging and positioning is an important part of the ArDM concept. A high granularity of the detector readout in combination with the light signal allows for an efficient recognition and rejection of background multiple scatter events, in particular neutron multiple scatters.
5.3.1 3D event positioning
Despite the large fiducial volume of the ArDM detector the above described readout devices allow for a precise event imaging. The horizontal x- and y-positions of an event are well local- ized by the segmented LEM readout. Since the planned strip width of the final LEM plates is approximately 1.5 mm, the pixel size in the x-y-plane is (1.5 mm)2. Due to diffusion of the drifting electron cloud produced by an event (as described in chapter 6), the charge signal can be spread over several strips. A simulation of this effect reveals that most signals are spread over two strips in the case of neutron and wimp signals, whereas the signal spreads over 2–5 strips in the case of electron and γ events which produce a larger number of ionization electrons. The z-position—which corresponds to the position along the detector axis—of an event is de- termined by the combination of light and charge signal. Since the light signal is instantaneous, its time tLight corresponds to the interaction time. The charge signal however is delayed since the drift speed vDrift of the electron is of the order of 3 mm/µs, depending on the electric field (see table 6.1). This corresponds to a maximum drift time of 400 µs if the entire drift length of 120 cm has to be crossed by the electrons. The time difference between light and charge signal t t is proportional to the distance d drifted by the electron, and therefore to the Charge − Light z-position of the event
d = v (t t ). (5.1) Drift · Charge − Light An example for the charge signals of a simulated event in the ArDM detector is displayed in fig. 5.5. The time axis is indicated in the figure. The length of the signals along the time axis correspond to their spread in time, whereas their width corresponds to the number of strips which get a charge signal. In this case a neutron multiple scattering event and an electron interaction event occur at the same time. The electron signal arrives earlier (lower on the time axis), 5.3 Event imaging 51
Figure 5.4: ArDM outer and inner detector. The photograph on the left shows the stainless steel dewar which contains the ArDM liq- uid argon target volume. The dewar is surrounded by concrete blocks in order to facilitate the access to the top flange. The photograph on the right displays the inner part of the ArDM detector. The central part consists of the field shaping rings, the white support pillars, the reflector foils and the blue Greinacher circuit. Below the field shaping rings, the support structure for the PMTs with hexagonal holes is mounted. 52 The ArDM detector
Figure 5.5: A neutron multiple scattering and electron event. A simulated event example with a strong charge signal produced by an elec- tron interaction (red small circles) plus several fainter neutron multiples scatter signals (green large circles). The plot on the left displays the x-direction whereas the plot on the right shows the y-direction. The time axis is displayed as well. The clear separation of the signals due to the fine LEM granularity allows for multiple scatter recognition.
indicating that it took place closer to the LEM plates than the neutron event. Furthermore, the electron signal is larger and longer due to the larger number of ionization electrons produced. Six neutron scatters are seen in the x direction plane while seven scatters are visible in the y direction plane. Thus, in this case two scatter signals overlap in the x direction. The many well separated signals from the neutron multiple scattering illustrate the fine granularity of the x-y-readout provided by the segmented LEM.
5.3.2 Signal shapes
The signals produced by the final LEM plates of the ArDM detector have not been measured yet. Their precise shape and characteristics is therefore currently unknown and remains to be tested. In order to simulated event characteristics like event overlaps, preliminary signal shapes were introduced into the simulation codes. Two such examples for the light and charge signals are displayed in fig. 5.6. 5.3 Event imaging 53
Figure 5.6: Simulated PMT and LEM signals. Examples for simulated signal time shapes for PMT and LEM signals are displayed. The precise signal shapes have to be adapted to the future measured signals of the ArDM detector. Light and charge production in liquid argon 6
A particle interacting inside a liquid argon volume deposits a certain amount of energy. As described in the last chapter, this energy goes into phonons, scintillation photons and ionization charge. Depending on the kind of the interacting particle, the relative amount of these three products varies. Two classes of events are of major importance for the ArDM experiment, namely the class of wimp and neutron events and the class of electron and γ events. Within the two classes the characteristics of the interaction is exactly the same, so particles within the same class cannot be distinguished by means of phonon, charge and light characteristics. This chapter is based on the Lindhard theory [30] which allows for the calculation of the number of produced ionization electrons and scintillation photons after an energy deposit from a particle of a certain kind. The formulae for the two classes stated above are outlined.
6.1 Scintillation mechanism
While the ionization electrons are directly generated via the production of electron-ion pairs, the scintillation light is created via the production of excited argon states. Excited argon atoms form excited dimers, leading to emission of scintillation light via the following process
Ar∗ + Ar Ar∗ → 2 Ar∗ 2Ar + hν. 2 →
Ionized argon atoms Ar+ can also contribute to the scintillation light via the formation of molecular ions, capture of thermalized electrons and decay with emission of scintillation light. The calculated and measured ratio of excitation to ionization is N /N 0.21 in liquid argon ex i ≃ [31, 32].
6.2 WIMP or neutron events
The class of wimp and neutron events is of particular relevance to ArDM since the detection of the wimp is the purpose of the experiment. Since neutrons can interact in precisely the same way as wimps, they are the most critical background source. Any experiment with the goal of detecting wimps needs to be carefully shielded against neutrons. More details and studies on the shielding are described in chapter 12. After a wimp or neutron interaction in liquid argon, a certain part of the energy goes into secondary atomic motion (ν), producing a phonon signal. Since the ArDM detector is not 6.2 WIMP or neutron events 55 sensitive to phonons, this part is not measured. The remaining energy goes into light and charge production, the total amount of this contribution is labelled η, which stands for electronic motion. The loss due to phononic signal production is described by the quenching factor qnc (nuclear quenching) and is proportional to η/(η + ν). The Lindhard theory [30] predicts a powerlaw for the nuclear quenching with two parameters A and α and the variable E which stands for the energy deposited in the interaction
E α q (E)= A . (6.1) nc 1 keV
The theory predicts A = 0.203 and α = 0.171, so qnc increases with increasing E. A second quenching mechanism which reduces the measured signal is the so-called bi-excitonic quenching. Only in first approximation the sum of the number of emitted scintillation photons and ionization electrons is constant and equal to the sum of produced excited and ionized atoms ∗ − (NAr + NAr+ = Nγ + Ne ). For high ionization densities however, this relation is violated for certain kinds of interacting particles. The signal loss due to this violation is caused by the bi-excitonic quenching process [33]
+ Ar∗ + Ar∗ Ar + Ar + e− + kinetic energy. (6.2) → Note that the kinetic energy on the right-hand-side is insufficient for secondary ionization. Nu- meric values for the bi-excitonic quenching depend on the kind of the interacting particle. For neutron and wimp events, the value 0.6 is used and motivated by [33]. The combined nuclear and bi-excitonic quenching is labelled q and given by
q = qnc qbi excitonic. (6.3) · − The energy q E remaining after quenching directly goes into the production of electron-ion pairs · and excited argon states. The average energy needed to create an electron-ion pair in liquid argon is measured to be W =23.6 eV. The number of electrons produced after the interaction is therefore equal to
N = q E/W. (6.4) e · The charge which can be drifted away from the interaction point by the electric field (ǫ) of the detector is however much smaller, since the high ionization density produced by the interaction causes a high local electric field. This local field draws back a certain fraction of the electrons, since it exceeds the drift field inside a certain region. The reduction of charge due to this effect is described by the so-called box model [34]
ǫ Q(ǫ)= Ne ln(1 + Cx/ǫ). (6.5) Cx
The constant Cx is not very well known. Measurements indicate that it approximately lies within the range 790–1856 cm/keV [33, 35]. The remaining final number of ionization electrons which are drifted away from the interaction point is given by
q E ǫ Q(E,ǫ)= ln(1 + Cx/ǫ). (6.6) W Cx 56 Light and charge production in liquid argon
The number of scintillation photons is determined by the energy Wγ =19.1 eV needed to produce an excited state with emission of a photon. The total number of photons is reduced by the number of electrons drifted away—and therefore not recombining—in a field dependent trade- off between light and charge signal
q E L(E,ǫ)= Q(E,ǫ). (6.7) Wγ − Fig. 6.1 displays the number of electrons and photons produced in this model in dependence on the energy deposited by the particle.
6.3 Electron and gamma events
The second class of electron and γ events is the dominant background source in terms of radiation rates. As described in chapter 11, significant numbers of background γs are produced from the uranium and thorium contaminations in detector components as well as surrounding facilities, whereas a comparably high rate of background electrons arises from the decay of the radioactive isotope 39Ar contained within the liquid argon volume. These background radiations are present in much larger numbers than neutron background, but they can be rejected much more easily and efficiently due to the different light and charge characteristics (see section 11.4). In the case of electron and γ events, the nuclear quenching factor is approximately equal to one, so the whole deposited energy is converted into charge and light. The main effect that reduces the number of signal electrons in this case is the stopping power of electrons moving in liquid argon. At low energy, i. e., below 100 keV, the stopping power increases significantly up to about a factor of five compared with higher energies. The consequent increase of the ionization density leads to an increased loss of signal electrons. The energy and electric field dependent quenching R according to the Lindhard theory [30] for electron and γ events depends on two parameters A and k and is given by
A R = . (6.8) dE/dx(E) 1+ k ǫ The measured values for A and k are: A = 0.8 and k = 0.0486 kV/MeV [35]. With a drift field strength of ǫ=5 kV/cm, this corresponds to values for R ranging between 0.698 (at 10 keV) and 0.778 (100 keV or more). dE/dx has been measured to vary between 2.9 MeV/cm and 15 MeV/cm [35]. The energy R E remaining after the quenching is converted into electron-ion pairs similar to · the case of wimp and neutron events described in section 6.2, i. e., the number of produced pairs is equal to R E . The reduction of ionization electrons due to the locally produced electric field · W is small in this case, since the ionization density is much smaller than in the case of wimp and neutron events. The total measured electron number is given by
− E E A Qγ,e (E,ǫ)= R = . (6.9) · W W dE/dx(E) 1+ k ǫ In the energy region between 10 keV and 100 keV, the change in the value of dE/dx(E) stated above has to be taken into account, e. g. by numerically integrating the above formula over energy steps. 6.4 Simulation of light and charge produced for WIMP/neutron and electron/gamma events57
3500
3000
2500
Electrons bg. 2000
1500 Photons bg.
Photons WIMP 1000 No. of electrons and photons
500
Electrons WIMP 0 0 10 20 30 40 50 60 70 80 90 100 Recoil energy (keV)
Figure 6.1: Light and charge versus energy for wimp/neutron and electron/γ events. The energy dependence of ionization charge and scintillation light production is displayed for wimp/neutron and electron/γ events. The upper dashed line is the number of electrons for electron/γ events, the upper solid line the number of photons for electron/γ events, the lower solid line is the num- ber of photons for neutron/wimp events and the lower dashed line the number of electrons for neutron/wimp events.
The total number of scintillation photons is determined by the trade-off between light and charge analogous to equation 6.7
− R E − Lγ,e (E,ǫ)= Q e (E,ǫ). (6.10) Wγ −
The number of electrons and photons produced after an electron or γ event dependent on the energy deposit is plotted in fig. 6.1.
6.4 Simulation of light and charge produced for WIMP/neutron and electron/gamma events
The summarized characteristic numbers for scintillation photons and ionization electrons versus transferred energy according to the last two sections are displayed in fig. 6.1. In order to take into account fluctuations due to realistic experimental conditions, simulations of the charge and light production, propagation and collection were performed. These simulations 58 Light and charge production in liquid argon
Electric field (kV/cm) Electron drift velocity (mm/µs) 1 2.0 2 2.6 3 3.0 4 3.4
Table 6.1: Drift velocities of electrons for different electric field strengths.
included fluctuations of the signal strengths due to statistical effects, which were assumed to be Poisson distributed for low produced numbers of photons and electrons, and Gaussian shaped for high produced numbers. The standard deviation of the Gaussian distribution is proportional to the square root of the produced number of photons and electrons
σ N . (6.11) e/γ ∝ e/γ q Furthermore, effects due to the electron drifting are taken into account. The electron drift velocity depends on the electric field E and on the mean time between two collisions τc
e v = Eτ . (6.12) d 2m c
Some values given in [36] are listed in table 6.1. For an electric field of 3 kV/cm the longest possible drift time in the ArDM detector is of the order of 400 µs. During the drifting of the electron cloud produced by a particle interaction, a diffusion in space takes place, which is described in the next section.
6.4.1 Diffusion of electrons
The distribution of electrons in a cloud which diffuses due to collisions is approximated by a Gaussian shape [36, 37]
dN N x2 = 0 exp , (6.13) dx √ −4Dt 4πDt where N0 is the total number of electrons, x the distance from the point of creation and D the diffusion coefficient, which is 4.8 cm2/s for liquid argon (at 89 K). It is assumed here that the diffusion is similar in longitudinal and transverse direction. The root mean spread in x in this case is
σ(x)= √2Dt, (6.14) which becomes significant only after comparably long drift distances, e. g., after 3 m drift in an electric field of 500 V/cm, the spread of the drifting electrons is σ(x) 1 mm. In the case of ≃ the ArDM detector, the spread typically leads to a distribution of the charge signal over more than one LEM strip, especially for events taking place far away from the LEM plates. 6.5 Scintillation light pulse shape 59
6.4.2 Results
The above described effects lead to a smearing out of the mean signal strengths predicted by the Lindhard theory, since effective electron and photon numbers are distributed around the Lindhard mean value. Furthermore, the electrons produced by an event are diffused after the drifting, and therefore smeared out in time and space. The readout devices of the ArDM detector are designed to convert the analog electric signals—due to electrons passing the LEM and photons being converted to photoelectrons inside the PMTs—into digital counts. Such devices are generically called ADCs (analog to digital converters). In order to mimic realistic detector signals, the ionization electrons and scintillation photons were converted into ADC counts in the simulation program. For the ionization electrons, the conversion included the LEM gain per single electron and the output in ADC counts generated per electron by the preamplifier. For the scintillation photons, the conversion included geometrical effects of the detector, the reflectivity of the reflector foils, the quantum efficiency of the PMTs and the output of ADC counts generated per photoelectron by the preamplifier (more details on the light collection are given in the next chapter). All assumed numbers were taken from preliminary setups, thus the conversion might be slightly different for the final detector version. The resulting signals are summarized in fig. 6.2, where the ADC counts of LEM and PMTs— corresponding to original charge and light signals—are displayed. All above described effects were included for the generation of this plot. The upper green band in the figure corresponds to simulated 39Ar, the lower blue band to simulated wimp events according to the Lindhard theory [30]. A significant spread of the signal bands compared with fig. 6.1 is visible and imposes a reduction of the rejection power of the detector. The precise amount of the spread and thereafter the reduction of the rejection power remains to be determined from actual measurements of the detector performance.
6.5 Scintillation light pulse shape
The scintillation light emitted by argon with a wavelength of 128 nm is in the deep UV region, and therefore not visible. Since there are no atomic transitions of the energy corresponding to this wavelength, argon is transparent to its own scintillation light. The scintillation light is emitted by excimer states created by one excited argon atom together with one ground state argon atom. Such excited states are induced by energy transfers to argon as for example due to interacting particles like wimps or γs. Two different excimer states exist, a singlet and a triplet state. They have different decay times leading to two distinguished components of the scintillation light. The singlet state has a comparably short decay time of 6 ns, and leads to a fast light component, whereas the triplet state has a relatively long decay time of 1.6 µs, leading to a slow light component. Transitions from the triplet to the singlet state are possible and the frequency with which they occur is proportional to the ionization density. Therefore, more transitions are expected for interactions with the nucleus, for which the ionization density is higher. Neutron and wimp interactions with the argon nucleus consequently result in a larger population of the fast component due to a higher rate of transitions from the triplet to the singlet state compared with electron and γ interactions. The ratio of fast light over slow light is about 3 for neutron and wimp events and about 0.3 for electron and γ events. The simulated typical time dependence of the light signal is displayed in fig. 6.3. The fast component is only visible as a peak at time zero, which corresponds to the time at which the particle interaction took place. Both interaction kinds—neutron/wimp events and electron/γ events—are displayed. The two curves are normalized such that the size of the fast components is the same for both interaction kinds. 60 Light and charge production in liquid argon
6 10
5 10
4 10
3 10 ADC LEM
2 10
1 10
0 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 4 ADC PMT x 10
Figure 6.2: Light versus Charge for wimp and 39Ar events. The ADC counts from LEM and PMTs are plotted for wimp and 39Ar events. The upper band corresponds to 39Ar, the lower band to wimp events. 6.5 Scintillation light pulse shape 61
5 10
4 10
3 10
2
No. of events 10
1 10
0 10 0 5000 10000 15000 Time of photon emission (ns)
Figure 6.3: Simulated scintillation light pulse shape. The number of pho- tons emitted at a certain time after the interaction is shown in a histogram for neutron (lower line) and electron (upper line) events. The fast component and the slow component are cleary distinguishable. The total number of photons is normalized such that the size of the fast component is the same for both curves. The electron events have a larger slow component. Light collection in the ArDM detector 7
In the last chapter the process of creating ionization charge and scintillation light from particle energy deposits was outlined, and the theoretically expected number of electrons and photons was computed. This chapter focuses on the scintillation light, and especially on the question how much of the emitted light can be collected and measured by the detector. Unlike in the case of ionization electrons, the scintillation photons cannot be forced to move towards the readout devices, but are ejected isotropically with a random direction. Therefore, the geometry of the detector and the position of the PMTs crucially influence the photon collection efficiency. After a short description of the hardware parts designed for the light readout, the collection efficiency due to these components is assessed.
7.1 Argon scintillation light
As described in section 6.5, argon scintillation light is produced by deexcitation of excimer states. Its wavelength of emission is 128 nm, i. e., in the deep UV region of the photon spectrum. The ArDM detector is designed to measure scintillation light with photomultiplier tubes (PMTs). Most commercially available PMTs however are only sensitive to visible light and—with less efficiency—for the near UV region. Due to this limitation it is necessary to shift the argon scintillation light to a larger wavelength in order to make it visible to the PMTs. The next two sections briefly describe the PMTs and the wavelength shifter used in the ArDM experiment. More details on the light readout are given in [38].
7.2 Photomultiplier tubes
Photomultiplier tubes are used in the ArDM detector in order to measure the argon scintillation light. The behaviour and handling of PMTs is generally quite well known. The difficulties in the case of the ArDM detector arise mainly from the fact that argon scintillation light is in the deep UV range, and therefore needs to be shifted. Furthermore, the detector including the photomultiplier tubes is operated at liquid argon temperature, i. e. at 87 K. As with all detector components, the behaviour of the PMTs at such low temperatures is not necessarily the same as at room temperature and needs therefore to be carefully tested. The final design of the detector includes 14 spherical PMTs at the bottom of the detector with a diameter of 25 cm each. The efficiency of the PMTs for detecting light is determined by several factors. The manufacturer indicates an efficiency of the PMT for converting photons to photoelectrons, i. e., the probability that a photon manages to undergo a photoelectric effect and thereby produce an electron, which is called photoelectron. This efficiency is named quantum efficiency, and is of the order of 20%– 7.3 Wavelength shifter and reflector 63
25% for commercial PMTs1. However, the quantum efficiency also depends on the wavelength of the incident photon, its incident angle on the PMT surface, and the temperature. Since the quantum efficiency is zero for the deep ultraviolet wavelength of the argon scintillation light, a wavelength shifter is necessary, as described in section 7.3. Furthermore, the quantum efficiency tends to decrease with decreasing temperature, and typically becomes 10%–15% at liquid argon temperature. A photograph of the partially filled PMT layer of the detector is displayed in fig. 5.3.
7.3 Wavelength shifter and reflector
A composite material called TPB (tetra-phenyl-butadiene) is used as a wavelength shifter. One compound of the TPB thereby absorbs the 128 nm light emitted by argon, transfers the absorbed energy to a second component, which reemits a photon in the blue range of the visible light spectrum, i. e., at approximately 430 nm. The shifted light is emitted isotropically in a random direction, independent of the incident photon direction. By default, at least 50% of the reemitted light leaves the detector without reentering the fiducial volume. In order not to loose this light, the TPB layer is evaporated on a reflecting foil, so photons emitted towards the outside of the detector are reflected back into the fiducial volume. The reflectivity of the foil is assumed to be about 95%–99%, a value which remains to be measured. Due to the rough surface the reflection is not specular but diffuse. A photograph of the inner detector with partially mounted reflector foils, coated with TPB, is shown in fig. 7.1. In the picture, the foils are illuminated with a UV lamp. The wavelength shifter coating shifts the wavelength of the photons emitted by the UV lamp to visible blue light.
7.4 Collection efficiency
In order to assess the ability of the detector to collect the scintillation light emitted after in- teractions, simulations of photon tracks inside the detector volume were performed with the Geant4 package [39]. The full detector geometry was implemented with all parts of the inner and outer detector including PMTs, wavelength shifters and reflector foils for the light collec- tion. A display of the Geant4 geometrical detector simulation is shown in fig. 7.2. The most important influence on the collection efficiency is exhibited by the reflectivity, the positioning of the wavelength shifter, the shifting efficiency and the quantum efficiency of the PMTs. Some results of the photon track simulations are presented in the next three sections.
7.4.1 Positioning of the wavelength shifter
In order to assess the question where the wavelength shifter is best to be positioned, a full detec- tor simulation of light-producing events and the scintillation photon tracks was performed. In particular, two solutions were considered, namely to add a wavelength shifting layer only onto the glass window of the PMTs or onto reflecting foils attached from inside to the field shaping rings which surround the fiducial volume. It turned out that the latter solution provides a much better collection efficiency, namely an increase of the percentage of collected photons from 21% to 53%. A diffuse reflection of 99% was assumed here for the reflector foils surrounding the fiducial volume in the latter case. If the reflector foils are made of a specularly reflecting material instead of diffuse reflectors,
1Models produced by Hamamatsu and ETL were used for first tests of the detector 64 Light collection in the ArDM detector
Figure 7.1: Reflector with wavelength shifter. The reflector foils coated with TPB wavelength shifter are shown when they are illuminated with a UV lamp. Due to the shifting, the reflected and shifted light shines in blue. Here, about 70% of the foils are mounted on the field shaping rings. 7.4 Collection efficiency 65
Figure 7.2: Simulated detector geometry. A picture of the Geant4 geometri- cal simulation of the ArDM detector is displayed.
the collection efficiency is significantly worse. The results of simulations of specular and dif- fuse reflectors are displayed in fig. 7.3. The upper line corresponds to the collection efficiency dependent on the z position of the event for diffuse reflection, whereas the lower line displays the result for specular reflection. The average collected percentage is 53.7% for diffuse reflec- tors and 31.6% for specular reflectors. Apart from the difference in absolute values, it is also remarkable that the z dependence is stronger for the latter case. This is undesirable since the scintillation photon collection and thereafter the reconstruction of the energy would in this case more strongly depend on the event position. It was therefore decided to add the TPB layer onto the reflector foils made of a diffuse reflecting material. In addition the PMTs were coated with TPB in order to collect the direct light—i. e., the light which did not hit any detector wall and therefore was not shifted—as well.
7.4.2 Angular distribution of incident photons
Since the quantum efficiency of the photomultiplier tubes does not only depend on the effects described above, but also on the incident angle under which the photons hit the PMT surface, angular distributions of incident photons were studied. In order to assess these angular effects, the average incident angles under which the photons hit an imaginary plane above PMTs was simulated. Fig. 7.4 shows the result. With an assumed reflectivity of 99%, the average incident angle turns out to be 42.8o. This illustrates the fact that most photons do not arrive straight downwards, but are shifted and reflected several times on the detector walls before they reach the PMTs. Simulations indicate that only 10% of the photons are direct, i. e., do not hit the detector walls before reaching the PMTs. The majority of photons hits the detector walls 5–10 times before arriving on a PMT surface. 66 Light collection in the ArDM detector
100
90
80
70
60
50 Diffuse reflection
40
30
% of photons arriving on PMTs Specular reflection 20
10
0 −600 −400 −200 0 200 400 600 800 z position of event (mm)
Figure 7.3: Photon collection at different positions in detector. The percent- age of collected photons is plotted as a function of the z-position in mm of the event. The upper line corresponds to diffuse re- flection of the reflector foils whereas the lower line displays the result for specular reflection. A reflectivity of 99% was assumed. The z-axis corresponds to the symmetry axis of the detector. The surface of the PMTs is located at z=-510 mm. The average collected percentage is 53.7% for diffuse reflection and 31.6% for specular reflection. 7.4 Collection efficiency 67
12000
10000
8000
6000 No. of events
4000
2000
0 0 10 20 30 40 50 60 70 80 90 Angle (deg)
Figure 7.4: Incident angles on PMTs. The angles under which the photons hit an imaginary plane just above the PMTs is displayed. The average value is 42.8o. A reflectivity of 99% and diffuse reflection was assumed for the reflector foils. 68 Light collection in the ArDM detector
7.4.3 Overall collection efficiency
Table 7.1 summarizes the above described effects. The numbers given therein are rough estima- tions deduced from simulations, measurements in small liquid argon test setups and preliminary measurements with the ArDM detector. The reflectivity is estimated to lie within the range 95%–99%. 3%–6% of the emitted light is collected by the PMTs with these estimations.
Effect Efficiency (%) % of signal left Detector geometry and reflectivity 37–53 37–53 Shifting efficiency of WLS 80 29–42 Quantum efficiency of PMTs 10–15 3–6
Table 7.1: Effects that limit the light collection efficiency. High Voltage Supply 8
As described in chapter 5 the design of the ArDM detector is based on three technical keypoints, namely the charge readout, the light readout and the electric drift field generation. A high electric field inside the fiducial volume is mandatory in order to drift the ionization electrons away from the interaction point, thereby facilitating the charge readout. The electric field should be as strong as possible in order to remove a significant amount of free electrons from the interaction region, preventing them from recombination with the argon ions. Furthermore, the extraction of the electrons out of the liquid argon into the gaseous phase is only achievable with electric field strengths above approximately 3 kV/cm [28]. The extraction into the gas phase is necessary to facilitate the charge readout, since only in argon gas the electrons can gain enough kinetic energy to produce avalanches inside the holes of the LEM. This chapter focuses on the high drift field generation. In the case of ArDM, a dedicated electric circuit called Greinacher or Cockcroft-Walton circuit was designed and constructed for this purpose. Here, the properties of the circuit are characterized by a theoretical model, and the results of measurements in air, vacuum and liquid argon are outlined.
8.1 Greinacher circuit
The Greinacher or Cockcroft-Walton chain is a circuit which allows to generate high DC output voltages with relatively low input AC voltages. It consists of a variable number of equal stages, each of which ideally increases the total output DC voltage by the peak-to-peak value of the AC input voltage. For example, an ideal Greinacher chain with ten stages generates an output voltage of ten times the input peak-to-peak voltage. One stage of a Greinacher circuit has a relatively simple scheme with two capacitors and two diodes, arranged as shown in fig. 8.1. An approximately stable output voltage which increases from left to right can be measured on the lower side of the circuit as indicated by the HV label in the figure. The voltage on the upper side is alternating. During a charging up of the circuit, the stage which is closest to the AC input is charged first. Several AC periods are needed to ramp up the further away stages as well. The time necessary for a complete loading of the circuit therefore increases with increasing number of stages. During a ramp-up, the capacitors of the circuit are charged during one half of the AC period, whereas the diodes prevent them from discharging during the second half of the AC period. The capacitors on the upper side of fig. 8.1 provisionally keep the charge which is going to be transferred to the next capacitor on the lower side, where it contributes to the final output DC voltage. Therefore, the capacitors on the upper side are called charging capacitors, whereas the ones on the lower side are labelled storing capacitors. The polarity is determined by the direction of the diodes. In fig. 8.1 the diodes are drawn such that the output voltage is positive. For negative output voltage all diodes have to be reversed. A detailed description of the charging up process of the circuit is given in [40]. 70 High Voltage Supply
Figure 8.1: Greinacher circuit scheme. The first and the last stage of a multiple-stage Greinacher circuit are shown. Each stage contains two capacitors and two diodes. The input voltage on the left is alternating, whereas the output voltage (labelled HV) is direct.
8.2 The Greinacher chain of the ArDM detector
The use of a Greinacher chain for the high voltage generation of the ArDM experiment has several advantages. Of major importance is the fact that only a relatively small input voltage is needed. Since the ArDM detector has to be kept at 87 K, voltage feedthroughs need to be well insulated, which is easier to achieve for lower voltages. Furthermore, the output voltage is quite stable over time, i. e., the voltage does not decrease significantly over several days once the circuit is charged. A Greinacher chain with 210 stages was constructed for the ArDM detector. For every capaci- tor symbol in fig. 8.1, several polypropylene capacitors with a capacitance of 82 nF each were added in parallel in order to increase the total capacitance. In stages one to 170 four such capacitors were added in parallel, whereas for the stages 171 to 210, the number of parallel capacitors was reduced to two. Every diode symbol in fig. 8.1 consists in the circuit of three diodes in series, in order to increase the breakdown voltage. The diode type used is Philips BY505 [41]. In total, 1520 capacitors and 1260 diodes were used to construct the circuit. The photographs in fig. 8.2 show the capacitor diode models used for ArDM. For the geometrical layout of the circuit a three-dimensional setup was chosen which is drawn in fig. 8.3. It displays two stages of the ArDM Greinacher chain with four capacitors in parallel as in stages one to 170.
A picture of the Greinacher circuit mounted to the top flange of the ArDM detector and attached to the field shaping rings is displayed in fig. 8.4. In addition to the 210-stage circuit for the ArDM detector a small Greinacher circuit with 10 stages was constructed in order to characterize and test this circuit type under easier conditions. A photograph of the small 10-stage circuit is displayed in fig. 8.14. The measurements of this circuit were carried out inside a 30 l stainless steel dewar, a photograph of which is shown in fig. 8.15. A more detailed description as well as the results of the measurements are given in section 8.6. All measurements of the Greinacher output voltage need to be taken in a closed container since the used BY505 diodes are photodiodes and therefore sensitive to light. Furthermore, safety is an issue since the high capacitance of the circuit makes it a dangerous device even at comparably low voltages. The planned total voltage during data taking of the ArDM detector amounts to 500 kV, which 8.2 The Greinacher chain of the ArDM detector 71
Figure 8.2: Components of the Greinacher circuit. The photograph on the left shows the 82 nF polypropylene capacitor used for the Greinacher circuit. The photograph on the right displays the diode BY505. One single diode is shown as well as three diodes soldered in series as they are used in the circuit.
Figure 8.3: CAD drawing of two Greinacher stages. Two stages of the ArDM Greinacher chain are schematically shown. Four capacitors are added in parallel here as in stages one to 170 out of 210 stages. One stage consists of the eight capacitors in the foreground plus the two diodes inbetween, the next stage consists of similar com- ponents in the background. From [27]. 72 High Voltage Supply
Figure 8.4: Greinacher circuit of the ArDM detector. The 210-stage Greinacher circuit (blue) attached to the top flange of the ArDM detector and connected to the field shaping rings is shown.
corresponds to an electric field strength of approximately 4 kV/cm.
8.3 Theoretical models for the voltage distribution on a Greinacher circuit
The total output voltage expected from a Greinacher chain is ideally equal to the value of the input peak-to-peak AC voltage multiplied by the number of stages. Under real conditions however, the output voltage is smaller. Losses are mainly due to effective capacitances of the diodes and several stray capacitances. Several theoretical approaches were proposed to describe the losses and to calculate the expected realistic output voltage. Not only the total voltage but also the voltage distribution over the stages is considered, since the output voltage does not linearly increase with the number of stages. Two of the models describing the voltage distribution are presented in the following sections. 8.3 Theoretical models for the voltage distribution on a Greinacher circuit 73
8.3.1 Model with peak-to-peak voltage attenuation
The first model described here involves as central point the calculation of the attenuation of the peak-to-peak voltage at each stage. It is therefore a recursive model. The parameters entering the attenuation are the effective capacitance of the diodes Cd and the effective threshold voltage of the diodes Ud. Both parameters are expected to vary with the applied voltage. Since the effects of shunt capacitances—due to the geometrical setup and the positioning of the circuit inside the detector—can not be separated from the diode effective capacitance, they are also included in the constant Cd. The procedure for the attenuation calculation is based on two steps. In a first step, capacitive effects are computed by substitung the diodes with capacitors of an effective capacitance Cd. The calculation focuses on one stage, whereas all upper stages are replaced by one effective capacitance. With this approach the capacitors of one stage can be added to the effective capacitance of the upper rest of the circuit, resulting in a new value for the effective capacitance of the upper rest plus the new stage. The result is a recursive formula for the effective capacitance replacing all upper stages
C C + C(Cd+CN ) d C+Cd+CN CN 1 = , (8.1) − C + C + C(Cd+CN) d C+Cd+CN where C is the nominal capacitance of the circuit capacitors (see scheme 8.1). The second step consists of computing the attenuation of the added voltage ∆U at each stage due to the effective capacitances given above. Without losses, ∆U is equal to the peak-to-peak input voltage at each stage, leading for the whole circuit to a multiplication of the input voltage by the number of stages as described above. With losses due to capacitive effects however, an attenuation of ∆U occurs. The reduced circuit with the effective capacitances CN and Cd as described above is a voltage devider, and the resulting formula for the voltage attenuation factor αN at stage N reads
C C α = . (8.2) N C(C +C ) C + Cd + CN · C + C + d N d C+Cd+CN In addition to the capacitive reduction, ∆U is also reduced due to the effective threshold voltage of the diodes Ud. Therefore,
∆UN = αN ∆UN 1 6 Ud. (8.3) · − − · The factor 6 is due to the fact that each stage contains six diodes. For the total output voltage UN at stage N we obtain
UN = UN 1 +∆UN . (8.4) −
The effective value of Ud was fitted to the measurements described below and turns out to be significantly smaller than the common value of 0.7 V for silicon diodes. This is presumably due to the fact that even at very low voltages a small current flows through the diodes, which is already capable of ramping up the Greinacher circuit over a relatively long time. Since the two parameters can not be fitted completely independently, a comparison with the second model described below and only containing Cd is useful in order to determine Cd. Only this first model takes into account the alternating part of the voltage and is therefore needed to describe the behaviour of capacitive connections (see section 8.4.2). 74 High Voltage Supply
8.3.2 Model with effective capacitance due to load resistance
The second calculation of the voltage distribution on a Greinacher or Cockcroft-Walton circuit described here is based on [42]. The joint effects of charge dissipation in an external load resistance RL and charge storage in the diode shunt capacitances are taken into account. The approach consists of distributing a potential external load resistance on all stages, i. e., R = RL/N, where RL is the total external load resistance, R the resistance per stage and N the number of stages. R is then replaced by two equivalent capacitances T/2R in parallel to the effective capacitances of the two diodes Cd at each stage. The dissipation is in this case determined by the parameter
T C γ = + d , γ 1, (8.5) r2RC C ≪ where T is the period of the voltage generator and C is the capacitance of the capacitors of the circuit. All given formulae are restricted to the case γ 1, i. e., C is significantly smaller than ≪ d C. For a relatively large number of stages (N > 4), the total output voltage V is given by
tanh(2γN) V = 2NE , (8.6) 2γN where E is the input voltage amplitude (E = 1/2 peak-to-peak voltage). In addition to the total output voltage, the model also describes the voltage ripple. Due to the alternating nature of the circuit charging the output voltage is not entirely constant over time, but shows a ripple with the same periodicity as the input voltage. The output voltage ripple δV according to [42] is given by
δV = E(1 sech(2γN)). (8.7) −
In order to determine how the voltage given by 8.6 is distributed over the circuit, the parameter
Eγk 1 exp( 2γk 1(k 1)) exp( 4γk 1N) exp(2γk 1(k 1)) Dk = 2− − − − − − − − − (8.8) γ 1 + exp( 4γk 1N) k − − is introduced. The additional output voltage δVk at each stage is then given by
δV = D D . (8.9) k k − k+1
The total output voltage Vk at each stage is then obtained by partially summing up δVk, i. e.,
k Vk = δVi. (8.10) Xi=1 8.3 Theoretical models for the voltage distribution on a Greinacher circuit 75
Figure 8.5: Voltage at different stages. Measured output voltages at differ- ent stages for 2E = 62.8 V. The line was calculated using the fitted model described in section 8.3.2.
8.3.3 Fit of Cd
As described above the parameter Cd describes capacitive effects of the diodes. By default, its value is unknown. A measurement of the Greinacher circuit output voltages at different stages was used to determine Cd by fitting the measured data with the model described in section 8.3.2 (see solid line in fig. 8.5). All other parameters of the model are known except for the effective resistance R of the circuit if no external load resistance is added. R can however be estimated by measuring the leak current through the diodes. Such a measurement was carried out—the measured value for the leak current is 200 pA, yielding for the resistance
R = U/I = Vpeak to peak/Ileakage = 0.314 TΩ. (8.11) − −
Assuming this value for R, Cd turns out to be
Cd = 2.323 pF, (8.12) which is significantly smaller than the capacitance of the charging and storage capacitors C (C = 4 82 nF or C = 2 82 nF, depending on the stage number). · ·
8.3.4 Comparison of the two models
The parameters Cd and Ud of the first model are estimated by comparing the two models and minimizing the differences in output voltages. Cd for the first model obtained with this approach turns out to be 76 High Voltage Supply
Figure 8.6: Difference of models. Calculated voltage difference of the first and second model versus the number of stages for an input peak- to-peak voltage of 62.8 V.
Cd = 2.334 pF, (8.13) thus, is approximately equal to the value given in equation 8.12. Ud obtained from the same fitting is 8.6 mV, which is significantly smaller than the usually assumed value of 0.7 V for silicon diodes. The two models agree very well for these values as is illustrated in fig. 8.6, where the calculated difference in output voltage of the two models is plotted for an input peak-to-peak voltage of 62.8 V.
8.4 Approaches for measuring the Greinacher circuit voltage in liquid argon
Since the connection of a common voltmeter to the Greinacher output would immediately cause a discharge of the circuit, alternative methods for measuring the output voltage need to be considered. Two possible approaches based on resistive and capacitive couplings to the circuit are presented in the following two sections.
8.4.1 Measurement with resistance
The behaviour of the circuit with a load resistance is described by the model outlined in section 8.3.2. Any finite resistance allows for a current to flow through it and thereby facilitates the discharge of the circuit. However, the loss of voltage due to the finite load resistance is described by the model of section 8.3.2, such that the voltage as it would be without external load (i. e., with an infinite load resistance) can be extrapolated. By measuring the current through the added resistor the total voltage at the connected point of the circuit can be determined. 8.4 Approaches for measuring the Greinacher circuit voltage in liquid argon 77
Figure 8.7: Setup with resistive and capacitive couplings. A possible setup with three resistors (left) or three capacitors (right) connected to different field shaping rings is displayed [27]. The capacitances C2 are needed for multiplication of the signal.
Resistance (TΩ) Voltage (kV), 60 V input 66 9.5 5 9.1 1 7.8 0.5 6.7 0.1 3.7 0.05 2.7
Table 8.1: Load resistances and resulting output voltages at the end of the Greinacher circuit, calculated with the model described in section 8.3.2.
It is considered to add at least one load resistance at the end of the circuit, or—in order to si- multaneously measure several points—e. g. three resistances to be connected to the 210th, 140th and 70th stage as shown in the left drawing of fig. 8.7.
The voltage attenuation for the case of one resistance connected to the 210th stage is illustrated in fig. 8.8 for different values of RL. RL 66 T Ω corresponds to the setup without external th≃ load. The values for RL and V at the 210 stage are also summarized in table 8.1 and in fig. 8.9. Fig. 8.9 shows that the V R curve saturates at approximately 1014 Ω. − L In the case of three added resistors the voltage attenuation is illustrated in fig. 8.10. No remark- able behaviour is observed at the 140th and 70th stage where a resistor is connected. 78 High Voltage Supply
Figure 8.8: Calculated voltage attenuation with one load resistance RL. Voltage attenuation for different values of the load resistance RL. The uppermost line R∗ corresponds to the internal resis- tance of the circuit without external load resistance.
Figure 8.9: Calculated ouput voltage versus load resistance. Voltage at- tenuation as a function of the load resistance RL. The curve saturates at approximately 1014 Ω. 8.4 Approaches for measuring the Greinacher circuit voltage in liquid argon 79
Figure 8.10: Three resistors. Voltage attenuation of a setup with three load resistors connected to stages 70, 140 and 210. The red points are the measurements of fig. 8.5.
8.4.2 Measurement with capacitance
If capacitive couplings instead of load resistors are added to the circuit the amplitude of the alternating part of the voltage δVk is measured instead of the total output voltage. Therefore, the first theoretical model outlined in section 8.3.1 is needed to theoretically describe this setup. The schematic setup of a Greinacher circuit with capacitive couplings Cx is illustrated in the right drawing of fig. 8.7. Fig. 8.12 illustrates the drop in δVk with increasing number of stages. The second capacitance C2 in the figure is needed for the multiplication of the signal before its readout. A proposal from [27] for the geometric shape of such a capacitive coupling is drawn in fig. 8.11, where a sphere with a diameter of 5 mm at a distance of 60 mm provides the capacitive coupling to the Greinacher circuit. The capacitance of this setup is of the order of 0.1 pF. The calibration of such a capacitance is carried out by placing it at the final position and comparing its output with the actual voltage measured with a field mill. Due to the field mill properties this calibration can only be undertaken in vacuum. When changing the medium, e. g., from vacuum to liquid argon, the change of the capacitance is governed by the dielectric constant ǫ of the involved medium.
8.4.3 Comparison of resistive and capacitive couplings
It remains to be tested and decided which of the above described couplings is more adequate for measuring and monitoring the voltage of the ArDM detector during data taking periods. Some advantages and disadvantages of the above described measurement methods are summarized here:
A high R is needed in order to avoid a fast discharge of the circuit. However, a high R • L L corresponds to a very low current which is difficult to measure precisely. 80 High Voltage Supply
Figure 8.11: Capacitive coupling with sphere. Setup with capacitive cou- pling to the Greinacher circuit via a sphere [27].
Figure 8.12: Voltage amplitude attenuation. Amplitude (peak-to-peak) of the alternating part at different stages given by the model de- scribed in section 8.3.1. 8.5 Measurements of the Greinacher output 81
Due to voltage ripple effects on the cathode, it might be necessary to switch off the circuit • for data taking. In this case the resistors facilitate the discharge of the circuit and therefore limitate the data taking period.
The coupling capacitance needs to be small and is therefore challenging to construct as • well as to calibrate.
8.5 Measurements of the Greinacher output
8.5.1 Voltage measurement with field mills
For the tests of the Greinacher circuit described here two different models of field mills were used for measuring the output voltage. Due to problems with operating field mills in liquid argon and the relatively large space they require, the monitoring of the voltage during ArDM data taking periods will not be done with field mills. One of the two methods described above will presumably be applied instead. A photograph of the two field mills used here is shown in fig. 8.13. The principle of a field mill consists of measuring the electric field between two metal plates with a fixed distance. The voltage to be measured is applied on the upper plate, whereas the lower plate is at ground. The lower plate is partially covered by a rotating propeller which periodically shields and uncovers regions sensitive to the electric field. The periodically rising and falling signal from the sensitive regions, which is proportional to the electric field between the plates is converted into a DC voltage measurement. A standard voltmeter cannot be used since its connection would cause a fast discharge of the circuit. A more detailed description of the field mill principle is given e. g. in [40].
8.5.2 Tests in air and nitrogen
A measurement of the voltage output at different stages of the ArDM 210-stage Greinacher circuit has been taken by using a field mill as described in section 8.13. The result of the measurement is plotted in fig. 8.5 (red dots), and listed in table 8.2. The input peak-to-peak voltage for this measurement was 62.8 V, and the total output voltage reached 9.56 kV. As expected by the theoretical models described above, a loss of output voltage compared with the ideal behaviour of the circuit is seen. Compared with the ideal case in which the input peak- to-peak value is multiplied by the number of stages a significant loss of 28% is observed. The loss is presumably due to capacitive effects of the diodes and diode leak currents. These effects are expected to become less significant at lower temperature and with higher input voltage. Furthermore, the voltage is not linearly distributed over the stages. It was attempted to increase the input voltage in order to check if the behaviour of the circuit scales linearly with the input voltage. However, the total reachable voltage in air is limited by discharges. After reaching the limit in air at approximately 70 V input peak-to-peak voltage, it was tried to flush the dewar with dry nitrogen in order to avoid discharges due to high humidity in air. The improvement was not substantial, the total output voltage does not reach stable values above 13–15 kV in air or gaseous nitrogen. 82 High Voltage Supply
Figure 8.13: Field mills used for measuring the Greinacher voltage output. Two field mill models with different motors were used for mea- suring the output voltage of the Greinacher chain.
Stage no. Output voltage (kV, 9.56 kV total) 11 0.647 31 1.78 41 2.29 56 3.055 64 3.466 71 3.763 78 4.188 120 5.661 141 6.879 210 9.555
Table 8.2: Voltage output in air of the Greinacher circuit at different stages. 8.6 Characterization of the Greinacher circuit with a 10-stage model 83
Figure 8.14: 10-stage Greinacher circuit. A photograph of the small Greinacher circuit with 10 stages is shown. Here, the voltage readout is connected to the 7th stage.
8.6 Characterization of the Greinacher circuit with a 10-stage model
Since the measurements of the 210-stage Greinacher circuit is rather complicated and time- consuming, a smaller 10-stage version was constructed in order to characterize and test the circuit under easier conditions. A photograph of the 10-stage version is displayed in fig. 8.14. The same capacitors and diodes as for the 210-stage circuit were used. Instead of four parallel capacitors however, only two pieces were soldered in parallel. The whole circuit is mounted in a three-dimensional setup onto a polyethylene plate similar to the 210-stage version. The polyethylene plate is mounted to the top flange of a 30 l dewar which is shown in fig. 8.15.
8.6.1 Measurements in air
For the measurement in air, a field mill (the model displayed on the right photograph in fig. 8.13) was attached to the lower end of the polyethylene plate such that it touches the bottom of the dewar when the flange is closed. The power for the motor as well as the output signal of the field mill were transferred to the outside via LEMO cable connections. A photograph of the setup is displayed in fig. 8.15. 84 High Voltage Supply
Figure 8.15: Setup for tests in air. Left: Photograph of the closed setup with the 30 liter dewar and the chimney with the turbopump on top. Right: photograph of the inner setup with the Greinacher circuit mounted to the top flange of the 30 liter dewar and the field mill attached below. 8.6 Characterization of the Greinacher circuit with a 10-stage model 85
10
9
8
7
6 Stage 10 (kV)
5 Stage 7
Greinacher 4 V Stage 4 3
2
1
0 0 100 200 300 400 500 600 700 800 900 1000 V (V) in
Figure 8.16: Output voltage versus input peak-to-peak voltage. The total output voltage is plotted versus the input peak-to-peak voltage for measurements at the 4th (lower line), 7th (middle line) and 10th (upper line) stage.
Results
The results of the measurements in air are summarized in fig. 8.16 and fig. 8.17. The output voltage of the Greinacher circuit was measured for different input voltages as well as at different stages, i. e., at the 4th, the 7th and the 10th stage. Fig. 8.16 displays the output voltage in dependence on the input voltage. The three lines correspond to the measurements at different stages as described in the figure caption. Fig. 8.17 displays the output voltage in dependence on the stage number. The various lines correspond to fixed input voltages, namely, the lowest line to approximately 50 V input peak-to-peak (a precise calibration of the power supply output is included in the results), the second lowest to 100 V peak-to-peak, the second upper line to 500 V input peak-to-peak, and the upper line to 1000 V peak-to-peak. In the ideal case, a multiplication of the input peak-to-peak voltage by ten is expected from a 10-stage circuit. It turns out that at comparably high input voltages, namely in the cases of 500 V and 1000 V input peak-to-peak voltage, the multiplication is almost perfect, whereas at lower voltages the output reaches a value below ten times the input. This is most likely explained by the fact that at low input voltage the threshold voltage of the diode reduces the output voltage more significantly, while the threshold voltage becomes negligible compared with the input voltage for high input voltages. 86 High Voltage Supply
10
9
8
7
6
(kV) 1000 V 5
Greinacher 4 V 500 V 3
2
100 V 1
50 V 0 0 1 2 3 4 5 6 7 8 9 10 stage
Figure 8.17: Output voltage versus number of stages. The total output volt- age is plotted versus the number of stages for different input peak-to-peak voltages. The lowest line corresponds to approx- imately 50 V input peak-to-peak, the second lowest to 100 V peak-to-peak, the second upper line to 500 V input peak-to- peak, and the upper line to 1000 V peak-to-peak. 8.6 Characterization of the Greinacher circuit with a 10-stage model 87
8.6.2 Measurements in vacuum
Before measurements in liquid argon—i. e., under conditions similar to the final experiment— can be taken, the dewar has to be pumped and a reasonable vacuum created (i. e., a vacuum 5 of the order of 10− mbar). The vacuum pumping is necessary in order to get rid of water and dirt which sticks to the dewar walls and the hardware parts inside the dewar. Furthermore, the setup has to be vacuum tight, so the inputs and outputs need to be transferred via dedicated vacuum tight feedthroughs. For the measurements described here, a glued SHV (secure high voltage) feedthrough with capton coated coaxial cables was used. The pumping of the dewar is 6 done by a forepump and a turbopump with magnetic bearings. A vacuum of about 10− mbar was reached within a reasonable time, i. e., within a few hours of pumping. The total output voltage for measurements in vacuum should not exceed 1 kV significantly, since x-rays are produced by accelerated electrons in vacuum at this voltage. Furthermore, discharges in vacuum are potentially very violent, since ionization electrons have a long mean free path and can be accelerated to high energies. The measurements in vacuum agreed very well with the curves in air displayed in fig. 8.16 and fig. 8.17.
8.6.3 Measurements in liquid argon
As a last and most important test measurements in liquid argon were performed in order to test the circuit under conditions similar to the ArDM experiment. Several preparations need to be made before cooling down the setup and filling the dewar with liquid argon at a temperature of 87 K. In order to keep the 30 l dewar at low temperature and minimize external heat input which can cause argon gas bubbles, an external liquid argon bath was added. The bath was kept inside a larger outside dewar which was first filled with liquid argon, and into which the 30 l dewar was inserted. As soon as the inside dewar was cooled by the bath it was filled with liquid argon as well. A PT10’0001 temperature sensor was attached above the Greinacher circuit in order to control the liquid argon level and make sure the circuit is entirely immersed. The SHV feedthrough described above which was used for measurements in vacuum and first tests in liquid argon was replaced by a dedicated high voltage feedthrough designed to reach up to 30 kV. A photograph of the whole setup with inner and outer dewar is shown in fig. 8.18. The second photograph of fig. 8.18 shows the inner setup with the Greinacher circuit attached to the high voltage feedthrough.
Results
The results of a measurement in liquid argon up to 1.6 kV input peak-to-peak voltage is displayed in fig. 8.19. A zoom of the measurements at low voltage is shown in fig. 8.20. The values for the output voltage obtained in liquid argon versus the input peak-to-peak voltage is displayed with a solid line and crosses. For comparison, the ouput in air for the same input voltages is shown with circles. Compared to the results in air, an almost constant parallel shift towards lower voltages of about 0.65 kV is visible. Furthermore, an input voltage threshold of about 40 V–50 V appears, which is visible in fig. 8.20. These two features are most likely due to the behaviour of the diodes which is strongly temperature-dependent. The parallel shift towards lower voltages as well as the threshold voltage is due to a higher effective threshold voltage of
1A platinum resistor with a resistance of 10 kΩ at 0o C 88 High Voltage Supply
Figure 8.18: Setup for measurements in liquid argon. The photograph on the left shows the whole setup. The outer dewar containing the liquid argon bath is visible as well as the chimney of the inner dewar with the turbo pump on top. The photograph on the right shows the circuit attached to the high voltage feedthrough. The PT10’000 at the end of a kapton cable at- tached to the white polyethylene plate is visible as well. 8.6 Characterization of the Greinacher circuit with a 10-stage model 89
25
20
15 (kV)
Greinacher 10 V
5
0 0 500 1000 1500 2000 2500 V (V) in
Figure 8.19: Measurements of the Greinacher circuit in liquid argon. The output voltage of the 10-stage Greinacher circuit was measured in liquid argon, i. e., at a temperature of 87 K (solid line with crosses) dependent on the input peak-to-peak voltage. For comparison the output of the measurement in air at the same input voltage is displayed as well (circles).
the diodes at low temperature. A more detailed description of this phenomenon is given in the next section. In addition to the difference in the reached output voltage the procedure of charging up the circuit looks different in liquid argon compared with air as well. The ripple on the current-sinusoidal which indicates the current drawn to charge up the circuit is larger and much more short-lived in liquid argon, whereas the ripple is smaller and smoother in time at room temperature. A picture of the voltage and current signals on the oscilloscope is displayed in fig. 8.21. The current ripple has a size of approximately 1.2 mA. It can be concluded that the behaviour of the circuit in liquid argon is significantly different from the one in air at room temperature. For the 210-stage circuit, the input voltage threshold is expected to be 21 times bigger than for the 10-stage circuit, i. e., approximately 840 V–1050 V. The highest stable voltage reached in liquid argon with the 10-stage circuit amounts to 24 kV. If the voltage is assumed to scale linearly with the number of stages, this corresponds to 504 kV for the 210-stage circuit. Thus, the tests described here show that the planned voltage of 500 kV during ArDM data taking is reachable.
Diode characteristics
The significant difference in behaviour at room temperature and at liquid argon temperature is due to the temperature dependence of the diode U-I-curve. The current ID through a diode in dependence on the forward voltage UD is given by
UD I (U , T )= I (T ) e nUT (T ) 1 , (8.14) D D S − 90 High Voltage Supply
1.5
1 (kV) Greinacher V 0.5
0 0 20 40 60 80 100 120 140 160 180 200 V (V) in
Figure 8.20: Low voltage measurements of the Greinacher circuit in liquid argon. The output voltage of the 10-stage Greinacher circuit was measured in liquid argon, i. e., at a temperature of 87 K (solid line with crosses) dependent on the input peak-to-peak voltage. This plot displays a zoom of the results for low input voltage. A smoothed-out voltage threshold of approximately 40 V–50 V input is visible. For comparison the output of the measurement in air at the same input voltage is displayed as well (circles). 8.6 Characterization of the Greinacher circuit with a 10-stage model 91
Figure 8.21: Current and voltage signals. The current and voltage signals during a period of charging up the 10-stage Greinacher circuit in liquid argon is displayed. The current is the pink signal whereas the voltage is the yellow line. A large ripple on the current signal can be seen indicating that the circuit draws current during the charging up. The scales of the signals are 10 V/kV for the voltage and 0.5 V/mA for the current. 92 High Voltage Supply
10
9
8
7
6
5 I (A) 4
3 Room temperature 2 Liquid argon 1 temperature
0 0.5 0.55 0.6 0.65 0.7 0.75 0.8 U (V)
Figure 8.22: Generic diode U-I-curve. A typical diode U-I-curve at room temperature (solid line) and at liquid argon temperature (dashed line) is displayed. The precise shape depends on the parameters of the diode in question.
where n is the emission coefficient of the diode, IS(T ) is the temperature dependent saturation current and UT (T ) is given by
k T U (T )= · , (8.15) T q where q is the electron charge and k the Boltzmann constant. The curves given by equation 8.14 are displayed in fig. 8.22 for room temperature and liquid argon temperature. The curve at liquid argon temperature starts to significantly rise at a higher voltage value compared to the room temperature curve. This indicates that the effective threshold voltage is higher for lower temperatures. Such an effect explains the parallel shift towards lower output voltages as well as the offset voltage of approximately 50 V seen in the liquid argon measurement displayed in fig. 8.19. The threshold voltage of the diodes needs to be overcome before any output voltage above zero of the Greinacher circuit is possible. Furthermore, the slope of the curve in fig. 8.22 is significantly steeper for liquid argon. Due to this, larger variations of the output voltage are seen at liquid argon temperature. A small fluctuation in the power supply voltage causes a comparably strong variation in the diode current and therefore in the output voltage.
8.7 Connection to the field shaper rings
As can be understood from the theoretical models described in sections 8.3.1 and 8.3.2 and seen in the plot of fig. 8.5, the voltage distribution on the 210-stage Greinacher chain is not linear. In order to create a uniform electric field over the ArDM drift volume however, the voltage distribution on the field shaping rings has to be linear. In order to create a constant electric 8.7 Connection to the field shaper rings 93
field a constant voltage difference between the field shaper potentials is therefore required. This is achieved by connecting the field shaping rings to the appropriate stage of the Greinacher circuit, i. e., by dividing the total output voltage by the number of field shaping rings ∆V = V /n , and connecting the nth field shaper such that V n = n ∆V . The out field shapers field shaper · resulting connections according to the measurement in air displayed in fig. 8.5 are summarized in table 8.3. 94 High Voltage Supply
Field shaper no. Stage no. Voltage (9.56 kV total) 1 0 0 2 5 0.313 3 10 0.620 4 16 0.980 5 21 1.274 6 27 1.619 7 32 1.900 8 38 2.231 9 44 2.555 10 50 2.872 11 56 3.182 12 62 3.485 13 69 3.831 14 75 4.121 15 82 4.452 16 89 4.777 17 96 5.094 18 103 5.404 19 111 5.751 20 118 6.049 21 126 6.382 22 134 6.710 23 141 6.991 24 150 7.345 25 158 7.655 26 166 7.961 27 175 8.299 28 183 8.594 29 192 8.920 30 201 9.241 Cathode 210 9.559
Table 8.3: Connection of Greinacher chain stages to field shaping rings. An alternative application of the ArDM detector 9
This thesis was so far focused on the measurement of dark matter with the ArDM detector. Since liquid argon is known to be an efficient target for any rare event detection it is thinkable to use the capabilities of the ArDM detector for alternative measurements as well. In this chapter the possibility of measuring neutrinoless double beta (0νββ) decays with the ArDM detector is investigated. The theoretical basis for 0νββ decays is briefly outlined, candidate elements and the question how they could be added to the liquid argon volume are studied and the proposed application of the ArDM detector for 0νββ searches is outlined.
9.1 Search for 0νββ decay
During the last years a lot of efforts have been put into the search for neutrinoless double beta decay (0νββ). This nuclear decay mode is only possible if the neutrino is a Majorana particle and its measurement is thus able to reveal the Majorana nature of the neutrino. Furthermore, this decay mode is sensitive to the effective Majorana electron neutrino mass m . h νi Electrons from ββ decays interact with the shell electrons of the argon atoms, thereby depositing their energy in the liquid volume. The energy deposit causes emission of scintillation light and ionization charge which are measured by the detector with the same principles as wimps. The total deposited energy can be determined with a good resolution, which is important for distinguishing 0νββ events from the 2νββ background.
9.1.1 Neutrinoless double beta decay
The lifetime for neutrinoless double beta decay in the absence of right-handed currents is given by [43]
2 1 0ν mν 0ν 2 0ν 2 (T )− = G (E , Z) h i M (g /g ) M . (9.1) 1/2 0 m | f − A V GT | e 0ν 0ν 0ν G is the two-body phase-space factor including coupling constants, Mf and MGT are the Fermi and Gamow-Teller nuclear matrix elements, gA and gV are the axial-vector and vector relative weak coupling constants, and m is the effective Majorana electron neutrino mass. | h νi | For simplification it is common to define F = G0ν M 0ν (g /g )2M 0ν 2 or the normalized N | f − A V GT | parameter η = F 1013, where F stands for the average over all nuclear models. This h N i · h N i leads to
2 1 mν (T )− = F h i . (9.2) 1/2 N m e 96 An alternative application of the ArDM detector
The current best limit comes from the Heidelberg-Moscow experiment [44] for the germanium isotope 76Ge: T > 8 1024 years. 1/2 ·
9.1.2 Candidate elements
Table 9.1 lists some of the candidates for 0νββ decay, and indicates a few of their relevant properties. Qββ is the energy endpoint of the 2νββ spectrum and corresponds to the total energy expected from the two electrons emitted in a 0νββ decay. A high value of Qββ is advantageous in several aspects, since it leads to a strong signal well above a lot of typical background radiation energies. Therefore, only elements with relatively high Qββ of a few MeV are displayed in the table. The natural abundance directly determines the decay rate. For most elements it is possible to enrich the sample with the 0νββ decay candidate isotope, for some at rather high costs, depending on the technique. The 2νββ halflife determines the background rate caused by the 2νββ decay mode, the end region of which can enter the 0νββ peak especially 2νββ if the energy resolution of the detector is comparably low. A high value of T1/2 is therefore desirable in order to suppress this background rate. The parameter η describes the nuclear and phase space factors as defined in Section 9.1.1. A higher η corresponds to a higher decay rate.
Parent nuclide Qββ (MeV) Natural abundance % 2νββ halflife (years) η 150Nd 3.367 5.64 7.0 1018 57.0 · 130Te 2.528 33.8 7.9 1020 4.26 · 82Se 2.995 8.73 1.08 1020 1.70 · 100Mo 3.034 9.63 7.8 1018 5.0 · 76Ge 2.039 7.44 1.0 1021 0.73 · 124Sn 2.288 5.64 unknown, limit 2.2 1018 ? · 136Xe 2.479 8.9 2.36 1021 0.28 · Table 9.1: Properties of some 0νββ candidates.
9.1.3 Measuring 0νββ in liquid argon
Liquid noble gases like argon or xenon have been shown to be suitable target materials not only for dark matter detection, but for any rare event searches [22, 23]. The concept of such a liquid noble gas detector consists of measuring the signals produced by the interaction of an incident particle with the target atoms similar to the case of wimp detection. Electrons from 0νββ or 2νββ decays interact with the shell electrons of the argon nucleus, thereby producing scintillation light and ionization charge in the noble liquids. Due to the low ionization potential and the high scintillation yield of argon or xenon, these noble liquids produce comparably strong signals and are therefore an efficient target. From an electron event of 2–3 MeV, about 100’000 photons and electrons are expected. Experiments using xenon instead of argon as target material for 0νββ searches are already running [45]. Argon does not contain an internal source for 0νββ as xenon (the 136Xe isotope). On the other hand, argon can be used as a multiple-source target by inserting 0νββ candidate isotopes from different elements, similar to e. g. in the multiple-source experiment NEMO [46]. A relative figure-of-merit for the comparison of different 0νββ experiments was proposed in [43]: 9.1 Search for 0νββ decay 97
aǫ M f = η . (9.3) W b δE r Here, η describes the nuclear and phase space factors and is defined as in Section 9.1.1, a is the isotopic abundance of the parent nuclide, ǫ is the detection efficiency, W the molecular weight of the source, M the mass of the source, b the background rate per keV, kg and year, and δE is the energy resolution of the detector. For a liquid argon experiment, the approximate values for these parameters are: ǫ=1 and δE=2– 4%, whereas the other parameters depend on the source, e. g. for 150Nd, η = 57.9, W = 150 g/mol and a=5.6–80% depending on the level of isotopic enrichment, the mass M of the source is scalable. The background rate b is difficult to estimate. At typical 0νββ decay energies, there is some background due to neutron capture as well as γs from the uranium and thorium decay chains, since detector components and surrounding facilities contain small amounts of uranium and thorium [47]. The background due to the internal radioactive isotope 39Ar [29] is of no 39Ar concern, since Qβ =565 keV which is low compared with all values of Qββ in table 9.1.
9.1.4 A multiple-source concept
The one ton ArDM detector is proposed for a test of the feasibility of measuring 0νββ decays in liquid argon. For this, the source for 0νββ decay needs to be added to the liquid argon volume. Since argon is not polar and very inert, other elements can be solved in liquid argon typically only at the level of a few ppm. It is therefore preferable to insert the 0νββ decay source in the form of small grains floating in the liquid argon target volume. The grains need to be small in diameter, i. e., a few µm, in order to avoid the partial absorption of the electron energies already inside the grains. The energy deposit inside the grain and in the liquid argon was simulated for the example of neodymium as source material, the result is plotted in fig. 9.1. Fig. 9.1 shows the deposited energy of both electrons from the ββ decay inside the liquid argon for a radius of the neodymium grain of 1 µm. The 0νββ peak (blue line) is clearly separated from the 2νββ spectrum (green line). Here, the ratio of the 2νββ and 0νββ rate is arbitrarily set to 103. The Nd average energy of the 0νββ distribution is 3.3625 MeV, to be compared with Qββ =3.367 MeV; i. e., the electrons loose on the average 4.5 keV inside the grain. A relatively big size of the grain provides more source mass, but has the disadvantage of a faster downwards movement of the grains due to gravity. The principle of the floating is comparable to the Millikan experiment, a description of which can be found in basic physics textbooks. Three forces act on the grains, namely gravity, buoyancy and the friction due to the liquid argon viscosity. Furthermore, the grain might be electrically polarized or catch a drift electron due to the moderate electronegativity of almost all candidate elements. In this case, the ArDM electric drift field which has a strength of 4 kV/cm also exerts a force on the grain. If the forces are at equilibrium
F F F = F , (9.4) Gravity − Buoyancy − Electric ± Friction holds, which leads to a resulting (downwards) speed of the grain
3 2r g(ρGrain ρArgon) qE vGrain = − , (9.5) 9rStokesη − 6πrStokesη where r is the radius of the grain, g is the earth gravitational acceleration, ρGrain and ρArgon are the densities of the grain and of liquid argon, respectively, and η is the viscosity of liquid argon. 98 An alternative application of the ArDM detector
5 x 10 2.5
2
1.5
No. of events 1
0.5
0 0 500 1000 1500 2000 2500 3000 3500 Deposited Energy (keV)
Figure 9.1: Deposited energy spectrum. The simulated energy deposited in liquid argon by double beta decay electrons from neodymium grains for a grain radius of 1 µm. The two curves show the 2νββ (green double beta spectrum) and the 0νββ spectrum (blue peak at the double beta spectrum endpoint of 3.3625 MeV). The 2νββ rate in this plot is arbitrarily assumed to be 103 times higher than the 0νββ rate. 9.1 Search for 0νββ decay 99
−3 10 Mo
Nd
Ge
−4 10 Downwards speed at equilibrium (m/s)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −6 Radius grain (m) x 10
Figure 9.2: Dependence of speed on radius. Speed of the grains in liquid argon for different radii. The lowest line is calculated for ger- manium, the middle line for neodymium and the upper line for molybdenum.
Furthermore, q is the charge of the grain and E is the electric field strength. In principle, rStokes, the Stokes radius, is different from the mass radius of the grain. It is given by
k T r = B , (9.6) Stokes 6πηD
where T is the temperature, kB denotes the Boltzmann constant, η the viscosity and D the frictional coefficient. Since D is not known for the considered elements moving in liquid argon, it is assumed for these calculations that the mass radius and the Stokes radius are equal. The resulting speed is of the order of 10 µm/s for a grain radius of 1 µm, which is rather slow. The stationary case (i. e. speed zero) is reached below r = 1 µm for the considered elements. Accordingly, for a grain radius of that range, the mixture of the grains with liquid argon is rather stable, thus a stirring or recirculation of the mixture is not often necessary. With a speed of 10 µm/s, the grains cross the fiducial volume of the detector in about 33 hours. If the radius is increased, the speed also increases, and a stirring of the mixture becomes necessary. For a radius of 50 µm, the speed is around 0.1 m/s, which means that the volume is crossed after twelve seconds. The speed of the grain for the elements germanium, neodymium and molybdenum depending on the grain radius is plotted in fig. 9.2. 100 An alternative application of the ArDM detector
Figure 9.3: Setup for measurement. Setup with liquid argon cell used for the measurements described in the text [48].
9.1.5 Measurement of the movement of µm size grains in liquid argon
In order to assess the feasibility of inserting 0νββ decay sources in the form of grains under re- alistic conditions, measurements of the movement of such grains in liquid argon were performed. The measurements presented here were carried out by [48]. The studied parameters were the diameter of the grains, the total density of the inserted powder and the effect of an external electric field. The setup used for the measurements described below containing a transparent liquid argon volume inserted in a liquid argon bath and a liquid nitrogen bath is shown in fig. 9.3. Powders of several substances and varying diameters were inserted from the top into the liquid argon volume. Their downwards movement was then observed by eye and with a camera through the quartz window as indicated in fig. 9.3. The substances used were copper oxide, vanadium, molybdenum and neodymium oxide of diameters ranging from 1 nm to 36 µm. As a second step, an electric field was added in order to assess a potential stabilization of the colloid by the electric field. The results of the downwards velocity measurements without external electric field are displayed in fig. 9.4. The theoretically calculated speeds given by equation 9.5 for the different substances are also plotted as dashed lines. The measurements follow equation 9.5 well for diameters be- tween 15 µm and 40 µm. For lower diameters, the velocity is higher than expected, indicating that it is difficult to create a colloid which is stable over a long time without external electric field.
The second parameter which was studied is the total amount of powder which can be added. If the density of the powder becomes high, it tends to undergo flocculation and thereby increases the effective diameter, resulting in a faster downwards movement and therefore faster loss of the added substance. The result is a very clear increase in the downwards velocity above approximately 150 ppm by mass (fig. 9.5). This effect is typical of unstabilized colloids of high concentration and is usually rectified by the addition of an emulsifier or steric stabilizer such as polyethylene oxide. However, due to the low temperatures involved and the immiscibility of liquid argon, no suitable agent exists that can mitigate the interparticle forces, and the only 9.1 Search for 0νββ decay 101
Figure 9.4: Downwards velocity. Measured downwards velocity of powders inserted in liquid argon. Several substances and diameters were considered (see labels in the figure) [48]. The curves correspond to the velocity calculated with equation 9.5.
recourse is the use of electric stabilization. In order to assess the stabilization efficiency of an external electric field, the field value within the liquid argon volume was increased for each powder until agitation due to the field strength resisted the downwards velocity. This was defined as the preservation of an isotropic suspension for over 6 hours in a 3 cm region. The results for the required electric field are shown in fig. 9.6 for a range of particle sizes and concentrations. Stabilization is achieved at electric fields of a few kV/cm for grains up to 4 µm, whereas the field needs to be significangly stronger to stabilize powders of larger sizes. Since the projected electric field of the ArDM detector is 4 kV/cm, it is suitable to stabilize powders up to about 3 µm of diameter. For larger diameters, other means of stabilization like stirring the colloid become necessary.
9.1.6 Scintillation light attenuation
The presence of grains inside the liquid argon fiducial volume affects the light readout insofar that a certain light attenuation is caused by the grains. In order to estimate this effect, a thin target model is applied. In this case, the attenuation length λ is estimated by
1 λ = , (9.7) σn where n = NGrains/V is the number density of the grains, i. e., the number of grains divided by the detector volume V , and σ is the geometrical cross section given by σ = πr2. By taking the geometrical cross section it is intrinsically assumed that a photon is absorbed when it hits a grain. This is the most pessimistic case since a partial reflection is thinkable, at least for the metallic sources. An attenuation length of at least two meters is desirable, since the typical 102 An alternative application of the ArDM detector
Figure 9.5: Concentration dependence. Measured downwards velocity ver- sus powder concentration in liquid argon [48].
Figure 9.6: Electric field dependence. Electric field required for a stable isotropic suspension of the powder inserted into liquid argon. The required field value is displayed for several grain sizes and concentrations [48]. 9.1 Search for 0νββ decay 103 distance travelled by the photons inside the ArDM detector geometry is about one meter. A certain photon loss is not dramatic, since an event of 2–3 MeV produces a big amount of photons. Furthermore, the charge readout—which is almost unaffected by the grains—still facilitates a determination of the energy of the event.
9.1.7 Conclusion and Outlook
The possibility of using liquid argon as a target for 0νββ decay electrons has been investigated. It has been shown that the source could be inserted in the liquid in the form of small grains with a radius of about 1–2 µm. At that size, and with an external electric field, the grains would move only slowly in the liquid, i. e. the mixture is stable over several hours to one day. Due to the small radii considered, the mass of one grain is small, i. e. if neodymium is considered, 2.94 10 11 g for a radius of 1 µm or 2.94 10 8 g for a radius of 10 µm. Therefore, a large · − · − number of grains is required in order to get a reasonable mass of the source. As an example, for N = 5 1010 and r = 1 µm, the attenuation length is 3.8 m and the total mass is 1.5 g, G · again for neodymium. If the radius is increased to r = 50 µm, and N = 3 107, the attenuation G · length is 2.5 m and the total mass is 110 g. This scale is comparable with currently running experiments, e. g. NEMO [46] has a neodymium source mass of 36.5 g. Adding the source in the form of grains allows for a multiple-source usage of the detector. Dif- ferent candidates for 0νββ could be investigated one after another or even simultaneously. The volume of the currently constructed ArDM detector is too small to reach current experi- mental limits for 0νββ because of the limited amount of mass that can be added. However, it is capable of demonstrating the feasibility of this approach. The scalability of this technique makes it a conceivable alternative to other multiple-source experiments like NEMO.
Part III
Background studies for ArDM Background radiation overview 10
Background assessment and rejection is a crucial task for any dark matter experiment. Since the wimp interaction with ordinary matter is a rare event, generally very low interaction rates are expected. Recent measurements of dark matter direct detection experiments limit the wimp- 6 nucleon cross section in the supersymmetric framework to values below 10− pb. A cross section of this size would lead to approximately 100 wimp events per day inside the ArDM detector, whereas a cross section of two orders of magnitude less proportionally reduces this event rate to one event per day and per ton of liquid argon. The remaining small number of events needs to be distinguished from a large sea of background radiation. There are two different classes of background radiation, namely electron- and γ-like particles, and neutrons. The former can be rather well distinguished from the wimp signal, since the relative amount of charge and light as well as the scintillation light pulse shape are different, as described in chapter 6. The major contributions to this class of background radiation are due to two sources, namely
Beta decay of the internal radioactive 39Ar isotope with emission of an electron • γs from the uranium and thorium decay chains •
The radioactive elements uranium and thorium are contained in most materials which consti- tute and surround the ArDM detector. The amount of the uranium and thorium contamination typically lies in the range of ppb (parts per billion of mass). Of major importance is the con- tamination of the detector components, since their radiation cannot be shielded. Furthermore, significant radiation is to be expected from the rock surrounding the underground laboratory in which the experiment is located, as well as from the concrete layer covering the walls of the laboratory. The second class of background radiations contains the neutrons. Neutrons are a worrisome background source since their interaction with liquid argon cannot be distinguished from wimp interactions. Neutrons arise from three different production mechanisms, namely
The uranium and thorium decay chains contain α decays which can entail (α,n) reactions • Uranium and thorium can undergo spontaneous fission, which typically includes the emis- • sion of two neutrons
Muons interact with material like rock, concrete layers and detector components. When • interacting with nuclei, muons produce neutrons up to very high energies which are called muon-induced neutrons 107
Figure 10.1: Vertical muon intensity versus depth. One km water equivalent corresponds to 105 g/cm2 of standard rock. From [49].
Above ground a large amount of background radiation is expected from cosmic muons. At sea level, the rate of muon raditation is 1 µ per minute per cm2 above 1 GeV. It is therefore essential for every dark matter experiment to be located underground. A rock overburden shields the detector from cosmic muon radiation, which decreases significantly with the thickness of the rock overburden. The muon flux dependent on the depth underground is displayed in fig. 10.1. The rock overburden is commonly measured in m. w. e., which stands for meters of water equivalent. In order to calculate the actual depth in meters, this number needs to be scaled with the rock density, which typically is of the order of 2.6 g/cm3. For dark matter experiments 8 aiming at sensitivites of the order of 10− pb, a depth of 2–3 km water equivalent is reasonable. Some laboratories at this depth in Europe are for example the Gran Sasso Laboratory in Italy, the Boulby Mine in United Kingdom or the Canfranc Laboratory in Spain, where the ArDM experiment will probably be positioned. Gamma and 39Ar electron background 11
After a summary of the types and origins of background radiation was given in the overview, this chapter focuses on the class of γ and electron radiation. As outlined in chapter 6, the relative amount of scintillation light and ionization charge produced by this type of events differs from the one due to wimp and neutron radiation. The two main background sources producing γ and electron radiation are presented, namely γs due to uranium and thorium contamination and electrons from the decay of 39Ar. The origin of the radiation is presented as well as its interaction characteristics in the ArDM detector.
11.1 Gammas from radioactivity in detector components
For the materials of detector components and surrounding facilities in the ArDM experiment, uranium and thorium contaminations cause the most significant backgrounds. These two natu- rally radioactive elements are contained in small amounts in almost all materials. Their decay chains include α, β and γ decays of varying energy. The α, β and γ count rates are given in tru per 1 ppb of source1 due to the entire uranium and thorium decay chains are listed in table 11.1 (from [50]).
Source Parent decays α β γ with α γ with β other γ U 1110 8880 6600 155 2300 0.1 Th 351 2100 1400 28.5 901 0
Table 11.1: Uranium and thorium decay chain count rates in tru per 1 ppb of source.
In order to calculate the number of γs expected to interfere with the detector region, the detector materials, their mass and their contaminations in ppb of mass need to be known. For the case of the ArDM detector these quantities are listed for the most relevant detector components in the following tables:
The γ count rates are summarized in table 11.1 • The contaminations are listed in table 11.2 • The masses of the detector components are given in table 11.3 • 11 tru = 1 total rate unit = 1 decay per day per kg 11.1 Gammas from radioactivity in detector components 109
Material ppb U ppb Th Glass of Vetronite 1000 1000 Vespel <2 <2 Stainless Steel 304L 0.6 0.7 Borosilicate glass 1000 1000 Standard PMT 400 400 (metal, glass, bialkali) Low bg. PMT 30 30 Polyethylene 20 20
Table 11.2: Uranium and thorium contaminations of materials.
Component Mass (kg) LEM Vetronite 2 (glass fibres) + 2 (epoxy resin) LEM low bg. 4 Dewar 1000 PMT first version 2.4 (80 tubes) PMT low bg. 9.8 (14 tubes) Support plate PMT (Vetronite) 2.9 Pillars 13 (8 Pillars) or 9.75 (6 pillars)
Table 11.3: Masses of detector components.
The detector components considered here are:
The dewar, made of stainless steel of the type 304L • The LEM plates, made of Vetronite in the standard version, and Vespel in the low back- • ground version
The photomultiplier tubes, partially made of borosilicate glass in the standard version, • and low background glass in the low background version
The pillars, made of polyethylene •
These are the detector parts with the highest masses and/or the highest contaminations with uranium and thorium. Metal parts with low mass like field shaping rings, cathode and PMT protection grid as well as low-mass polyethylene parts do not contribute significantly to the γ background. The contamination levels can vary significantly from sample to sample, even for the same ma- terial. The numbers indicated in table 11.2 are estimations based on measurements published in [50]. In general, materials consisting of minerals like sand or glass contain high levels of uranium and thorium, whereas metals and alloys typically have a contamination of a factor one hundred less. For some products like e. g. the photomultipler tubes, low background versions with reduced contaminations are available. For the case of the LEM plates, the originally used material Vetronite is replacable by plastics containing no glass parts like PEEK or Vespel. 110 Gamma and 39Ar electron background
Putting mass, contamination levels and emission rates together, the resulting numbers of emit- ted γ per year (second column) and per second (third column) for the four considered detector components are summarized in table 11.4. The most important contributions in the case of the use of standard materials come from the photomultiplier tubes and the LEM plates. If these two components are replaced by low background materials, the radiation rate decreases significantly and falls below the calculated rate for the stainless steel dewar. It is therefore crucial to use low background materials as far as possible for all detector compo- nents. Component γs per year γs per second Dewar 7.75 108 24.6 · Pillars 3.21 108 10.2 · LEM Vetronite 2.47 109 78.35 · LEM low bg. <2.47 107 <0.784 · PMT first version 2.98 109 94.41 · PMT low bg. 3.48 108 11.01 · Table 11.4: γ emission numbers.
11.1.1 Gamma interactions in the detector
The impact on the detector performance caused by γ background radiation does not only depend on the contamination level, but also on the energy of the γs. Fig. 11.1 displays the 20 most frequent γ energies for uranium and thorium and their probabilities normalized to one parent decay. γs at moderate energies below 1 MeV travel only short distances within liquid argon, and are therefore shielded by the outer part of the liquid argon volume. Higher energy γs however are able to penetrate more than 20 cm of liquid argon. The simulated average attenuation length in liquid argon for all γs from the decay chains is 11 cm.
Relevant interactions
The three relevant interactions of γs in liquid argon are:
Photoelectric effect • Compton scattering • Electron-positron pair production • Low energy γs usually produce an electron via the photoelectric effect. Medium energy γs most likely undergo several Compton scatters before they produce an electron via photoelectric effect as well. Electron-positron pair production occurs at comparably high γ energies, and is less relevant to the γs of the uranium and thorium decay chain. The electron which results from the photoelectric interaction deposits its energy inside the liquid argon volume within a very short distance. As an example to indicate the typical energy ranges of the three above mentioned + interactions, fig. 11.2 shows the cross sections for Compton effect, photoelectric effect and e e− pair production dependent on the γ energy for γs in a sample of carbon. 11.1 Gammas from radioactivity in detector components 111
0.5
0.4
0.3
0.2 Probability
0.1
0 0 500 1000 1500 2000 2500 3000 Gamma energy (keV)
Figure 11.1: Uranium and thorium γs. Energies of the γs from uranium and thorium decay chains are shown. The height of the bars corresponds to their probability.
Figure 11.2: Cross sections of γ processes. The cross sections for several γ interactions in carbon dependent on the γ energy are displayed. σp.e. denotes the photoelectric effect, σCompton the Compton scattering, σRayleigh the Rayleigh scattering, κnuc the pair con- version in the nuclear field and κe the pair conversion in the electronic field. From [49]. 112 Gamma and 39Ar electron background
Gamma interaction points in the detector
The interaction of background γs from uranium and thorium with the liquid argon volume was simulated with the Geant4 package [39]. As an example, fig. 11.3 displays the interaction points of γs emitted by the pillars. The pillars themselves are identifiable as the eight white circles. The interaction points are visibly concentrated around the pillars, revealing that the majority of the γs stop within a short range of a few centimeters. The same is shown for γs from the dewar in fig. 11.4. The vicinity of γ interactions to the emitting point is also illustrated by fig. 11.5, in which the radial dependence of γ interactions for dewar γs is shown. The number of interactions is normalized with 1/R to the area of infinitesimal disks between R and R + dR. The num- ber of events decreases substantially with the distance to the dewar wall which is located at R=50 cm. However, there are still some events at R=0 cm—which corresponds to the center of the detector—indicating that a few γs travel quite far before depositing their entire energy.
Interaction rates
The rate of γ interactions inside the liquid argon volume of the ArDM detector was simulated with Geant4 as well. Table 11.5 summarizes the number of γs per second emitted by the de- tector components and the percentage entering the active volume. Geometrical effects influence the latter significantly. The distance between the dewar walls and the active volume is 11.5 cm, reducing the solid angle under which the emitted γ sees the fiducial volume, and therefore the rate of entering γs. The same holds for the PMTs, which are located at a distance of approxi- mately 10 cm to the fiducial volume. Furthermore, the PMTs have a considerable height, such that a majority of γs is emitted at a distance of about 10 cm–20 cm to the active volume. On the other hand, the LEM and the pillars are located at the border of the active volume, which results in a higher percentage of γs being able to enter the active volume.
Component γs per second % in active vol. Dewar 24.6 8.7 Pillars 10.2 23.0 LEM Vetronite 78.35 39.9 LEM low bg. <0.784 39.9 PMT first version 94.41 7.5 PMT low bg. 11.01 7.5
Table 11.5: Gammas emitted per second and the percentage which enters the active volume.
WIMP-like γ interaction rates
Table 11.6 summarizes the frequency of γ events with a total energy deposit comparable to the typical wimp energy deposit. The wimp energy deposit in most cases amounts to values below 100 keV, and is further reduced by nuclear recoil quenching effects as described in chapter 6. The lower energy threshold for γ energy deposits is expected to be of the order of 8 keV, which corresponds to a 30 keV threshold for wimp events. As a conservative range for the γ energy 11.1 Gammas from radioactivity in detector components 113
Figure 11.3: γ interaction points for γs from pillars. The points of γ inter- actions, namely Compton scattering and photoelectric electron production, are plotted in the detector cross section. The eight white circles indicate the position of the pillars. Right inside the pillars the field shaping rings are visible. In the upper right, the cross section of the Greinacher circuit is indicated as a rectangle. 114 Gamma and 39Ar electron background
Figure 11.4: γ interaction points for γs from the dewar. The points of γ in- teractions, namely Compton scattering and photoelectric elec- tron production, are plotted in the detector cross section. The eight white circles indicate the position of the pillars. Right in- side the pillars the field shaping rings are visible. In the upper right, the cross section of the Greinacher circuit is indicated as a rectangle. 11.1 Gammas from radioactivity in detector components 115
120
100
80
60
40 No. of events in R−bin ⋅ 1/R 20
0 0 5 10 15 20 25 30 35 40 45 50 Radius (cm)
Figure 11.5: Radial dependence of dewar γ interactions. The number of γ interactions for γs emitted by the dewar (at R=50 cm) nor- malized with 1/R is displayed. The number strongly decreases with increasing distance to the dewar wall.
deposits counted as wimp-like, 5 keV and 100 keV was chosen. The percentage of events with such energy deposits compared with the number of emitted γ is low, i. e. a few percent, resulting in absolute rates below 10 Hz (see third column in table 11.6). This background rate is small compared with the internal 39Ar background rate of 1 kHz (see section 11.3).
Component % in fiduc. in [5,100] keV Events in [5,100] keV per s Dewar 1.1 0.28 Pillars 3.1 0.32 LEM Vetronite 3.9 3.08 LEM low bg. 3.9 <0.031 PMT first version 1.1 1.07 PMT low bg. 1.1 0.13
Table 11.6: Percentage and absolute numbers of γs inside the WIMP-like energy deposit range (5 keV–100 keV).
Gamma energy deposit spectra
The simulated spectrum of total deposited energy (i. e., the energy deposited by γs and their daughter electrons due to photoelectric effect and Compton scatter) is displayed in fig. 11.6. It roughly corresponds to an exponentially shaped spectrum. Additionally, the original γ lines from uranium and thorium (see fig. 11.1) are clearly recognizable in the spectrum, reflecting 116 Gamma and 39Ar electron background
Dewar Pillars 200 800
150 600
100 400 No. of events No. of events 50 200
0 0 0 1000 2000 3000 0 1000 2000 3000 Deposited energy (keV) Deposited energy (keV)
PMTs LEM 250
200 1500
150 1000
100 No. of events No. of events 500 50
0 0 0 1000 2000 3000 0 1000 2000 3000 Deposited energy (keV) Deposited energy (keV)
Figure 11.6: Deposited energy spectra. The total deposited energy by γs and their daughter electrons is displayed for γs from the four main detector components.
the γs which deposit their entire energy inside the active volume. The height of the lines with respect to the exponential distribution is bigger for the detector parts which are located close to the active volume, i. e. pillars and LEM, since γs from these components have a higher chance of only interacting inside the active volume, and not depositing any energy before entering it.
11.2 Expected gamma background above ground
As outlined in the background overview, the ArDM experiment will be positioned underground for wimp-search runs. However, first tests and datataking of the detector will take place above ground. It is evident that the background radiation above ground is far too strong to allow for wimp-searches. Such tests and first measurements are however useful to know the characteris- tics of the detector and calibrate its response. The experiment is currently located at CERN (Geneva, Switzerland). In order to assess the amount of γ background in the CERN laboratory, a measurement of γ rays in the keV to MeV range has been taken [51]. The γ radiation was thereby measured with a sodium iodide (NaI) scintillating crystal, which was calibrated with a 11.2 Expected gamma background above ground 117
160
140
120
100
80
No. of events 60
40
20
0 0 500 1000 1500 2000 2500 3000 3500 ADC counts
Figure 11.7: Measured γ energy spectrum. The measured spectrum of back- ground γs in the laboratory of the ArDM detector at CERN is displayed. A calibration of the crystal indicates a threshold of 580 ADC counts or 71.5 keV. One ADC count corresponds to 0.216 keV. The pedestal peak is visible at 249 ADC counts [51].
511 keV 22Na positron source. The measured γ spectrum is displayed in fig. 11.7. One ADC count corresponds to 0.216 keV, and the calibration of the readout reveals a pedestal at 249 ADC counts. The lower and upper energy thresholds are 71.5 keV and 780 keV, respectively. The total measured γ rate in the crystal above threshold was 305 events per second. Scaling with the surface area of the ArDM detector this corresponds to 46’613 events per second within the total ArDM detector volume. The four stainless steel walls of the detector have a thickness of 5 mm, 6 mm, 3 mm and 6 mm, i. e., 20 mm in total. These stainless steel layers decrease the amount of γs reaching the fiducial volume significantly. A Geant4 simulation of the interactions of these background γs within the fiducial volume reveals that 2% of the background γs interact and deposit energy within the liquid argon fiducial volume (the energy threshold was assumed to be 8 keV for γ interactions). This result corresponds to an event rate of approximately 1 kHz due to background γs in the CERN laboratory. A comparison with the internal 39Ar rate of 1 kHz shows that these two background sources are of comparable importance above ground. 118 Gamma and 39Ar electron background
11.3 39Ar electron background
A similar type of background radiation as described above is due to electrons emitted by the radioactive isotope 39Ar. Since this isotope is evenly distributed within the liquid argon volume, and the emitted beta electrons deposit their energy almost precisely at the position where the decay occured, the signals from 39Ar are uniformely distributed over the detector volume. This fact is a disadvantage for background rejection since the wimp signal is expected to be evenly distributed as well. On the other hand, this background with a precisely known rate could facilitate a detector calibration. The next three sections deal with the origin of 39Ar, the characteristics of its beta decay and a possible means to avoid 39Ar contamination.
11.3.1 Natural atmospheric argon
Argon is usually procured by liquefaction of air, a process which takes advantage of the different boiling points of the air components for their separation. Natural atmospheric argon consists of 99.6% 40Ar, 0.337% 36Ar, 0.063% 38Ar and a small amount of the radioactive isotope 39Ar. The concentration of 39Ar in atmospheric argon is (7.9 0.3) 10 16 g/g [29]. ± · − The production of 39Ar in the atmosphere is due to cosmic ray interactions with the stable and most abundant isotope 40Ar. The two most relevant production processes are the (n,2n) reaction
40Ar + n 39Ar + 2n (11.1) → with a production rate of 5 Mio. per day per ton of 40Ar at sea level, and the (γ,n) reaction
40Ar + γ 39Ar + n (11.2) → with a production rate of 70’000 per day per ton of 40Ar at sea level [52]. Since the neutron flux increases significantly with increasing altitude, process 11.1 occurs far more frequently at high altitudes. The major part of 39Ar isotopes is therefore produced at an altitude of approximately 10 km, where the neutron flux is most prominent. A detailed description of the neutron flux in the atmosphere at different altitudes is given in [53].
11.3.2 Decay of 39Ar
39Ar decays via β-disintegration into 39K:
39 39 Ar K+ e− +ν ¯ . (11.3) → e The halflife of 39Ar is 269 years, the endpoint of the beta spectrum is at Q=565 keV and the mean energy of the emitted beta electron is 218 keV. Fig. 11.8 displays the 39Ar beta energy spectrum. The decay rate due to the 39Ar quantity contained within the ArDM detector volume is of the order of 1 kHz, which is a considerable background radiation rate. Assuming one wimp event per day a rejection power of 108–109 is required to sufficiently reject this background rate. The rejection of interaction signals from the class of electron and γ events is facilitated by two means: the charge over light ratio discrimination and the scintillation light pulse shape discrimination. Details concerning electron and γ background rejection by these two approaches are given in 11.3 39Ar electron background 119
3000
2500
2000
1500 No. of events
1000
500
0 0 100 200 300 400 500 600 Electron energy (keV)
39 Figure 11.8: β− spectrum of Ar. The energy spectrum of the electrons from beta decay of 39Ar is displayed. The endpoint is at 565 keV and the average energy is 218 keV.
section 11.4.
11.3.3 Relevant electron interactions
The electron which is emitted in the decay of 39Ar deposits its energy in the liquid argon volume within a very short distance. Relevant interaction processes of electrons in liquid argon are
Electron (multiple) scattering. Charged particles typically scatter many times within a • very small volume. The resulting energy deposit and the change of the electron momentum is often approximated by multiple scattering models instead of computing every single scatter separately. Electron ionization. Within a material an electron deposits a certain part of its energy via • ionization. Electron bremsstrahlung. Another fraction of the electron energy is converted into brems- • strahlung. Photons are thereby emitted in the field of a nucleus of the material.
Due to the very short length of the electron tracks the signals from 39Ar decay electrons occur at the decay point. It is highly unlikely that a decay electron might leave the liquid argon volume and not leave any signal of the decay. Therefore, the precisely calculable rate and the well-known energy spectrum facilitate a detector calibration with 39Ar events. It remains to be assessed whether the background rejection power due to light over charge ratio and scintillation light pulse shape discrimination is high enough. If this is not the case, alternative solutions have to be considered. The possibility of using argon with a smaller 39Ar concentration is studied in the following section. 120 Gamma and 39Ar electron background
11.3.4 39Ar depleted argon
Instead of relying on background rejection to deal with the 39Ar signal it is also thinkable to use 39Ar-depleted argon as detector target material. Such argon with a smaller fraction of 39Ar and a larger fraction of 40Ar instead could probably be obtained from underground well gases. If gases that were once part of the atmosphere are enclosed underground, the radioactive isotopes contained therein might disappear over time due to their decay. Their number however only decreases if there is no production process which substitutes the decaying isotopes. Such a production process could be induced by radiation present underground. It is currently under study at several locations if argon obtained from underground sources is significantly more pure than atmospheric argon [54]. If 39Ar depleted argon could be procured one should be careful to avoid an activation of this argon above ground. As soon as the sample is exposed to cosmic rays 39Ar is reproduced via the processes stated in section 11.3.1. The following estimation however shows that pure 40Ar can be kept at sea level for a reasonably long time. The evolution of the number of 39Ar nuclei produced by cosmic ray interactions is governed by the 39Ar production constant α 5 Mio./day/ton and ≃ its decay constant λ = 7.06 10 6/day, and is described by the following differential equation · − dN = Production Decay = α λN(t). (11.4) dt − − The solution for the boundary condition N(0)=0, assuming no 39Ar contamination at time zero reads
α λt N(t)= (1 e− ). (11.5) λ − E. g., after two years of exposure 0.03% of the natural 39Ar concentration is reached. A significant amount of 39Ar is therefore only produced after a very long exposure. Since the ArDM detector is planned to be moved underground for dark matter measurements within smaller time scales the storage of 39Ar depleted argon should not be an issue. 11.4 Gamma and electron background rejection 121
11.4 Gamma and electron background rejection
This last section outlines the two principal approaches for rejecting the above described γ and electron background radiations, namely the light over charge ratio and the scintillation light pulse shape discrimination.
11.4.1 Light over charge ratio
As described in chapter 6 there are two classes of interactions with liquid argon. Electrons and γs interact with the shell electrons of the argon atoms, whereas neutrons and wimps interact with the argon nucleus. These different impacts lead to different quenching factors and different ionization densities. Due to a higher ionization density in the case of interactions with the nucleus, a smaller number of ionization electrons can be drifted away from the interaction region by an external electric drift field. Therefore, substantially less electrons are seen from neutron and wimp interactions compared with the case of electron and γ interactions. The number of scintillation photons is of the same order of magnitude for the two event classes if the transferred energy is the same. The characteristic numbers of scintillation photons and ionization electrons versus transferred energy as calculated with the Lindhard theory [30] are displayed in fig. 11.9. A more detailed description is given in chapter 6. Fluctuations of these numbers due to statistical effects as well as preliminary hardware properties are taken into account in fig. 11.10, where the ADC signals of LEM and PMTs are displayed. The upper green band corresponds to simulated 39Ar events, the lower blue band to simulated wimp events according to the Lindhard theory. A detailed outline on how the ADC counts are obtained is given in chapter 6. The parameter which is usually used for discrimination of these two classes of events is the charge over light ratio. As described above, this ratio is expected to be significantly smaller for neutron and wimp events compared with electron and γ events. The light over charge ratio is plotted in fig. 11.11 versus the PMT ADC signal for 39Ar and wimp events. The two bands visible in fig. 11.11 correspond to the same classes of events as the bands in fig. 11.10. The rejection power due to charge over light ratio discrimination has not been measured yet, but it is estimated to reach a value of the order of 108. In the case of argon, it can be combined with scintillation light pulse shape discrimination which is described in the next section.
11.4.2 Scintillation light pulse shape
The different ionization densities after neutron/wimp and electron/γ interactions described above do not only lead to different charge over light ratios, but also to a different popula- tion of the fast and slow component of the argon scintillation light as described in section 6.5. This different population provides for a further rejection possibility by determining the rela- tive amount of fast and slow scintillation light components (see fig. 6.3). However, a sufficient number of photoelectrons is necessary to recognize the population of fast and slow components with high enough statistical significance. Due to a low number of produced photoelectrons, the recognition becomes more difficult for low energies, namely below 30 keVr or 6 keVee. A rough estimate of the number of photoelectrons produced by an interaction with an energy transfer of 6 keVee based on the numbers given in table 7.1 and Wγ = 19.1 eV yields about 10–20 photo- electrons. Wγ is the energy need to produce an excited argon state with emission of a photon (see chapter 6). 122 Gamma and 39Ar electron background
3500
3000
2500
Electrons bg. 2000
1500 Photons bg.
Photons WIMP 1000 No. of electrons and photons
500
Electrons WIMP 0 0 10 20 30 40 50 60 70 80 90 100 Recoil energy (keV)
Figure 11.9: Light and charge versus energy for wimp/neutron and electron/γ events. The energy dependence of ionization charge and scintillation light production is displayed for wimp/neutron and electron/γ events. The upper dashed line is the number of electrons for electron/γ events, the upper solid line the number of photons for electron/γ events, the lower solid line is the num- ber of photons for neutron/wimp events and the lower dashed line the number of electrons for neutron/wimp events. 11.4 Gamma and electron background rejection 123
6 10
5 10
4 10
3 10 ADC LEM
2 10
1 10
0 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 4 ADC PMT x 10
Figure 11.10: Light versus charge for wimp and 39Ar events. The ADC counts from LEM and PMTs are plotted for wimp and 39Ar events. The upper band corresponds to 39Ar events, the lower band to wimp events. 124 Gamma and 39Ar electron background
6
4
2
0
−2 log(ADC LEM/ADC PMT) −4
−6
−8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 4 ADC PMT x 10
Figure 11.11: Charge over light ratio. The charge over light ratio versus ADC counts from PMTs are plotted for wimp and 39Ar events. The upper band corresponds to 39Ar events, the lower band to wimp events. Neutrons 12
After the last chapter has dealt with γ and electron background radiation, which is in principle rejectable (see section 11.4), this chapter describes the neutron background radiation, which belongs to the same class as wimp-events. Although the number of background γs and electrons by far exceeds the number of background neutrons, they are more worrisome since they entail irreducible contributions to the background. Neutron background is caused by two different processes, namely radioactivity of elements and muon interaction with materials. So-called muon-induced neutrons arise from muon interactions with materials. Highly energetic muons are able to penetrate even very large rock overburdens, interact near the detector and produce high energy neutrons. These may penetrate the shield- ing of the detector and are thereby moderated down to the MeV region. Shielding and detector components can also act as a target for muons, however the expected production rates are low. Muon-induced neutrons are not further investigated here. Studies on their production and in- teractions can be found elsewhere [55]. This chapter focuses on the neutron background caused by radioactivity. The number of ex- pected neutrons, their spectra and their interactions with the detector are described.
12.1 Radioactivity
The neutrons from radioactivity arise mainly from contaminations of detector materials or rock by the two radioactive elements uranium and thorium. The decay chain of 238U contains on the average eight α-decays with α energies of 3.5 MeV to 8 MeV1. The same holds for 232Th, its decay chain containing 6 α-decays with α energies of 3.5 MeV to 11 MeV2. Apart from α-decays, the uranium and thorium decay chains contain several β- and γ-decays. Detailed information on the α-energies and the decay chains can be found e. g. in [50]. The α energy lines with their probabilities per parent decay are shown in fig. 12.1.
12.1.1 (α,n) reactions
The process of neutron creation via (α,n) reaction is induced by α particles from the uranium and thorium decay chain. When crossing a material, such an α particle interacts with nuclei of the material with a certain probability. When an (α,n) reaction takes place, the nucleus absorbs the α particle, thereby changing its charge and nucleon number, and emits a neutron. An example is the reaction on beryllium
9Be + α 12C+ n or 9Be (α, n) 12C, (12.1) → 1Natural uranium consists of 99.275% 238U and 0.72% 235U. 2There is no other isotope in the natural composition of thorium. 126 Neutrons
0 10
−5 10 Probability
3 4 5 6 7 8 9 Uranium α energy (MeV)
0 10
−5 10 Probability
3 4 5 6 7 8 9 10 11 Thorium α energy (MeV)
Figure 12.1: Uranium and thorium alphas. Energies of the alphas from ura- nium and thorium decay chains are shown. The height of the bars corresponds to their probability per parent decay. 12.2 Neutrons from radioactivity in detector components 127
The (α,n) process typically produces neutrons with energies in the MeV range. The (α,n) cross section significantly depends on the material and on the α-energy. Typical neutron yields per α 8 5 particle are of the order of 10− to 10− [56]. The neutron yield in compound materials is the sum of the elemental yields, weighted by their contribution to the total stopping power [56]
S R Y = i Y , where Y = n σ (E)dx, i,c S i i i i c Z0 where Si and Sc denote the stopping powers of the element i and of the compound c, whereas Yi and Yi,c are the neutron yields of element i in pure material and in the compound. R is the range of the α partice and ni the number density of element i.
12.1.2 Spontaneous fission
Besides (α,n) reactions, neutrons can arise from spontaneous fission as well. Spontaneous fission is a process that occurs in heavy nuclei, which typically decay into two medium mass nuclei, thereby emitting several neutrons. The probability for spontaneous fission is negligible for thorium (T =1.4 1018 years [57]). For uranium, the branching ratio is 5.5 10 5% and the 1/2 · · − halflife due only to spontaneous fission is 8.3 1015 years [57]. The activity is given by λ N, · · where
log 2 λ = . T1/2
On the average, 2.01 neutrons are emitted per spontaneous fission. The relative size of neutron numbers generated via (α,n) reaction and via spontaneous fission is variable, since the former process strongly depends on the material in which the uranium and thorium contamination is encountered, whereas the latter process does not. For ArDM detector materials the number of neutrons arising from the (α,n) reaction and from spontaneous fission is typically of the same order of magnitude.
12.2 Neutrons from radioactivity in detector components
ArDM detector parts mainly consist of the following materials: stainless steel, Vetronite, polyethy- lene, borosilicate glass, ceramics and copper. In general, metallic materials contain much less uranium and thorium, i. e., typically a few ppb, whereas minerals and glasses are generally found to contain higher contamination levels of the order of a few hundred ppb. Contamination levels have been measured for several materials by different groups and do not always agree. For the simulations carried out to obtain the numbers stated here, the contaminations shown in table 11.2 and mainly taken from [50] were assumed. The numbers of emitted neutrons were computed based on the data from [56]. Furthermore, the emission numbers have been simulated with the code SOURCES4a—a neutron production and energy spectrum simulation code [55]—for cross-check. Apart from the contamination level the mass of the components—listed in table 11.3 also enters the calculation. The neutron emission numbers obtained with these two different approaches are summarized in table 12.1. It turns out that the biggest contribution to the neutron emission number is due to the pho- tomultiplier tubes and from the LEM plates, if standard materials are considered. For the low 128 Neutrons
Component n per year (Heaton) n per year (SOURCES) Dewar 494 266 Pillars 342 280 LEM Vetronite 12107 9422 LEM low bg. <40 - PMT first version 14590 10196 PMT low bg. 1400 -
Table 12.1: Total neutron emission numbers per year obtained with two dif- ferent approaches.
background versions there is still a big contribution from the PMTs, but the LEM neutrons decrease in number by more than two orders of magnitude. The total number of emitted neu- trons per year is of the order of 2’300 if low background materials are chosen. This number is to be compared with a wimp interaction rate of approximately 3’500 events per year at a 7 wimp-nucleon cross section of 10− pb. It is evidently essential to use low background materials for all detector parts if a reasonable wimp sensitivity is to be achieved.
12.2.1 Neutron spectra
The energy spectra of neutrons coming from uranium and thorium decay chains are the sum of two contributions, namely the one from spontaneous fission and the other from (α,n) reactions. The spontaneous fission spectrum is described by
dN √E exp( E/1.29) (12.2) dE ∝ − and is plotted in fig. 12.2. The spectrum of neutrons coming from (α,n) reactions is more involved, mainly because it depends on the material in which the decay takes place, since the (α,n) cross section is material- dependent. For the computation of the total resulting spectra in detector component materials, equation 12.2 was used for the spontaneous fission contribution, and the simulation program SOURCES4a for the (α,n) spectra [55]. The resulting spectra for stainless steel 304L, Vetronite, Borosilicate glass and polyethylene are shown in fig. 12.3.
12.3 Neutrons from radioactivity in rock and concrete
As outlined in the background overview, a dark matter experiment has to be located underground due to the cosmic muon background radiation. Like the detector component materials, the mi- nerals constituting the rock overburden in an underground laboratory contain small amounts of uranium and thorium, causing neutron radiation in the same way as in the detector components. The level of contamination strongly depends on the location and the elemental composition of the rock. Usually the contamination is of the order of a few hundred ppb uranium and thorium. In order to protect the experiment from the resulting neutron radiation, a shield consisting of hydrocarbon (CH2) will surround the detector. 12.3 Neutrons from radioactivity in rock and concrete 129
100
90
80
70
60
50
40 No. of events
30
20
10
0 0 1 2 3 4 5 6 Neutron energy (MeV)
Figure 12.2: Spontaneous fission neutron energy spectrum. The energy dis- tribution of the neutrons from uranium spontaneous fission is shown.
The next two sections deal with the contamination level to be expected in the Canfranc Un- derground Laboratory in Spain and with the neutron shield planned to surround the ArDM detector.
12.3.1 Setup and contamination of the underground laboratory
The studies described here have been carried out for the Canfranc Underground Laboratory. It is a cavern located in the Pyrenees near an old railway tunnel at a depth of 2450 m. w. e. (meters of water equivalent). The neutron emission of several samples of the rock has been measured, and the corresponding contaminations differ by more than a factor ten. Since the precise location of the experiment is not known, typical average values for the contamination and the neutron emission have been assumed: 900 ppb uranium and 1’800 ppb thorium for the contamination 4 n and 10− kg s for the neutron emission rate. A concrete layer· covers the walls of the cavern, which also affects the neutron radiation flux. On the one hand, the water contained in concrete shields the neutrons coming from the rock. On the other hand, the concrete layer emits neutrons itself. Data for the concrete used in the Canfranc Laboratory were not available. An estimation of the elemental composition of concrete was obtained from general information on the web, whereas the contamination was taken based on data measured in the SNOLAB underground laboratory: 500 ppb uranium and 500 ppb thorium. The neutron emission obtained with SOURCES4a is 2 10 5 n . · − kg s The elemental compositions of the rock and concrete layer which were assumed· for the investi- gations described here are summarized in fig. 12.4. 130 Neutrons
−12 −9 x 10 Stainless steel (Average energy: 1.688 MeV) x 10 Vetronite (Average energy: 2.740 MeV) 3 6
2.5 5
2 4
1.5 3
1 2
0.5 1 Neutron number (arbitrary units) Neutron number (arbitrary units)
0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Neutron energy (MeV) Neutron energy (MeV)
−9 −11 x 10 Borosilicate (Average energy: 2.584 MeV) x 10 Polyethylene (Average energy: 3.267 MeV) 6 1.6
1.4 5
1.2
4 1
3 0.8
0.6 2
0.4
1 Neutron number (arbitrary units) Neutron number (arbitrary units) 0.2
0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Neutron energy (MeV) Neutron energy (MeV)
Figure 12.3: Neutron energy spectra. The x correspond to the spontaneous fission contribution, the + to the (α,n) reaction contribution, the diamonds are the total. The average neutron energy is indicated above the figures. 12.3 Neutrons from radioactivity in rock and concrete 131
Figure 12.4: Elemental composition of rock and concrete. The assumed el- emental compositions of the rock (left plot) surrounding the Canfranc Underground Laboratory and of the concrete layer (right plot) covering the cavern walls are displayed.
12.3.2 Simulation of neutron attenuation by a hydrocarbon shield
As stated above, the neutron radiation expected from rock and concrete will be shielded. A typical shield for such an experiment consists of a layer of neutron absorbing material. Most commonly, hydrocarbon is chosen, since the energy transfer by elastic scattering is highest if the masses of projectile and target are similar, which is the case for neutrons hitting hydrogen nuclei. Hydrocarbon is a general term for materials consisting of carbon and a varying number of hydrogen (CHn). For the simulations described here, n=2 was assumed. Sometimes a layer of lead is added to the shielding of dark matter experiments which is an efficient shielding against γs. For the ArDM experiment there is currently no lead layer foreseen. In order to assess how the rock and concrete neutrons affect the detector performance, a Geant4 [39] simulation study with the following assumptions has been carried out: the geometrical setup includes the rock, a 20 cm thick concrete layer on the walls, the detector on the floor of the cavern, and five layers of CH2 shielding with a thickness of 10 cm each and a density of 0.91 g/cm3. The number of neutrons coming from the rock as well as from the concrete cover and reaching each layer of the shielding was then simulated and counted. A Geant4 simulation of the tracks of neutrons from rock revealed that only neutrons generated inside the closest two meters of rock are able to reach the cavern, as illustrated in fig. 12.5. The neutrons coming from the closest two meters of floor, cavern wall including the ceiling and imaginary end wall of the cavern (the presence of an end wall within a reasonable distance depends on the final position of the experiment) were considered separately. Neutron energy emission spectra in rock and concrete were obtained with SOURCES4a and are plotted in fig. 12.6. The number of neutrons entering the cavern and the various shielding layers are listed in table 12.2. 132 Neutrons
60
50
40
30
20
% of neutrons entered tunnel 10
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Distance to tunnel (m)
Figure 12.5: Percentage of neutrons reaching the cavern. The percentage of neutrons emitted by the rock radioactivity which are able to reach the cavern is displayed in dependence on the distance to the cavern.
−9 −9 x 10 Rock (Av.: 2.234 MeV) x 10 Concrete (Av.: 1.915 MeV) 2.5
5 2
4 1.5
3
1
Neutron number 2 Neutron number
0.5 1
0 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Neutron energy (MeV) Neutron energy (MeV)
Figure 12.6: Emission spectrum of neutrons from rock and concrete. The neutron energy spectrum of neutrons emitted by the Canfranc rock (left plot) and the concrete layer on the cavern walls (right plot) due to uranium and thorium decay chain reactions was simulated with the SOURCES4a program. The x correspond to the spontaneous fission contribution, the + to the (α,n) re- action contribution, the diamonds are the total. 12.4 Detector response to neutrons 133
Emitting part Vol. (m3) n per hour Cavern 0 cm 20 cm 40 cm Rock wall 507 456’000 15’300 1’100 7.3 0 Rock floor 179 161’000 4’800 563 3.9 0 Rock end 693 624’000 12’400 835 6.4 0 Concrete wall 44 8’240 5’026 444 4.1 0.02 Concrete floor 18 3’370 1’920 273 2.4 0.02 Concrete end 69 12’900 6’130 439 3.4 0.02
Table 12.2: Emitted neutron numbers from rock and concrete and neutrons reaching the cavern and different thicknesses of shielding.
12.3.3 Attenuation of neutron energy spectra by hydrocarbon
Due to the low rate of neutrons entering the shielding in the setup described above, the neutron spectra after different layers of CH2 were again simulated with a simplified setup. Neutrons were directly shot towards seven flat layers of CH2 with a thickness of 10 cm each. The angle of the neutron momenta with respect to the perpendicular direction isotropically varied between 0o and 45o. The neutron flux decreases by approximately one order of magnitude after every 10 cm of CH2 at energies up to 6 MeV, for higher energies the suppression is slightly less. Fig. 12.7 shows the attenuation after 0 cm, 20 cm, 40 cm and 60 cm of CH2. The suppression for concrete neutrons is slightly lower, especially for higher energies. From this section and from the last section it can be concluded that a hydrocarbon shield of a thickness of 50 cm–60 cm is able to sufficiently suppress background neutrons coming from the 8 rock and from concrete layers if a sensitivity of 10− pb is to be reached.
12.3.4 Comparison of hydrocarbon and water
As a cheaper alternative to a hydrocarbon shielding the use of a water shielding was considered. Since water (H2O) contains two hydrogen atoms out of three atoms, similar to hydrocarbon (CH2), an effective attenuation of neutron fluxes is also expected from water, although oxygen might be less advantageous compared with carbon. The neutron attenuation by a 50 cm layer of hydrocarbon and a a 50 cm layer of water was simulated with the Geant4 package [39], the results are displayed in fig. 12.8. It turns out that the neutron flux after 50 cm of hydrocarbon is about one order of magnitude lower than the one after 50 cm of water.
12.4 Detector response to neutrons
In order to assess the neutron background not only the neutron numbers and spectra are relevant, but also their interactions with the detector, i. e., with argon nuclei. The imparted recoil energy caused by a neutron with energy En and a scattering angle θ is
Mn MAr ER 2En 2 (1 cosθ), (12.3) ≃ (Mn + MAr) − where Mn and MAr are the neutron and argon masses, respecitvely. The ArDM detector res- ponse to background neutrons was simulated with the Geant4 package [39]. Neutrons were 134 Neutrons
7 7 10 10
6 6 10 10
5 5 10 10
4 4 10 0 cm hydrocarbon 10 0 cm hydrocarbon
3 3 20 cm hydrocarbon 10 20 cm hydrocarbon 10 Neutron number Neutron number 2 2 10 10 40 cm hydrocarbon 1 1 10 10 40 cm hydrocarbon
0 60 cm hydrocarbon 0 60 cm hydrocarbon 10 10 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Neutron energy (MeV) Neutron energy (MeV)
Figure 12.7: Attenuation of neutrons from rock and concrete by CH2. The simulated flux of neutrons from rock (left plot) and concrete (right plot) after crossing different thicknesses of CH2 is shown. The upper correspond to 0 cm CH2, the second upper line to 20 cm, the third line to 40 cm and the lowest line to 60 cm of CH2.
6 10
5 10
4 10
3 10 Water
Hydrocarbon
No. of neutrons 2 10
1 10
0 10 0 5 10 15 20 25 30 35 40 45 50 Shielding thickness (cm)
Figure 12.8: Attenuation of neutrons by water and hydrocarbon. The simu- lated neutron attenuation by the two shielding materials water (solid line) and hydrocarbon (dashed line) is displayed. 12.4 Detector response to neutrons 135
1400
1200
1000
800
600
No. of recoils 400
200
0 0 50 100 150 200 250 300 Argon recoil energy (keV)
4 10
3 10
2 10 No. of recoils 1 10
0 10 0 100 200 300 400 500 600 Argon recoil energy (keV)
Figure 12.9: Argon recoil spectrum caused by neutrons from detector com- ponents. The upper plot shows the spectrum in linear scale, the lower plot in logarithmic scale.
thereby placed inside the detector components, the rock and the concrete layer with an energy corresponding to the energy spectra simulated with SOURCES4a [55]. The neutrons then un- dergo interactions with argon nuclei. The following three interaction types are expected to occur within the ArDM liquid argon volume:
Elastic scattering of the neutron off an argon nucleus • Neutron capture by an argon nucleus with subsequent emission of a γ • Inelastic interactions with argon other than neutron capture •
Relevant to dark matter searches is the elastic scattering, since a wimp would also interact in this way with argon nuclei. In the simulation, the number of recoils imparted by neutron elastic scattering in liquid argon has been counted and the imparted argon recoil energy registered. The typical argon recoil spectrum induced by neutrons from detector components is shown in fig. 12.9. It roughly has an exponential shape. 136 Neutrons
15000
10000 No. of events
5000
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 No. of recoils above 30 keV
Figure 12.10: Neutron multiple scattering. The simulated multiplicity of neutron scatters in the ArDM liquid argon volume is dis- played. Approximately 46% single scatters are constitute the first bin, the remaining 54% multiple scatters can be rejected. Here, background neutrons due to uranium and thorium in the LEM are considered.
12.4.1 Multiple scattering
An important means to distinguish neutron interactions from wimp events is due to the high probability of multiple scattering of neutrons. Since its interaction cross section is very small, a wimp certainly does not scatter more than once inside the ArDM detector volume. The neutron multiple scattering is illustrated in fig. 12.10, where a histogram of the scatter mulitiplicity is displayed. For the simulation of this figure, background neutrons due to uranium and thorium in the LEM were considered. 54% of the interactions are multiple scatter events and are therefore rejectable. The number of recognized neutron scatters depends on the size of the fiducial volume and on the detector energy threshold. Here, a fiducial cylindrical volume with a height of 116 cm and a radius of 40 cm is assumed. These numbers might be slightly different in the final ArDM setup. The distance of the neutron emitting components to the fiducial volume has a big influence on the number of interactions as well. An important parameter is the assumed detector energy threshold. For wimp events, the thres- hold is assumed to be about 30 keV recoil energy for the final runs, and 60 keV for the first non optimized detector runs. This roughly corresponds to 6 keV or 12 keV electron equivalent, respectively, assuming a nuclear quenching factor of 0.2. For the recognition of multiple scatters however, it might be enough to only require one recoil to be above 30 keV. Since the time differ- ence between different scatters of the same neutron is very small (i. e., of the order of fractions of a nanosecond), the light signal from the scatter above threshold is a time trigger. The drift 12.4 Detector response to neutrons 137
Higher thr. Lower thr. Dewar Pillars PMTs LEM 30 keV 30 keV 55.16 54.66 58.74 54.01 30 keV 10 keV 74.86 73.34 75.73 70.58 60 keV 60 keV 43.55 42.15 47.43 42.79 60 keV 10 keV 80.04 78.93 80.53 75.45
Table 12.3: Percentage of neutrons emitted from different detector compo- nents and scattering more than once above the indicated upper and lower thresholds.
time of the electrons providing the corresponding charge signal is below 1 ms (approximately 600 µs for the maximal drift length, depending on the electric field strength), such that two or more charge signals within approximately 0.5 ms after the light signal most likely indicate multiple scatters, even if the light from the scatter below threshold cannot be detected (it typ- ically “drowns” inside the triggering light signal which is much stronger). Therefore, a second energy threshold for the definition of multiple scatters is introduced such that a multiple scatter event requires one scatter above the higher threshold (30 keV or 60 keV) plus a second scatter above the lower threshold, e. g. 10 keV. Table 12.3 indicates the multiple recoil percentages for different pairs of higher and lower thresholds. Percentages are defined as: number of multiple scatters above the corresponding threshold pair devided by the number of events with at least one scatter above the higher threshold, or in other words: number of multiple scatters devided by the number of detectable events. Fig. 12.11 illustrates the simulated variation of the multiple recoil percentage for different lower thresholds. The higher threshold was set to 30 keV, whereas the lower threshold varied between 0 keV and 30 keV. The percentage of multiple recoils significantly decreases for increasing lower threshold, since this makes the requirement for multiple scattering more severe. Fig. 12.12 shows the same for an upper threshold of 60 keV instead of 30 keV. One has to be careful when comparing the results for upper thresholds of 30 keV and 60 keV. The number of events that are measurable in the detector is smaller for 60 keV, thus, the normalization is differ- ent. The pair 60 keV/60 keV is less advantageous than 30 keV/30 keV, whereas 60 keV/10 keV is more advantageous than 30 keV/10 keV. The multiple recoil percentages for the upper and lower threshold pairs 30 keV/30 keV, 30 keV/10 keV, 60 keV/60 keV and 60 keV/10 keV are summarized in table 12.3 for neutrons from different detector components.
12.4.2 WIMP-like events
The most crucial kind of neutron events are the neutron interactions which precisely look like wimp interactions. We call such events wimp-like events. They are most worrisome since their rejection is impossible, and they therefore directly limit the final detector sensitivity. A neutron event which mimics wimp interactions has to fulfil two conditions: first, the number of scatterings has to be one. Second, the transferred energy has to be similar to the typical recoil energy imparted by a wimp, i. e. below 100 keV with a higher probability for low energies (the energy spectrum decreases exponentially with ascending energy, as for the neutrons in fig. 12.9). Assuming a detector energy threshold of 30 keV, a wimp-like neutron event is defined as a single recoil causing a recoil energy between 30 keV and 100 keV. The percentage of such wimp-like events—compared with the number of generated neutrons— 138 Neutrons
Dewar neutrons Pillar neutrons 85 85
80 80
75 75
70 70
65 65
60 60
55 55 Percentage of multiple recoils Percentage of multiple recoils 50 50 0 10 20 30 0 10 20 30 Lower threshold energy (keV) Lower threshold energy (keV)
PMT neutrons LEM neutrons 85 85
80 80
75 75
70 70
65 65
60 60
55 55 Percentage of multiple recoils Percentage of multiple recoils 50 50 0 10 20 30 0 10 20 30 Lower threshold energy (keV) Lower threshold energy (keV)
Figure 12.11: Percentage of multiple neutron recoils with a higher threshold of 30 keV.. The number of multiple scatters compared with the number of events above the higher threshold is displayed for the lower threshold varying between 0 keV and 30 keV. The higher threshold is set to 30 keV. Background neutrons from the dewar, the pillars, the PMTs and the LEM are considered (see titles in the figure). 12.4 Detector response to neutrons 139
Dewar neutrons Pillar neutrons 100 100
90 90
80 80
70 70
60 60
50 50
40 40 Percentage of multiple recoils Percentage of multiple recoils 30 30 0 20 40 60 0 20 40 60 Lower threshold energy (keV) Lower threshold energy (keV)
PMT neutrons LEM neutrons 100 100
90 90
80 80
70 70
60 60
50 50
40 40 Percentage of multiple recoils Percentage of multiple recoils 30 30 0 20 40 60 0 20 40 60 Lower threshold energy (keV) Lower threshold energy (keV)
Figure 12.12: Percentage of multiple neutron recoils with a higher threshold of 60 keV.. The number of multiple scatters compared with the number of events above the higher threshold is displayed for the lower threshold varying between 0 keV and 60 keV. The higher threshold is set to 60 keV. Background neutrons from the dewar, the pillars, the PMTs and the LEM are considered (see titles in the figure). 140 Neutrons
Higher thr. Lower thr. Dewar Pillars PMTs LEM 30 keV 30 keV 3.30 4.92 5.77 8.37 30 keV 10 keV 1.72 2.79 3.20 5.09 60 keV 60 keV 2.053 3.106 3.686 5.08 60 keV 10 keV 0.597 1.006 1.191 1.907
Table 12.4: Percentage of neutrons causing wimp-like events, assuming the indicated upper and lower thresholds.
with varying lower threshold is displayed in fig. 12.13 for an upper threshold of 30 keV and in fig. 12.14 for an upper threshold of 60 keV. The percentage decreases with descending lower threshold, due to the fact that more events can be identified as multiple scatters if the lower threshold becomes smaller. As in the case of multiple scatters (see section 12.4.1), the comparison of an upper threshold of 30 keV and an upper threshold of 60 keV is not straight forward. On the first glance, the case of 60 keV looks advantageous, since it has smaller percentages of wimp-like events. However, the number of detected events is altogether smaller, so the reduction of background is naturally payed with a loss of true wimp events. The percentage of background neutrons due to detector components which cause such a wimp- like interaction is listed in table 12.4, assuming the energy threshold pairs 30 keV/30 keV, 30 keV/10 keV, 60 keV/60 keV and 60 keV/10 keV.
12.5 Neutron background rejection
Due to the similar nature of wimp and neutron interactions, neutron background rejection is a difficult issue. As stated above, rejection due to recognition of multiple scattering is the only promising ansatz. Depending on the detector energy threshold, 50%–80% of the interacting neutrons can be rejected in this way. The remaining neutron events are wimp-like events. Their number can be estimated by counting the multiple scatters and extrapolating the corresponding number of single scatters. Due to the high uncertainty of this estimate, it is not possible to clearly identify single wimp events. In order to have a convincing wimp signal it is therefore necessary to achieve high enough statistics to recognize unique wimp signal features like the annual modulation (see section 4.4). 12.5 Neutron background rejection 141
Dewar neutrons Pillar neutrons 10 10
8 8
6 6
4 4
2 2
% single recoils in [30,100] keV 0 % single recoils in [30,100] keV 0 0 10 20 30 0 10 20 30 Lower threshold energy (keV) Lower threshold energy (keV)
PMT neutrons LEM neutrons 10 10
8 8
6 6
4 4
2 2
% single recoils in [30,100] keV 0 % single recoils in [30,100] keV 0 0 10 20 30 0 10 20 30 Lower threshold energy (keV) Lower threshold energy (keV)
Figure 12.13: Percentage of single neutron induced recoils with a threshold of 30 keV. The number of single recoil events with a recoil energy lying between 30 keV and 100 keV, divided by the total number of generated neutrons is displayed as a function of the lower threshold used to recognize multiple scattering events. Background neutrons from the dewar, the pillars, the PMTs and the LEM are considered (see titles in the figure). 142 Neutrons
Dewar neutrons Pillar neutrons 6 6
5 5
4 4
3 3
2 2
1 1
% single recoils in [60,100] keV 0 % single recoils in [60,100] keV 0 0 20 40 60 0 20 40 60 Lower threshold energy (keV) Lower threshold energy (keV)
PMT neutrons LEM neutrons 6 6
5 5
4 4
3 3
2 2
1 1
% single recoils in [60,100] keV 0 % single recoils in [60,100] keV 0 0 20 40 60 0 20 40 60 Lower threshold energy (keV) Lower threshold energy (keV)
Figure 12.14: Percentage of single neutron induced recoils with a threshold of 60 keV. The number of single recoil events with a recoil energy lying between 60 keV and 100 keV, divided by the total number of generated neutrons is displayed as a function of the lower threshold used to recognize multiple scattering events. Background neutrons from the dewar, the pillars, the PMTs and the LEM are considered (see titles in the figure). Summary and Outlook 13
The evidence for the existence of dark matter is compelling. Its impact on the formation of the universe, the rotation of galaxies as well as on the movement of large-scale galaxy clusters has been observed. Still, the nature of dark matter remains unknown. Several experiments aim at revealing what dark matter consists of. Many among them rely on the most common candidate particle, the lsp (Lightest Supersymmetric Particle), and optimize the detector properties in order to discover signals from lsps interacting with a dedicated detector target. This thesis presented investigations for one of these experiments—the ArDM detector.
13.1 Status of the ArDM detector
The target chosen for the ArDM detector is a liquid argon volume of approximately one ton. If an lsp or wimp (Weakly Interacting Massive Particle) interacts with argon nuclei, small amounts of scintillation light and ionization charge is produced. The ArDM detector is designed to measure these tiny light and charge signals. As by May 2008, the ArDM detector is drawing towards the end of its construction phase. Two of the three technical keypoints—the high ionization electron drift field generator and some of the PMTs for scintillation light readout—have extensively been tested in small setups, and are already inserted into the final one ton detector. The third main technical component—the LEM-based charge readout—is currently tested in a small setup, before a larger model will be constructed and added to the one ton detector.
13.1.1 Scintillation light and ionization charge readout
It is an important issue to assess the quantity, quality and the characteristics of the scintilla- tion light and ionization charge readout devices. Detector parameters like energy resolution or background rejection power heavily rely on the quality of the readout.
Scintillation light readout
The scintillation light production, propagation, collection and conversion into ADC signals within the ArDM detector was simulated. The amount of light produced after an event de- pends on the interacting particle and the transferred energy, and is described by the Lindhard theory [30]. The light propagation is determined by the detector geometry, the reflectivity of the inner detector components and the efficiency of the wavelength shifter. It has been shown that with the help of dedicated reflector foils coated with a wavelength shifter and surround- ing the fiducial volume a good photon collection is achieved. Furthermore, the collection does not strongly depend on the distance of the photon emission point to the photomultiplier tubes, which facilitates a reconstrution of events at all regions of the fiducial volume. The collection 144 Summary and Outlook of photons and their conversion into photoelectrons is determined by the photomultiplier tube characteristics, which are described in detail elsewhere [38].
Ionization charge readout
The ionization charge is read out with the help of two LEM plates, the upper of which contains two segmented readout layers. A planned pixel size of (1.5 mm)2 allows for a precise positioning of events in the horizontal x-y-plane of the detector. Together with the light signal which indi- cates the time of the event and the drift velocity of the electrons, the z-coordinate is determined by the LEM signal as well, allowing for a positioning of the event in three dimensions.
13.1.2 High voltage supply
Besides the above described light and charge readout, a third technical keypoint makes part of the ArDM detector principle, namely the generation of a electric drift field. This drift field is required in order to move the ionization electrons towards the LEM plates. Since the electron collection strongly depends on the field strength, very high DC voltages are involved. The technique chosen to generate these voltages relies on the Greinacher or Cockcroft-Walton circuit. With the help of capacitors and diodes, this circuit allows to convert an alternating input voltage into a much higher DC output voltage. The multiplication of the input voltage is determined by the number of stages of the circuit. In the case of the ArDM detector, a 210-stage circuit was constructed. Furthermore, a 10-stage model was built and operated in order to test the circuit behaviour at smaller scales. Tests of the 210-stage Greinacher circuit in air as well as measurements of the 10-stage model in air, vacuum and liquid argon were performed. They prove that the circuit can be operated in liquid argon, and the voltage reached with the 10-stage model corresponds to the planned voltage of 500 kV of the ArDM detector during data taking.
13.2 Background sources for ArDM
The search for dark matter is a rare event search. Depending on the model which describes the dark matter particle, event rates of the order of at most one event per day in one ton of liquid argon are expeced. It is therefore crucial to distinguish this tiny signal rate from much larger background radiation rates. The background radiation relevant to ArDM can be divided in two classes: the class of electron/γ interactions and the class of neutron interactions. The former is larger in terms of background event rates, whereas the latter is more worrisome due to the fact that it is much more hardly distinguishable from wimp signals.
13.2.1 Electron and gamma background
Two origins of electron and γ radiation are the main sources for background radiation of this kind. Electrons arise from the beta decay of the radioactive isotope 39Ar at a rate of 1 kHz in one ton of liquid argon. In liquid argon, they stop within very small distances to the decay point, and the uniform distribution as well as the known energy spectrum of these events facilitates a detector calibration. γ radiation arises from the decay chains of uranium and thorium, which is contained in detector components and surrounding facilities. The interaction rate and the 13.3 Future of ArDM 145 thereby transferred energy was studied extensively. It turns out that γ background radiation is much less worrisome compared with 39Ar radiation in terms of rates. Both electron and γ radiation is in principle distinguishable from wimp signals, since the relative amount of produced light and charge as well as the scintillation light pulse shape is different for the two interaction kinds. The precise rejection power which can be reached with these two methods remains to be determined when the readout characteristics of the ArDM detector will be measured.
13.2.2 Neutron background
As γ background radiation, neutron background arises mainly from the uranium and thorium decay chains. Neutrons are thereby produced via (α,n) reactions as well as via spontaneous fission. Uranium and thorium is contained within detector components and surrounding facilities like rock and concrete layers of an underground laboratory. The neutron production, energy spectrum, propagation and interaction with the liquid argon volume has been studied in detail. Neutrons coming from rock and concrete can be sufficiently shielded by a 50 cm–60 cm thick 8 hydrocarbon shield, if a sensitivity of 10− pb is to be reached. Neutrons arising from the detector components are more worrisome since the are emitted inside the shielding. The closer to the fiducial volume the detector component is located, the higher the percentage of neutrons interacting with liquid argon. It is therefore especially important for the LEMs and the PMTs to consist of low background materials. Standard materials like Vetronite or standard borosilicate glass turn out to be insufficient. Since neutrons interact with argon nuclei exaclty in the same way as wimps, the only way to reject neutron background relies on multiple scattering. Neutron interactions and the percentage of multiple scatters was studied extensively. Depending on the detector energy threshold, a multiple scatter percentage of 50%–80% is expected from simulation results.
13.3 Future of ArDM
Before the hunt of the ArDM detector for dark matter will begin, the following final steps of the construction need to be completed:
Tests of a small-size LEM and construction of the final LEM version • Completion of the photomultiplier tube array, 14 tubes in total are planned • Operation and tests of the 210-stage Greinacher circuit in liquid argon • Test of the liquid argon recirculation system •
These steps are planned to be undertaken in the second half of 2008. First runs of the detector above ground are scheduled for the end of 2008. After successful tests above ground, the detector will move underground in order to begin its search for dark matter. Hopefully it will be able to contribute to the unravelling of dark matter, the nature of which has eluded us for so long.
Acknowledgements
My greatest and profound thanks go to my supervisor Prof. Dr. Andr´eRubbia for giving me the opportunity to work on such an exiting and diversified subject. His continuous and competent support as well as many inspiring discussions made my time at CERN most instructive and enriching. I thank Prof. Dr. Ralph Eichler for his most useful comments and discussions on my thesis and for acting as a coreferee inspite of his extensive duties. I will keep my colleagues at CERN and at ETH Zurich in warmest memory. They enriched my stay at CERN and ETH with many pleasant discussions in various languages as well as with lots of common activities. They were just there for me whenever I needed them. My great thanks go to Ans, Yuanyuan and Thierry for explaining the mysteries of the Geant4 package and of software in general to me, to Marco, Alberto, Polina and Pol for introducing me into the world of hardware and to Rico for his daily and cheerful support as my office mate. I thank Gusti and Leo for their patient support concerning electronics and mechanics, and I am deeply indebted to Rosa for her help in many administrative issues and for her kind and warm way of taking care of the group. Special thanks go to Res for the careful reading of my thesis and his most useful comments. Finally, I am grateful for the continuous support, motivation and love I received from Dani, from my parents Ruth & Willy, from my sister Olivia and my brother Florian, and from my friends, especially from Marion. I am happy to have experienced the fascination of physics and I dedicate this thesis to all those who continue the quest for the true nature of our world.
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Personal Data
Family name Kaufmann First names Lilian Dominique Date of birth 10 January 1980 Place of birth Grabs (Switzerland) Nationality Swiss
Education
1987–1992 Primary school in K¨anerkinden and Wittinsburg (Switzerland) 1992–1996 Secondary school in Sissach (Switzerland) 1996–1999 High school in Liestal (Switzerland) October 2000–April 2005 Study of physics at the Swiss Federal Institute of Technology Zurich (ETHZ) (Switzerland) October 2004–February 2005 Diploma Thesis at the Swiss Federal Institute of Technology Zurich (ETHZ) in particle physics with the title “Direct Detection of WIMPs in Supersymmetric Models” under the supervision of Prof. Dr. Andr´eRubbia September 2005–June 2008 PhD Thesis at the Swiss Federal Institute of Technology Zurich (ETHZ) in particle physics with the title “Detector Performance and Background Studies for the ArDM Experiment” under the supervision of Prof. Dr. Andr´eRubbia
Zurich, May 2008