Validation of a model for Radon-induced background processes in electrostatic spectrometers
N. Wandkowsky, G. Drexlin, F.M. Fränkle, F. Glück, S. Groh, S. Mertens
VValidation of a model for Radon-inducedbackground processes in electrostatic spectrometers
N. Wandkowsky , G. Drexlin , F.M. Fr¨ankle , , F. Gl¨uck , , S.Groh and S. Mertens , KCETA, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany Department of Physics, University of North Carolina, Chapel Hill, NC, USA Research Institute for Nuclear and Particle Physics, Theory Dep., Budapest,Hungary Institute for Nuclear & Particle Astrophysics, Lawrence Berkeley NationalLaboratory, CA, USAE-mail: [email protected]
Abstract.
The Karlsruhe Tritium Neutrino (KATRIN) experiment investigating tritium β -decay close to the endpoint with unprecedented precision has stringent requirementson the background level of less than 10 − counts per second. Electron emission duringthe α -decay of , Rn atoms in the electrostatic spectrometers of KATRIN is aserious source of background exceeding this limit. In this paper we compare extensivesimulations of Rn-induced background to specific measurements with the KATRIN pre-spectrometer to fully characterize the observed Rn-background rates and signaturesand determine generic Rn emanation rates from the pre-spectrometer bulk materialand its vacuum components. a r X i v : . [ phy s i c s . i n s - d e t ] A p r . Introduction The observation of flavor oscillations of atmospheric, solar, reactor and acceleratorneutrinos has provided conclusive evidence for lepton mixing and non-zero neutrinomasses [1]. However, neutrino oscillation experiments only allow to assess the masssplittings of the three neutrino mass eigenstates, but yield no information on theirabsolute mass scale. The latter is of fundamental importance for both cosmology andparticle physics [2]. In cosmology, relic neutrinos acting as hot dark matter could playa distinct role in the evolution of large-scale structures such as galaxies [3]. In particlephysics, the determination of the neutrino mass scale would discriminate among differentmass patterns, such as hierarchical or quasi-degenerate scenarios[4].Various methods and techniques are employed at present to assess the absoluteneutrino mass scale. Galaxy redshift surveys and observations of the cosmic microwavebackground provide information on the large-scale structure of the universe, from whichupper limits on the sum of neutrino masses in the range from 200-600 meV have beenderived [5]. In addition, experiments searching for neutrinoless double beta decayyield information on the so-called effective Majorana neutrino mass m ββ with presentsensitivities of m ββ < −
400 meV [6]. In the future, these efforts are expected toreach sensitivities below 100 meV [7]. However, one has to note that the interpretationsof these observations and experiments with regard to the absolute neutrino mass scalecontinue to remain rather model-dependent.On the other hand, the measurement of the electron energy spectrum close to theendpoint of nuclear β -decays such as H and
Re or of the electron capture of
Ho [8]provides the only direct and model-independent way to determine the absolute neutrinomass scale, relying only on the relativistic energy-momentum relation and energyconservation [9]. The Troitsk and Mainz experiments studying the decay of (molecular)tritium T → ( HeT) ∗ + e − + ¯ ν e with electrostatic spectrometers have yielded themost stringent experimental upper limits on the effective electron antineutrino mass m ¯ ν e < β -decay experiment designed to determine m ¯ ν e with a sensitivity of 200 meV (90% C.L.) [11]. It is currently being assembled by aninternational collaboration at the Karlsruhe Institute of Technology (KIT) in Germany.KATRIN will investigate the kinematics of tritium β -decay with unprecedentedprecision in a narrow region close to the β -decay endpoint E ≈ . m ¯ ν e . Figure 1 gives an overview of the 70 m long experimental setup,which is based on a combination of an ultra-stable high luminosity tritium source [12]with a spectrometer of the MAC-E filter ‡ type [13, 14, 15]. The latter is based on themagnetic adiabatic collimation of electron momenta to be analyzed by the electrostaticpotential applied to the spectrometer and will be described in more detail in section 3.1.A segmented Si-PIN diode array allows to count the transmitted electrons as a function ‡ Magnetic Adiabatic Collimation and Electrostatic filter
INTRODUCTION β -decay spectrum close to E . Anessential pre-requisite to obtain the reference sensitivity of 200 meV is a low backgroundlevel of < − counts per second (cps) in the signal region close to E . a) b) c) d) e) Figure 1.
Overview of the KATRIN exprimental setup: a) windowless gaseous tritiumsource (WGTS): β -decay of molecular tritium, b) transport section: adiabatic guidanceof β -electrons and removal of tritium, c) pre-spectrometer: option of pre-filtering of β -electrons below 18 keV, d) main spectrometer: high precision β -electron energyanalysis, e) detector: detection of transmitted electrons. In a previous publication [16] we have reported on measurements with the KATRINpre-spectrometer in a test set-up configuration where α -decays of , Rn atoms inthe volume of an electrostatic spectrometer were identified as a significant backgroundsource. In particular, we could demonstrate that a single radon α -decay can produce upto several thousands of detector hits in the energy region-of-interest over an extendedtime period of up to several hours. This background results from the emission of electronsin the energy range from eV up to several hundreds of keV. The considerable range ofelectron energies is a consequence of the variety of processes related to the emission ofthe energetic α -particle as well as the reorganization of the atomic shell. A detaileddescription of these so called internal conversion, inner shell shake-off, relaxation andouter shell reorganization processes can be found in [17]. Over almost the entire energyrange, those electrons are trapped in the sensitive volume of the spectrometer due tothe known magnetic bottle characteristic of a MAC-E filter [18, 19]. Owing to theexcellent ultra-high vacuum (UHV) conditions of p < − mbar [20] in the KATRINspectrometer section, electrons remain trapped over very long periods of time, and canproduce secondary electrons via ionization of residual gas molecules. A fraction ofthese secondaries can reach the detector, resulting in a background rate exceeding theKATRIN design limit of 10 − cps.In this paper we combine the detailed model of electron emission processes following α -decays of the isotopes , Rn of [17] with precise electron trajectory calculations ina MAC-E filter, which allows to describe the initial background investigations reportedin [16], as well as the more in-depth studies performed in the course of this work andin [21, 22, 23]. In a separate publication [19] we made use of the model of [17] to deriveestimates of the background rates and topologies for the final KATRIN set-up, while anactive background reduction technique concerning trapped electrons is described in [24].This paper is organized as follows: The field calculation and particle trackingsoftware package
Kassiopeia , used for our extensive Monte Carlo simulations, will
SIMULATION TOOLS α -decay can leadto a significant increase in background over a time period of up to several hours. Insection 4, the background model of this work will further be validated by new dedicatedmeasurements with the KATRIN pre-spectrometer.
2. Simulation Tools
The study of event topologies of electrons from the α -decay of , Rn atoms, and theestimation of background rates and characteristics due to their subsequent magnetictrapping are an essential requirement in order to understand and optimize the KATRINmain spectrometer. To meet this task, a detailed code for particle trajectory calculationsin the complex electromagnetic field configuration of the KATRIN spectrometers hasbeen developed in the frame of the code
Kassiopeia [25]. This package allows to tracktrapped electrons over long periods of time with machine precision. For the purposeof this work a Monte Carlo generator to describe electron emission following , Rn α -decay was developed, which is described in detail in [17]. Therefore, section 2.1 willgive only a short recap of the physics processes taken into account. Section 2.2 thendescribes the field, tracking and scattering modules of the Kassiopeia package, whichare based on FORTRAN and C codes developed between 2000 and 2008 by one of us(F. G.). The simulation software allows an extremely precise and fast computation ofthe relativistic motion of charged particles in electromagnetic fields.
A major part of the
Kassiopeia package is devoted to event generators for the modelingof different physical processes occurring within KATRIN. For the investigations ofthis paper, a Monte Carlo event generator was developed to describe the processesaccompanying the initial radon α -decay.When an α -particle passes the fast inner atomic electrons, the direct collisionprocess can lead to the emission of a shake-off electron [26, 27, 28]. The resultingelectron energy spectrum shows a higher-order potential dependence [29] because thedecay energy is shared between the α -particle and the emitted electron, which carriesonly a small fraction, usually of the same order of magnitude as the shell binding energy E b . In the decay Rn → Po ∗ , there is a probability of about 3% for the daughternucleus to be found in an excited state. The inner shell electron wave function inparticular can extend into the nucleus and interact with the excited state, resulting inthe emission of a high-energy (up to 500 keV) internal conversion electron [30, 31].Both processes leave vacancies in the atomic shell, which gives rise to complexrelaxation cascades [32, 33]. Non-radiative transitions lead to the emission of Auger orCoster-Kronig electrons. The resulting discrete energy spectrum ranges from a few eVup to several keV. SIMULATION TOOLS p → p ) share an energy of 230 eV,which results in a flat energy spectrum [34, 35]. Due to their identical nuclear charge,the inner shell shake-off and shell reorganization contributions of the two poloniumisotopes are assumed to be identical. Magnetically trapped electrons from radon α -decay with energies up to severalhundred keV have to be tracked over path lengths of several km down to very lowenergies of a few eV to fully understand their impact on background issues. In doingso, a challenging requirement is to reach a position resolution in the µ m range whichcorresponds to the typical cyclotron radius in a strong magnetic field region of several T.In order to perform this task, the Kassiopeia package includes a full particle trackingmodule. The equations of motion of the electrons are being solved using Runge-Kuttamethods described in [36, 37, 38]. Owing to the complexity of the inner electrode [39]and magnet system [40] realized in the KATRIN experimental setup, the calculationof electric and magnetic fields is most challenging. To do so we make use of the zonalharmonic expansion [41, 42], and, in the case of electric field computations, the boundaryelement method [43].For the investigations of this paper, all processes resulting in an energy loss ofstored particles play a major role. The corresponding
Kassiopeia modules to describeelectron cooling include the processes of elastic scattering, excitation and ionization of H molecules (dominant residual gas species within the KATRIN main spectrometer).The corresponding cross sections [44, 45, 46, 47], energy loss values [48, 49] and scatteringangles have been implemented in the scattering routine of Kassiopeia .The scattering cross sections and energy losses vary significantly for different gasspecies. Correspondingly, primary electrons with identical start parameters experiencedifferent storage times and generate different numbers of secondary electrons. Initialmass spectrometry measurements [21] showed that the residual gas inside the pre-spec-trometer mainly consists of hydrogen, water and nitrogen, while argon was used withinspecific test measurements to increase the pressure to a desired value. When studyingelectron cooling by scattering off residual gas, the ionization process is the dominantenergy loss mechanism, contributing to >
80% of the total energy loss for electrons above1 keV when scattering off hydrogen takes place. Hence, molecule-specific ionizationcross sections and energy losses are used within the simulation (water, nitrogen [50],argon [51]). In the case of elastic or excitation processes, energy losses are computedusing molecular hydrogen input data, which is a sufficient approximation. Arbitraryresidual gas compositions consisting of hydrogen, water, nitrogen or argon can be definedvia specific configuration files. The fact that electron cooling strongly depends on theresidual gas pressure and composition has been used to gain insight into backgroundprocesses by comparing measurements and simulations at different pressures, which will
RADON-INDUCED BACKGROUND WITHIN KATRIN t (inSI units) by this radiative process is given by∆ E ⊥ ∆ t = 43 e m e c · B · E ⊥ ≈ . · B · E ⊥ , (1)where B denotes the magnetic field, c the velocity of light, and e and m e the electroncharge and mass. To good approximation only the transversal kinetic energy component E ⊥ is reduced by this process. In our simulation, synchrotron energy losses within aRunge-Kutta step are determined by using the average magnetic field during the step.From eq. (1) follows that the cooling effect due to synchrotron radiation is most efficientfor large transversal kinetic energies and large magnetic fields. At the same time,the scattering cross section decreases steeply for increasing electron kinetic energies,so that synchrotron losses dominate at higher energies. As an example for the standardoperation mode of the KATRIN pre-spectrometer ( p = 10 − mbar, B max = 4 . B min = 15 . Kassiopeia package thus allows tostudy background generating processes of trapped electrons from , Rn α -decays ingreat detail.
3. Radon-induced Background within KATRIN
When discussing the background processes from electrons following radon α -decays,we first briefly outline the working principle of the KATRIN spectrometers, whichis based on the MAC-E filter principle (section 3.1). Section 3.2 then describes thetrapping mechanism of electrons in a MAC-E filter and the resulting significant increasein background. The final section 3.3 is devoted to the specific case of radon-inducedbackground. Electrons from tritium β -decay are emitted isotropically in the source (WGTS) andhave to be guided adiabatically to the spectrometer by a magnetic guiding systemwhich consists of a series of superconducting magnets (see fig. 1). In the spectrometer,the energy analysis takes place via the MAC-E filter technique, which is illustratedin figure 2. Two superconducting magnets provide a magnetic guiding field for β -electrons, while an electrostatic retarding potential U , applied to the spectrometer andits inner electrode system, allows to filter the signal β -electrons. The area where the RADON-INDUCED BACKGROUND WITHIN KATRIN U reaches its maximum is defined as the so-called analyzing plane.The kinetic energy of incoming electrons is composed of a longitudinal component E (cid:107) parallel to the magnetic field lines and a transversal component E ⊥ corresponding tothe electron’s cyclotron energy. The electrostatic potential, however, only affects andfilters E (cid:107) . Therefore, E ⊥ has to be transformed into E (cid:107) by the magnetic gradient force.In order to achieve this, the magnetic field strength has to decrease from its maximumvalue B max at the center of the superconducting magnets to its minimum value B min at the analyzing plane. The field gradient ∇ B , however, should not be too steep toguarantee a fully adiabatic electron motion, thereby conserving the magnetic moment µ = E ⊥ /B . This principle allows for a high-resolution energy analysis by the retardingpotential. Electrons with sufficient kinetic energy to pass the electrostatic barrier arere-accelerated and counted at the detector, thus yielding an integral energy spectrum. transmitted electronspectrometer on potential U trapped electronmagnetsource detectormagnetanalyzing planeBmax Bmin Bmax Figure 2.
MAC-E filter principle. Superconducting magnets produce a magneticguiding field. On the one hand, signal electrons, created in the source with sufficientkinetic energy, can pass the potential barrier at the analyzing plane and are countedat the detector. On the other hand, electrons generated inside the volume of thespectrometer can be trapped due to the magnetic mirror effect.
While the magnetic field setup of a MAC-E filter allows for unsurpassed precision inthe scanning of the tritium β -decay spectrum close to E , it also acts inherently as amagnetic bottle for electrons created in the flux tube of the spectrometer (see fig. 2).The longitudinal energy E || of such an electron is transformed into transversal energy E ⊥ when propagating towards the increasing magnetic field strength at the entranceand exit region of the spectrometer. At the same time, the electron concurrently gainslongitudinal energy by the accelerating electric potential. If the transversal energy ofthe electron is above a certain threshold, the magnetic transformation is dominant and E || will be converted completely into E ⊥ . Consequently, this electron is reflected bythe magnetic mirror effect [18], which results in a stable storage condition within thespectrometer volume.When trapped, electrons scatter off residual gas species, thereby slowly coolingdown until their transversal energy drops below the storage threshold and they can RADON-INDUCED BACKGROUND WITHIN KATRIN <
100 eV) are produced via ionizing collisions. Thesesecondaries are accelerated by the retarding potential and, when escaping the magneticbottle, will hit the detector within the energy region-of-interest, thus producing anirreducible background class.Depending on its initial kinetic energy, a single stored primary electron can produceup to several thousands of secondary electrons which contribute to the background.Due to its non-Poissonian nature, this background source can significantly constrain theneutrino mass sensitivity of KATRIN [19], if no countermeasures [24] are taken.
In the framework of the pre-spectrometer electromagnetic test measurements [21, 16],a background source with the characteristics described above was identified to stemfrom electrons emitted during the α -decay of single , Rn atoms. While backgroundrates close to the intrinsic detector background of (6 . ± . · − cps were observedmost of the time, specific time intervals of up to two hours duration showed enhancedbackground rates of up to 250 · − cps. These distinct intervals occurred about 7 timesper day, each caused by a single nuclear decay of a specific radon isotope.There are various potential sources of radon emanation to take into account. First,the vessel of the pre-spectrometer with its diameter of 1.7 m and length of 3.3 m (seefig. 2) features a large inner surface of 25 m including weld seams which are a potentialsource of radon emanation [52]. In addition, several auxiliary devices (vacuum gauges,glass windows etc.) are attached to the vessel, which can also emanate radon atoms asa result of their primordial abundance of Th,
U and
U. A major source of
Rnemanation was identified to be the non-evaporable getter (NEG) material [53], used asan efficient pump for hydrogen. Details on different sources of radon emanation can befound in [16].While the α -particle itself and the fluorescence X-rays of atomic relaxation processesdo not contribute to the background, energetic electrons, which are emitted during thenuclear α -decay (see section 2.1 and [17]), have a large probability to be stored insidethe pre-spectrometer. Thus, they will lose their kinetic energy via secondary processessuch as scattering or synchrotron radiation. If we assume that electrons cool downexclusively via scattering off molecular hydrogen, the average energy lost per producedsecondary electron is ω ≈
33 eV. This value was determined with the scattering routinesimplemented in
Kassiopeia and is in good agreement with the calculated value of 37 eVin [54].For primary electrons trapped within the pre-spectrometer flux tube, the numberof secondary electrons is influenced by several effects: • For the pre-spectrometer field configuration detailed in fig. 2, only electrons with akinetic energy above about E min ⊥ = 60 eV are stored magnetically. Hence, a high-energy (keV) electron will not transform its entire kinetic energy into secondary VALIDATION OF BACKGROUND MODEL • Electrons experience non-negligible energy losses due to synchrotron radiation.According to eq. (1), the synchrotron losses increase for larger electron transversalenergies. • Above 100 keV starting energy, electron trapping is affected by non-adiabaticeffects, resulting from the specific electromagnetic field configuration of the pre-spectrometer. Non-adiabaticity is induced if the magnetic field changes significantlywithin one gyration, so that the transformation of E ⊥ into E (cid:107) and vice versa is nolonger proportional to the change of the magnetic field. Consequently, the polarangle of the electron will change randomly, eventually hitting a value below thetrapping threshold. • Additionally, electrons with very high energies have large cyclotron radii which canlead to electrons hitting the spectrometer vessel, thus prematurely terminating thebackground-generating process.To study background-generating processes and non-adiabatic effects,
Kassiopeia simulations with the
Rn event generator described in [17] were performed. A total of10000 electrons was tracked in the pre-spectrometer under standard operating conditions( p = 10 − mbar, B max = 4 . B min = 15 . , U ≈ − ω = 33 eV. This reduction is mainly due to the ratherlarge synchrotron energy losses in the pre-spectrometer. In addition, electrons releasedfrom the spectrometer magnetic bottle due to non-adiabatic effects contribute to thisbehavior.When transferring these numbers into background rates it is important to notethat only a fraction of the produced secondary electrons will actually reach the detector.First, only half of the electrons will escape towards the detector side of the spectrometer.Second, the electrostatic field configuration of this setup features a small Penning trapin the center of the pre-spectrometer with a depth of up to 12 V in the sensitive volume.As a result, low-energy secondary electrons are stored within this trap with a probabilityof about 60 %. Despite these background-reducing factors, radon-induced events canstill induce enhanced background rates where up to 2000 detector hits were observedover up to 2 hours ( N bg ≈ · − cps).
4. Validation of Background Model
In the following we report on a detailed experimental validation of our radon eventgenerator [17] and the corresponding Monte Carlo simulations described above. Theexperimental information is based on specific measurements with the pre-spectro-
VALIDATION OF BACKGROUND MODEL primary energy [keV] nu m be r o f s e c onda r i e s adiabaticnon-adiabaticscattering only Figure 3.
Number of produced secondary electrons as a function of the startingkinetic energy of the primary electron. In this case the
Rn event generator wasused and electrons were tracked in the pre-spectrometer. The red line corresponds toan average energy loss of ω = 33 eV per ionization. The actual number of secondaryelectrons remains below this limit because the primary electrons also lose energy dueto synchrotron radiation. The non-adiabatic events are marked as full circles. meter, described in [21], motivated to give complementary high-precision information onbackground characteristics and mechanisms. In the first section 4.1 an overview of thedifferent measurements will be given. Section 4.2 discusses the specific event topologyof trapped electrons in the form of ring structures at the detector, which gives access tothe spatial distribution of radon decays inside the spectrometer. A further importantbackground characteristic is the rate of single events where Monte Carlo simulations arecompared to measurements within section 4.3. In the final section 4.4 the Monte Carloresults are used to determine the radon activities in the pre-spectrometer setup, whichthen are compared to the independent values derived in [16]. In order to validate our model of radon-induced background more reliably, three differentpre-spectrometer background measurements have been investigated in detail. A fullMonte Carlo simulation of each measurement configuration has yielded consistentresults, which will be presented in sections 4.3 and 4.4. This section first gives anoverview of the measurement strategy and experimental results.As outlined above, the storage time of an electron strongly depends on the residualgas pressure inside the spectrometer. Therefore, two measurements at different pressureswere performed, first a measurement at the standard pre-spectrometer operating
VALIDATION OF BACKGROUND MODEL p LPG = 10 − mbar with the residual gas composed mainly of hydrogen,water and nitrogen. Secondly, a measurement was performed at a higher pressureof p HPG = 2 · − mbar while injecting argon gas into the spectrometer. In bothmeasurements, the vacuum system consisted of the NEG pump (emanating Rn) andone turbo molecular pump (TMP) for non-getterable species. In the following, theseconfigurations are labeled LPG (low pressure with getter) and HPG (high pressure withgetter), respectively. In order to definitely confirm the getter material as a major sourcefor
Rn, the NEG pump was removed for a third measurement. A second TMP thenhad to be activated to compensate for the loss in pumping power. As these modificationsresulted in a relatively high pressure value of p HP = 10 − mbar, this measurement islabeled HP (high pressure - without getter). The number of active TMPs influences thepump-out time for gases, and thus the decay probability of the different radon isotopes,as shown in table 1. In all cases, the decay of Rn can be neglected.
Table 1.
Pumping speeds and decay probabilities inside the pre-spectrometer for
Rn,
Rn and
Rn, depending on the number of active TMPs [16]. The totalpre-spectrometer volume amounts to V = 8 . . Rn Rn Rn1 194 0.885 0.353 9 . · − . · − The intervals with elevated background rate caused by a single radon decay were(in close analogy to [16]) categorized into three different event classes, depending on thenumber of counts (cts) at the detector: CI (10-50 cts), CII (51-500 cts) and CIII ( > Rn, with the NEG pump identified as amajor source of this isotope. However, even after the complete de-installation of theNEG pump (measurement HP), the distinct CIII signature of
Rn events was stillobserved, though at a greatly reduced rate. Consequently, we have implemented abackground model where three different sources contribute to the total radon activityinside the spectrometer:
Rn from the getter ( Rn G ), and Rn as well as
Rnfrom the spectrometer and auxiliary equipment attached to it ( Rn B , Rn B ).Table 2 gives a summary of the measurement conditions in the three configurations,which have been used as input for our Monte Carlo simulations. Furthermore, theobserved occurrence of CI-III events and their contributions to the total spectrometerbackground are given. These values will be compared to those derived via simulations(section 4.4). VALIDATION OF BACKGROUND MODEL Table 2.
Overview of UHV measurement conditions and resulting radon-inducedbackground rates. For the three different measurement conditions (low-pressure (LPG)and high-pressure (HPG) with getter installed, and high-pressure without getter (HP))the events were categorized into three different classes according to the number ofradon-induced counts (cts) at the detector: CI (10-50 cts), CII (51-500 cts), CIII( >
500 cts). Event rates and contributions to the total spectrometer background r bg are shown for the individual classes. measurement LPG HPG HPgetter (cid:88) (cid:88) × · − · − · − gas composition H , H O, N Ar H , H O, N events/day ( CI ) 4 . ± . . ± . . ± . r bg ( CI ) [10 − cps] 0 . ± . . ± . . ± . CII ) 1 . ± . . ± . . ± . r bg ( CII ) [10 − cps] 3 . ± .
15 1 . ± . . ± . CIII ) 1 . ± . . ± . . ± . r bg ( CIII ) [10 − cps] 8 . ± . . ± . . ± . Apart from generating elevated levels of background over extended periods of time, theevent topology of radon-induced background is an important tool to characterize thebackground-generating mechanism. The rather complex motion of stored electrons ina magnetic bottle results in a specific topology. Due to the excellent radial mappingcharacteristics of a MAC-E filter (see fig. 4), radon-induced background at the 8x8silicon pixel detector will form a generic ring pattern [21, 22]. This radon-induced eventtopology can be understood by first principles of particle motion, as well as by moredetailed simulations of electron trajectories in the pre-spectrometer set-up. The electronmotion is composed of a fast cyclotron motion around the guiding magnetic field line, anaxial motion between the reflection points of the magnetic mirror, and a slow magnetronmotion around the beam axis. The magnetron motion is caused by the (cid:126)E × (cid:126)B and the (cid:126) ∇| (cid:126)B |× (cid:126)B drift, which result from the inhomogeneous electric ( (cid:126)E ) and magnetic ( (cid:126)B ) fieldconfigurations inside the spectrometer. Secondary electrons, originating from ionizingcollisions of the stored primary electron with residual gas molecules, thus monitor thismotion by following the magnetic field lines when escaping the magnetic mirror trap.Consequently, they produce a characteristic ring structure at the detector. The examplein fig. 4 shows a main hit region (green to red pixels, multiple hits per pixel) which caneasily be identified from the surrounding rather fuzzy region (blue pixels, single hits perpixel) which is caused by the cyclotron motion of the primary electron. This uniquefeature of ring-structures allows to make use of a ring-fitting algorithm to unambiguously VALIDATION OF BACKGROUND MODEL cyclotronaxialmagnetron
Figure 4.
Simulated trajectory of a single trapped electron with start energy E = 1000 eV. The electron motion consists of a very fast cyclotron motion aroundthe magnetic field line, a fast axial motion and a slower magnetron motion around thebeam axis. Secondary electrons generated by the primary electron along its path aretherefore seen as rings on the pixel detector. One can identify the main hit region(green to red colors, corresponding to a large number of hits) and a surrounding fuzzyregion (blue, only a few hits) due to the cyclotron motion of the primary electron. Thesame signature was found within the measurements of [16], where figure 6 shows someexample events. The ring radius fit determines the radial position r of the primary α -decayresponsible for producing the primary electron relative to the central axis. For ahomogeneous distribution of α -decays inside the spectrometer volume, the number ofrings N ( r ) in a fixed interval [ r, r + d r ] is expected to increase linearly with the radius(see figure 5). When comparing measured and simulated spatial ring distributions,the good agreement visible in fig. 5 implies that α -decays indeed occur with uniformprobability over the entire flux tube, as expected for neutral atoms emanating into theUHV region. The smaller number of ring structures with radii r fit >
20 mm is a resultof the limited dimensions of the Si-PIN diode array (length= 40 mm), which does notcover the entire flux tube (see fig. 4). Nevertheless, events which produce a significantamount of detector hits in the corner pixels with r fit >
20 mm can still be identified,albeit with a reduced geometrical efficiency.
While the event topology clearly points to a uniform radon decay probability per unitvolume over the entire spectrometer volume, we now investigate whether the two other
VALIDATION OF BACKGROUND MODEL radius [mm] r i ng e v en t s Figure 5.
Distribution of fitted ring radii r fit as determined via measurement andMonte Carlo simulation, and normalized to the total measured event rate. Themeasured data was adopted from [16]. The good agreement verifies the assumption ofa uniform distribution of radon decays inside the spectrometer volume. parameters of radon-induced background, namely the number of secondaries and theevent duration, also agree with expectations. For this investigation we consider twomeasurements at different pressures (measurements HPG and LPG). Figure 6 comparesresults of measurements and corresponding simulations.The storage time of a primary electron and the number of secondary electrons itproduces strongly depend on the primaries’ starting kinetic energy and on the residualgas pressure in the spectrometer volume. The number of secondary electrons willincrease for higher pressure levels as scattering energy losses increase at the expenseof synchrotron energy losses. By the same token, the storage time decreases becausesuccessive scattering events will happen faster. Accordingly, for the HPG measurement,the electron energy losses are dominated by scattering processes (see fig. 6 (a)).Interestingly, both measurement and simulation show two separate, distinct regionswith regard to the event duration ( t s ≤ s, t s > s). The simulation, whichcan distinguish between conversion and shake-off events, reveals that this characteristicseparation is due to differing primary electron emission processes. While the majority ofthe shake-off electrons has less than 20 keV kinetic energy, conversion electrons typicallyare found above 100 keV. For this pressure regime, the parameter event duration t s allows to distinguish conversion electrons ( t > s) from inner shell shake-off processes( t ≤ s). On the other hand, at low pressures in the LPG measurement (figure 6 (b)),synchrotron energy losses tend to smear out this difference. While shake-off electrons atlow energies are barely affected by synchrotron losses, these losses are dominant in thecase of conversion electrons. Consequently, the gap between the two emission classesis closed. The impact of increased losses due to of synchrotron radiation at excellent VALIDATION OF BACKGROUND MODEL event duration [s] de t e c t o r h i t s shake-off (simul.)conversion (simul.)measurementp = 2 10 -9 mbar . (a) event duration [s] de t e c t o r h i t s shake-off (simul.)conversion (simul.)measurementp = 1 10 -10 mbar . (b) Figure 6.
Number of detector hits over event duration for the HPG measurement (a)and the LPG measurement (b). The simulations (open circles) reproduce the featuresof the measurements (full circles), which is described in more detail in the main text.
UHV conditions is further confirmed by the fact that the overall number of secondaryelectrons is reduced by a factor of 1.5 for the LPG measurement.
VALIDATION OF BACKGROUND MODEL Following the above considerations, the cooling time of a single electron varies betweena few seconds for very low energies at high pressures, and a few hours for the largestenergies at low pressures. In case of the pre-spectrometer background measurementsthe radon activity was low enough so that the time between two events was larger thanthe event duration. Therefore, individual α -decays can be clearly discriminated, whichallows for their counting.The excellent agreement between Monte Carlo simulations and experimental data,as well as the different vacuum conditions of the three measurements (LPG, HPG andHP), which influence shake-off and conversion electrons differently, can now be used todetermine the α -decay activities of the two isotopes ( Rn or
Rn), as well as theirorigin (getter, bulk) yielding the four observables Rn B , Rn G , Rn B and Rn G .To discriminate between Rn and
Rn induced events, we use the simulated decayprobabilities for CI-III events to fit the experimental data of table 2. We finally comparethe more detailed results of this work to our earlier results in [16], which were based onmeasurements only.Table 3 summarizes the simulated probabilities of CI-CIII events following
Rnand
Rn decays for the three experimental configurations. The key experimentalparameters pressure and gas composition are identical to table 2. Furthermore, theaverage number of detector hits per event (cid:104) N det (cid:105) is shown, which is required to determinethe actual background contribution. Table 3.
Overview of simulation results, comprising 10000 electrons for eachconfiguration and radon isotope. The probability P for the occurrence of CI-III eventsper decay and the average number of detector hits (cid:104) N det (cid:105) per event are shown. measurement LPG HPG HPradon type Rn Rn Rn Rn Rn Rn P [10 − ] (CI) 8 5.8 9.2 5 6.8 5.7 (cid:104) N det (cid:105) /event (CI) 22.8 19 24.3 21.9 25.3 21.4 P [10 − ] (CII) 3.9 2.1 3.3 0.8 3.3 0.8 (cid:104) N det (cid:105) /event (CII) 130.3 71.6 123.2 58.6 134.4 51.3 P [10 − ] (CIII) 4.2 0 2.7 0 5.3 0 (cid:104) N det (cid:105) /event (CIII) 677.9 0 932.7 0 1033.8 0The event rates r i for the individual classes C i , with i = I, II, III , are determinedfrom the activities of the three different radon sources A ( Rn B ), A ( Rn G ) and A ( Rn B ), the corresponding probabilities P i for the occurrence of an event of class C i and the decay probability (cid:15) : r i = (cid:88) k = Rn B , Rn G , Rn B (cid:15) ( k ) · A ( k ) · P i ( k ) . (2) VALIDATION OF BACKGROUND MODEL P i ( k ) are taken from table 3 and the decay probabilities (cid:15) ( k ) fromtable 1. The only free parameters remaining are thus the radon activities A ( k ), whichcan be determined by a three-parameter χ -fit of the simulated event rates r i to themeasured rates of table 2. In fig. 7 we show the fit results for the radon activitiesper unit volume in the pre-spectrometer (total volume: 8.5 m ) and compare themto the activities which were observed in the measurements of Fr¨ankle et al. [16]. Thesimulated activities in general are somewhat larger than the measured ones, which can beexplained by two facts. First, the effects of non-adiabaticity were not considered in [16].Furthermore, our extensive simulations have revealed that some CI events do not appearas rings on the detector, and, consequently, could not be attributed to radon-inducedbackground within the analysis of [16]. ] a c t i v i t y pe r un i t v o l u m e [ m B q / m -1 nkle et al.aFrsimulation Rn
219 G Rn
219 B Rn
220 B
Figure 7.
Total activity of Rn B (bulk material of the spectrometer vessel), Rn G (getter material) and Rn B inside the pre-spectrometer. The values havebeen determined by a three-parameter fit of simulated to measured event rates.The simulation results of this work (circles) are compared to values derived frommeasurements of Fr¨ankle et al. [16] (squares). Table 4 gives the emanation rates of , Rn B into the KATRIN pre-spectrometerstainless steel vessel per unit volume. The values are compared to the independentmeasurement of the Rn emanation for the empty and fully equipped GERDA cryostat,as reported in [55, 56]. Unfortunately, the measurement technique applied in [55]does not allow detection of the short-lived , Rn isotopes. As the authors of [55]point out, stainless steel vessels show much larger radon emanation rates than purestainless steel samples, which can be caused by surface impurities, in particular due towelding procedures. Furthermore, any auxiliary equipment attached to the vessel willsignificantly increase the radon emanation rate, an effect both observed in KATRIN andGERDA for different isotopes.Figure 8 compares the event rates determined according to eq.(2) to those derived
VALIDATION OF BACKGROUND MODEL Table 4.
Comparison of radon emanation rates per unit volume in stainless steelvessels. The simulated , Rn B concentrations for the fully equipped KATRIN pre-spectrometer stainless steel vessel ( V = 8 . , A = 25 m ) are compared to the Rnconcentrations in case of an empty and a fully equipped GERDA cryostat [55, 56]( V = 65 m , A = 70 m ). concentration [mBq/m ] Rn [this work] 0 . ± . Rn [this work] 6 . ± . Rn [55] (empty) 0 . ± . Rn [56] (fully equipped) 0 . ± . e v en t s / d det <5O 5O LPG (simul.) HPG (meas.) HPG (simul.) HP (meas.) HP (simul.) Figure 8. Event rates for the individual classes and measurements, determinedaccording to eq.(2). The simulations (full symbols, blue) are in good agreement withthe measurement results (open symbols, red). In figure 9, the background contributions of the individual classes are shown. Thesevalues are determined by multiplying the calculated event rates with the simulatedaverage number of detector hits per event (cid:104) N hit,MC (cid:105) of each class for the different radonisotopes.After subtracting the contributions of CI-III events from the total measuredbackground rate, a background component of about 3 · − cps remains. A fractionof this background results from radon decays which produce less than 10 detector hits,or are not detected as ring events by the analysis software (in the following labeled C0 CONCLUSIONS ba ck g r ound [ - c p s ] LPG (meas.) LPG (simul.) HPG (meas.) HPG (simul.) HP (meas.) HP (simul.) det <5O 5O Figure 9. Background contribution from the individual classes. The simulations (fullsymbols, blue) are in agreement with the measurement results (open symbols, red). events). These are mainly α -decay events where only two low-energy shell reorganizationelectrons are emitted [17], which have a low probability of being magnetically storedin the pre-spectrometer. The simulations reveal that these radon decays produce onaverage 0.2 detector hits. Table 5 summarizes the C0 contributions to the backgroundrate for the three measurements considered. The fact that all simulated rates contributesignificantly, but do not exceed the remaining measured single hit background rate isanother important validation of our background model, showing that radon-inducedprocesses also contribute to the measured C0 class (possibly saturating it). Table 5. Simulated and measured background rate ( r C0 , simu , r C0 , meas ) due to C0single hit events. measurement r C0 , simu [10 − cps] r C0 , meas [10 − cps]LPG 1 . ± . 03 3 . ± . . ± . 03 3 . ± . . ± . 02 2 . ± . 5. Conclusions In the course of this work we have developed a detailed model of electron emissionprocesses following the α -decays of the two radon isotopes Rn and Rn. Theseinvestigations were motivated by our earlier observations, reported in [16], of periods CONCLUSIONS α -emission. The radon event generator described in [17]has been used as input for extensive Monte Carlo simulations with the Kassiopeia simulation package. The validity of our background model and corresponding MonteCarlo simulations has been confirmed by a comparison with key experimental observablessuch as event duration and number of detector hits. The relative contribution of thetwo isotopes Rn and Rn has been determined by varying the pressure in the UHVrecipient. In addition, by removing the NEG strips from the pre-spectrometer pumpport, we were able to assess the contributions from the spectrometer surface. As a result,the radon-induced background has been fully characterized. An important outcomeof these investigations is the realization that low-energy shell reorganization electronscomprise a significant fraction of the single hit background rate.These findings are of major importance for the upcoming KATRIN measurementswith the main spectrometer. In [19] we extrapolated the background model of thiswork to the different electromagnetic layout (minimum magnetic field 3 mT instead of156 mT here) at the large main spectrometer, taking into account also the much largerNEG pump in operation there. The work presented in this publication has also beeninstrumental in developing active [24] as well as passive [57] countermeasures againsttrapped electrons following radon α -decays.It is only by developing and by validating detailed models of background processesthat the KATRIN experiment can realize its full physics potential in measuring theabsolute mass scale of neutrinos. Acknowledgement This work has been supported by the Bundesministerium f¨ur Bildung und Forschung(BMBF) with project number 05A08VK2 and the Deutsche Forschungsgemeinschaft(DFG) via Transregio 27 “Neutrinos and beyond”. We also would like to thank theKarlsruhe House of Young Scientists (KHYS) of KIT for their support (S.G., S.M.,N.W.). References [1] Y. Fukuda et al. , “Evidence for oscillation of atmospheric neutrinos,” Phys. Rev. Lett. , vol. 81,pp. 1562–1567, 1998.[2] S.F. King, “Neutrino Mass,” arXiv:0712.1750v1 , 2007.[3] J. Lesgourguesa and S. Pastor, “Massive neutrinos and cosmology,” Phys. Rep. , vol. 429, nr. 6,pp. 307–379, 2006.[4] N. K. Francis and N. N. Singh, “Quasi-Degenerate Neutrino Masses with Normal and InvertedHierarchy,” J. Mod. Phys. , vol. 2 pp. 1280–1284, 2011. CONCLUSIONS [5] S. Hannestad, “Neutrino physics from precision cosmology,” Prog. Part. Nucl. Phys. , vol. 65pp. 185–208, 2010.[6] J.J. Gomez-Cadenas et al. , “The search for neutrinoless double beta decay,” Riv. Nuovo Cim. ,vol. 35, pp. 29–98, 2012.[7] A.S. Barabash, “Double Beta Decay Experiments,” Phys. Part. Nucl. , vol. 42, no. 4, pp. 613–627,2011.[8] M. Galeazzi et al. , “The Electron Capture Decay of 163-Ho to Measure the Electron Neutrino Masswith sub-eV Accuracy (and Beyond),” arXiv:1202.4763v2 , 2012.[9] G. Drexlin et al. , “Current Direct Neutrino Mass Experiments,” Adv. High , 2013.[10] C. Kraus et al. , “Final Results from phase II of the Mainz Neutrino Mass Search in Tritium β Decay,” Eur. Phys. J. C , vol. 40, pp. 447–468, April 2005.[11] “KATRIN Design Report (FZKA Report 7090),” tech. rep., , KIT,2004.[12] W. K¨afer, “The Windowless Gaseous Tritium Source of KATRIN,” Prog. Part. Nucl. Phys. , vol. 64,pp. 297–299, April 2010.[13] G. Beamson, H. Q. Porter, and D. W. Turner, “The collimating and magnifying properties of asuperconductiong field photoelectron spectrometer,” J. Phys. E , vol. 13, no. 64, 1980.[14] V. M. Lobashev and P. E. Spivak, “A method for measuring the electron antineutrino rest mass,” Nucl. Instrum. Meth. A , vol. 240, no. 2, pp. 305–310, 1985.[15] A. Picard et al. , “A solenoid retarding spectrometer with high resolution and transmission for keVelectrons,” Nucl. Instrum. Meth. B , vol. 63, no. 3, pp. 345–358, 1992.[16] F. Fr¨ankle et al. , “Radon induced background processes in the KATRIN pre-spectrometer,” Astropart. Phys. , vol. 35, no. 3, pp. 128–134, 2011.[17] N. Wandkowsky et al. , “Modeling of electron emission processes accompanying Radon- α -decayswithin electrostatic spectrometers,” submitted to J. Phys. G , 2013.[18] H. Higaki, K. Ito, K. Kira, and H. Okamoto, “Electrons Confined with an Axially SymmetricMagnetic Mirror Field,” AIP Conference Proceedings , vol. 1037, no. 1, pp. 106–114, 2008.[19] S. Mertens et al. , “Background due to stored electrons following nuclear decays at the KATRINexperiment,” Astropart. Phys. vol. 41, no. 52, 2013.[20] J. Wolf, “Size matters: The vacuum system of the Katrin neutrino experiment,” Journal of theVacuum Society of Japan , vol. 52, pp. 278–284, 2009.[21] F. Fr¨ankle, Background Investigations of the KATRIN Pre-Spectrometer . PhD thesis, KarlsruheInstitute of Technologie (KIT), 2010.[22] S. Mertens, Study of background processes in the electrostatic spectrometers of the KATRINexperiment . PhD thesis, Karlsruhe Institute of Technologie (KIT), 2012.[23] N. Wandkowsky, PhD thesis in preparation . Karlsruhe Institute of Technologie (KIT), 2013.[24] S. Mertens et al. , “Stochastic Heating by ECR as a Novel Means of Background Reduction in theKATRIN spectrometers,” JINST et al. , “KASSIOPEIA - the simulation package for the KATRIN experiment,” to bepublished.[26] M. S. Freedman, “Ionization by Nuclear Transitions,” Summer course in atomic physics, Carry-le-Rouet, France , Aug 1975.[27] M. S. Rapaport, F. Asaro, and I. Perlman, “ K -shell electron shake-off accompanying alpha decay,” Phys. Rev. C , vol. 11, pp. 1740–1745, May 1975.[28] M. S. Rapaport, F. Asaro, and I. Perlman, “ M - and L -shell electron shake-off accompanying alphadecay,” Phys. Rev. C , vol. 11, pp. 1746–1754, May 1975.[29] J. Bang and J. M. Hansteen, “Coulomb deflection effects on ionization and pair-productionphenomena,” K. Dan. Vidensk. Selsk. Mat. - Fys. Medd. , vol. 31, no. 13, pp. 1–43, 1959.[30] E. Browne, “Nuclear Data Sheets for A = 215 , , , , Nuclear Data Sheets , vol. 93,no. 4, pp. 763–1061, 2001.[31] S.-C. Wu, “Nuclear Data Sheets for A = 216,” Nuclear Data Sheets , vol. 108, no. 5, pp. 1057–1092, CONCLUSIONS ≤ Z ≤ At. Data Nucl.Data Tables , vol. 20, no. 4, pp. 311–387, 1977.[33] E. Pomplun, “Auger Electron Spectra - The Basic Data for Understanding the Auger Effect,” ActaOncologica , vol. 39, no. 6, pp. 673–679, 2000.[34] J. S. Hansen, “Internal ionization during alpha decay: A new theoretical approach,” Phys. Rev. A ,vol. 9, pp. 40–43, Jan 1974.[35] M. S. Freedman, “Atomic structure effects in nuclear events,” Annu. Rev. Nucl. Sci. , vol. 24.[36] J. H. Verner, “Explicit Runge-Kutta methods with estimates of the local truncation error,” SIAMJ. Numer. Anal. , vol. 15, pp. 772–290, 1978.[37] P. Prince and J. Dormand, “High order embedded Runge-Kutta formulae,” J. Comput. Appl. Math. ,vol. 7, no. 1, pp. 67–75, 1981.[38] C. Tsitouras and S. N. Papakostas, “Cheap error estimation for runge–kutta methods,” SIAM J.Sci. Comp. , vol. 20, no. 6, pp. 2067–2088, 1999.[39] K. Valerius, “The wire electrode system for the KATRIN main spectrometer,” Prog. Part. Nucl.Phys. , vol. 64, no. 2, pp. 291–293, 2010.[40] F. Gl¨uck et al. , “Electromagnetic design of the KATRIN large volume air coil system,” , to bepublished, 2013.[41] F. Gl¨uck, “Axisymmetric electric field calculation with zonal harmonic expansion,” Progress InElectromagnetics Research B , vol. 32, pp. 319–350, 2011.[42] F. Gl¨uck, “Axisymmetric magnetic field calculation with zonal harmonic expansion,” Progress InElectromagnetics Research B , vol. 32, pp. 351–388, 2011.[43] P. W. Hawkes and E. Kasper, Principles of Electron Optics , vol. 1. Academic Press, 1989.[44] J. Liu and S. Hagstrom, “Dissociative cross section of H by electron impact,” Phys. Rev. A , vol. 50,no. 4, 1994.[45] S. Trajmar and D. F. Register and A. Chutjian, “Electron scattering by molecules II. Experimentalmethods and data,” Phys. Rep. , vol. 97, pp. 219–356, 1983.[46] Y.-K. Kim and M. E. Rudd, “Binary-encounter-dipole model for electron impact ionization,” Phys.Rev. A , vol. 50, no. 5, 1994.[47] W. Hwang and Y.-K. Kim and M. E. Rudd, “New model for electron-impact ionization cross sectionof molecules,” J. Chem. Phys. , vol. 104, no. 8, 1996.[48] G. Arrighini, F. Biondi, and C. Guidotti, “A study of the inelastic scattering of fast electrons frommolecular hydrogen,” Mol. Phys. , vol. 41, no. 6, pp. 1501–1514, 1994.[49] Z. Chen and A. Z. Msezane, “Calculation of the excitation cross sections for the Σ + u and C Π + u states in e − H scattering at 60 eV,” Phys. Rev. A , vol. 51, no. 5, pp. 3745–3750, 1995.[50] E. Gargioni and B. Grosswendt, “Electron-Impact Cross Sections for Ionization and Excitation,” http://physics.nist.gov/PhysRefData/Ionization/molTable.html .[51] E. Gargioni and B. Grosswendt, “Electron scattering from argon: Data evaluation and consistency,” Rev. Mod. Phys. , vol. 80, pp. 451–480, 2008.[52] W. Maneschg et al. , “Measurement of extremely low radioactivity levels in stainless steel forGERDA,” Nucl. Inst. Meth. A , vol. 593, pp. 448–453, 2008.[53] X. Luo, L. Bornschein, C. Day, and J. Wolf, “KATRIN NEG pumping concept investigation,” Proceedings of the European Vacuum Conference (EVC-9) , vol. 81, no. 6, pp. 777–781, 2007.[54] S. P. Khare, “Ionizing Collisions of Electrons with Atoms and Molecules,” Radiation Research ,vol. 64, no. 1, pp. 106–118, 1975.[55] G. Zuzel and H. Simgen, “High sensitivity radon emanation measurements,” Appl. Rad. Isot. ,vol. 67, no. 5, pp. 889-893, 2009.[56] H. Simgen, “Radon Background in Low Level Experiments,” talk given at the XIX. KATRINCollaboration meeting , 2010.[57] S. G¨orhardt et al.et al.