International audienceULTIMA is a project which proposes to use superﬂuid 3He as a sensitive medium for direct dark matter search. In this paper we report on new, detailed calibrations of our bolometric cells as a function of the magnetic ﬁeld. An inﬂuence on the order of 20% is observed for magnetic ﬁelds up to 330 mT. Simultaneous measurements of neutron capture and heater events, releasing both a well deﬁned energy, show that the effect is similar for both, and that it is possible to maintain a good calibration by an appropriate correction

Bunkov, Yuriy M.

Collin, Eddy

Elbs, Johannes

Godfrin, Henri

Winkelmann, Clemens

Hal - Université Grenoble Alpes

ULTIMA: Magnetic field dependence of the calibrationfactorJohannes Elbs, Clemens Winkelmann, Yuriy M. Bunkov, Eddy Collin, HenriGodfrinTo cite this version:Johannes Elbs, Clemens Winkelmann, Yuriy M. Bunkov, Eddy Collin, Henri Godfrin. UL-TIMA: Magnetic field dependence of the calibration factor. Journal of Low TemperaturePhysics, Springer Verlag (Germany), 2008, 151, pp.860. <10.2007/s10909-008-9756-z>. <hal-00921388>HAL Id: hal-00921388https://hal.archives-ouvertes.fr/hal-00921388Submitted on 20 Dec 2013HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Noname manuscript No.(will be inserted by the editor)J. Elbs · C. Winkelmann · Yu. M. Bunkov ·E. Collin · H. GodfrinULTIMA: Magnetic field dependence of thecalibration factor18.07.2007Keywords superfluid 3He, bolometry, magnetic field dependenceAbstract ULTIMA is a project which proposes to use superfluid 3He as a sensitivemedium for direct dark matter search. In this paper we report on new, detailed cal-ibrations of our bolometric cells as a function of the magnetic field. An influenceon the order of 20% is observed for magnetic fields up to 330 mT. Simultaneousmeasurements of neutron capture and heater events, releasing both a well definedenergy, show that the effect is similar for both, and that it is possible to maintain agood calibration by an appropriate correction.1 INTRODUCTIONThe basic building block of our bolometers is a closed cell with a small orifice, im-mersed into superfluid 3He at very low temperatures. At temperatures T ≈ 0.15 TC,where TC is the superfluid transition temperature, the heat capacity is small enoughthat if one measures the temperature inside the cell, this can be used for detectingelementary particle events1,2.A substantial advantage of this type of bolometers is the possibility to cali-brate it by direct heating of the quasiparticles by a mechanical moving object. Forthe purpose of both, thermometry and heating, we have used Vibrating Wire Res-onators (VWR). VWR thermometers at ultra low temperatures are well studiedobjects3,4. For the calibrated heat pulses we have used a second VWR also lo-cated in the cell5. The direct calibration procedure makes this type of bolometersa very special particle detector, as it does not rely on a relative or “theoretical"calibration.Institut Néel, CNRS/UJF,25, av. des Martyrs, BP 166, 38042 Grenoble cedex 9, FranceTel.: +33 4 76 88 12 52Fax: +33 4 76 87 50 60E-mail: yuriy.bunkov@grenoble.cnrs.fr2Until now, the magnetic field dependence of this calibration was considered tobe negligible. New measurements show that with fields up to 330 mT, the calibra-tion factor changes by as much as 20%. Even if under usual working conditionsthe magnetic field is limited to about 120 mT, for precise calibrations, magneticfield corrections thus have to be applied.2 BOLOMETRIC CALIBRATION BY HEATER PULSESThe bolometrical cells are 0.13 cm3 copper boxes filled with superfluid 3He-Band linked to an outer 3He-B reservoir by a small orifice. The temperature insidethe cell is monitored by a Vibrating Wire Resonator (VWR). The damping of theVWR is dominated by the interaction with the quasiparticle gas, whose densityexponentially depends on temperature. A frequency sweep over the resonance thusdelivers a Lorentzian whose FWHM W (T ) contains the information about thetemperature. In the zero field limit, W (T ) writes6W (T ) = α exp(−∆/kBT ), (1)where ∆ is the superfluid gap at zero temperature and zero field, and α a prefactorwhich depends on the geometry of the VWR and pressure dependent propertiesof the liquid. For to obtain this equation, the influence of quasiparticles incomingfrom all different directions ˆk has to be integrated. At zero field, where the disper-sion relation is isotropic, the integral is analytic and the above result is obtained.For finite magnetic field, the superfluid gap deforms7 and to get the correspond-ing relation W (T,B), a correction has to be applied to the above formula. Thetheoretical magnetic field dependence W (T,B) has not yet been determined, butmeasurements done by the Lancaster group8 give experimental evidence that fornon zero field, W indeed increases.After a heating event caused for example by a cosmic particle, the tempera-ture inside the cell will suddenly rise, and then go back to its initial temperatureby thermalisation via the hole. A method used to simulate such an event is to in-troduce by a second VWR a well known energy by mechanical friction2,9 (seefig. 1) For small enough pulses, the height of the resulting peak (H, in Hz) is pro-portional to the heat injected (E), and we can define the calibration coefficient asσ = H/E. A detailed calculation shows that this calibration coefficient is propor-tional to the temperature derivative of W (T ), W ′(T ) and inversely proportional tothe heat capacity (C) :σ =1CdW (T )dT =1CW ′(T ). (2)The heat capacity is dominated by the quasiparticle gas. As the total number ofquasiparticles strongly depends on the gap, a distortion of the gap should modifythis term too, so that the magnetic field dependence of the calibration coefficientis the result of both factors, C and W ′, depending on magnetic field.For zero field, the temperature dependence for both factors is known, and aremarkable feature of this kind of bolometer is that the exponential temperaturedependence cancels, and a weak 1/√T dependence is expected, meaning that thecalibration factor does not change much over the temperature range of interest.3Fig. 1 (Color on-line) Example of a typical heater pulse. The heater wire is excited during ashort time (80 ms) with a current I (inset, red bold line). The VWR starts to move and induces avoltage U (inset, black dashed line). The total energy E injected is obtained as the integral overthe product E =∫UIdt. At the same time, an increase of the width on the thermometer VWRcan be observed (black circles). The peak shape is well understood and can be fitted (red line).After some corrections 5, the peak height divided by the energy gives the calibration factor σ .Fig. 2 (Color on-line) Calibration factor for different baseline widths and magnetic fields(29.3 bar). The exact conversion between W (T,B) and the temperature is only known for B =0 T,so that the temperature scale on the top only has indicative character. For constant magnetic field,the expected 1/√T dependence is found.43 MAGNETIC FIELD DEPENDENCEThe working temperatures down to 130 µK are reached using a nuclear demag-netisation cryostat. We use a Lancaster style nuclear stage, so that the experimentalcells are in the main coil, and the magnetic field is the final field of the demagneti-sation. This in turn means that changing the field without changing the temperatureis impossible. Changing the temperature at constant field can be done by heating,but due to the huge solid liquid thermal boundary resistance (Kapitza resistance),thermalisation after such heating takes to long time (>3 h). The most efficientmethod which was found was to change the magnetic field stepwise and measureat the resulting temperature. Fig. 2 presents the results from calibration pulses, alltaken during one demagnetisation run. The data are taken at different “baselinewidths”, i.e. the equilibrium VWR width W0 observed between events. Each pointcorresponds to a total of 25 heater pulses with different heating powers. The cal-ibration factor σ is then taken as the slope in the peak height-energy plot. It canbe clearly seen that the magnetic field has a systematic influence. The magneticfield dependence of σ for constant temperature would be interesting for a quan-titative study of this phenomena, but unfortunately no independent thermometryexists, and the field correction for the VWR width is not known. In fig. 3, σ−1 asfunction of magnetic field is plotted for three different baseline widths. This graphas well as similar graphs for other W0 show linear behavior, with almost the sameslope for the different temperatures. The total of experimental results can thus bedescribed well byσ(W,B) =β√T (W )· 11+ γB , (3)where β is a constant which depends on superfluid 3He parameters and the VWRgeometry, T (W ) is the temperature as obtained using the zero field formula (eq. 1),and γ a phenomenological constant.4 DISCUSSIONThe presented results were taken at 29.3 bar, because at higher pressures, the su-perfluid transition temperature TC is higher and a higher field range can be mea-sured. Measurements at lower pressures qualitatively show the same behavior.The linear dependence in B for constant baseline width is at first very surpris-ing, especially because one expects for symmetry reasons a quadratic correction infield for both, the specific heat and the VWR width. Preliminary numerical sim-ulations however show that under certain conditions, quadratic field correctionsfor constant temperatures can lead to a linear correction of calibration factor forconstant baseline width. More detailed simulations are still a work in progress.A second method which can be used for calibration is to use a neutron sourcefor the production of nuclear capture reactions. This reaction releases a well de-fined energy of about 764 keV, of which about 652 keV are transfered to heat.Using this second method and applying at the same time heater pulses demon-strates that the influence of the magnetic field is not limited to heater pulses. This5Fig. 3 (Color on-line) 1/σ for three different, almost constant baseline widths W0. Similargraphs at different W0 indicate that for the whole measured range 0.2 to 20 Hz, 1/σ is linearwith magnetic field strength: σ(W0 = cst) ∝ 1/(1 + γB). The precision is not sufficient to con-clude whether or not γ varies with W0 but in any case, the dependence is rather weak.is a very important observation for the ULTIMA project, as it shows that the influ-ence of the magnetic field introduces an additional correction factor which needsto be considered, but that it does not prevent achieving a proper energy calibration.To conclude, we observed a magnetic field dependence of the calibration fac-tor. While a complete numerical understanding is still missing, a phenomenolog-ical characterisation is possible. Accounting for this effect opens the way for afuture dark matter detector with an accurate energy resolution.ACKNOWLEDGMENTSThis work was done in the framework of the ULTIMA project of the “Agence Na-tionale de la Recherche", France. We are thankful to the ESF Program COSLABfor many stimulating discussions during workshops and conferences.References1. D. I. Bradley, Yu. M. Bunkov, D. J. Cousins, M. P. Enrico, S. N. Fisher, M. R.Follows, A. M. Guénault, W. M. Hayes, G. R. Pickett and T. Sloan, Phys. Rev.Lett. 75 1887 (1995)2. C. Bäuerle, Yu. M. Bunkov, S. N. Fisher and H. Godfrin, Phys. Rev. B 57,14381 (1998).3. A. M. Guénault, V. Keith, C. J. Kennedy S. G. Mussett, and G. R. Pickett, J.Low Temp. Phys. 62, 511 (1986)4. C. B. Winkelmann, E. Collin, Yu. M. Bunkov and H. Godfrin, J. Low Temp.Phys. 135, 3 (2004)65. C. B. Winkelmann, J. Elbs, E. Collin, Yu. M. Bunkov and H. Godfrin, Nucl.Instr. and Meth. A 574, 264 (2007)6. S. N. Fisher, G. R. Pickett and R. J. Watts-Tobin, J. Low Temp. Phys. 83, 225(1991).7. L. Tewordt N. and Schopohl, J. Low Temp. Phys. 37, 421 (1979)8. D. I. Bradley, S. N. Fisher, A. M. Guénault, R. P. Haley, H. Martin, G. R.Pickett, J. Low Temp. Phys. 138, 583 (2005)9. S. N. Fisher, A. M. Guénault, C. J. Kennedy and G. R. Pickett, Phys. Rev. Lett.69, 1073 (1992).

ULTIMA: Magnetic ﬁeld dependence of the calibration factor

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ULTIMA: Magnetic ﬁeld dependence of the calibration factor

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