Download Study of the Response Function of the CUORE Bolometers towards

Study of the Response Function of the CUORE
Bolometers towards a Neutrinoless Double Beta Decay
Measurement at CUORE
PhD Thesis Project
PhD Candidate: Marco Vignati
Supervisor: Prof. Fernando Ferroni
Università di Roma “La Sapienza”, Dottorato in Fisica, XXII ciclo
1
Introduction
In the last few years very important results have been reached in the study of the neutrinos
and of their properties. The discovery of oscillations and of the non zero neutrino mass
show a reasonably complete picture of this elusive particle [1]. Nevertheless, while precision
measurements on the oscillation parameters are planned for the near future, there are still
two important missing pieces in the neutrino puzzle: the understanding of its nature, Dirac
or Majorana, and the measurement of the absolute mass scale. Neutrinoless Double Beta
Decay (0νDBD) is a unique tool to discriminate the neutrino nature and eventually to
measure its absolute mass. Many different experiments have been proposed and realized in
these years to measure the 0νDBD looking toward the 0.1 − 1 eV neutrino mass region. A
second generation of detectors is now aiming to look inside the 0.01 − 0.1 eV mass region.
The bolometric TeO2 detectors for the search of the 0νDBD of 130 Te play a leading role in
this new generation of detectors. One of the most important advantages of this technique
is that the detector, a TeO2 crystal, contains the 0νDBD emitter (130 Te natural isotopic
abundance is 34%), allowing simple production and operation.
This Ph.D. work is being performed in the framework of the CUORE (Cryogenic Underground Observatory for Rare Events) experiment [2] hosted at Laboratori Nazionali del
Gran Sasso (LNGS). It is a TeO2 array of 988 bolometric detectors of 790g each, arranged
in 19 towers which aims to reach a sensitivity on the neutrino mass better than 80 meV.
Most of the knowledge necessary to operate large mass detectors comes from the experience
of running CUORICINO [3], an array of 62 TeO2 bolometers, that ended the data taking
in June 2008. In the path towards CUORE, which is scheduled to start in 2011, an R&D
on the choice of the materials and on assembly procedures is being performed and two test
runs are scheduled: the Three Tower Run will test three different cleaning techniques for the
copper frames holding the crystals and eventually CUORE0 (CUORE-zero), the first cuore
tower, will test all the assembly procedures.
My thesis will be dedicated to the study of the detector response function and its optimization.
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2
Bolometric Detectors
Conventional techniques for energy deposition measurements are based on the detection of
the energy released in the form of ionization and excitation of the atoms in the detector.
Unfortunately, the amount of energy lost in channels different from the detected ones is quite
large. Most of the energy is converted in phonon excitations inside the detector and it is
not measured. Thermal detectors on the other hand measure the portion of the deposited
energy converted into phonons through the corresponding temperature rise and guarantee
a better intrinsic energy resolution. On the other hand they are slow detectors and cannot
support high rates making these detector suitable only for the search of rare events.
A bolometer consists normally of two main components: the energy absorber, where the
particles deposit their energy, and the sensor, which converts the excitations produced by
the particle into a signal. If we assume that the detector operates as a perfect calorimeter,
the height of the signal corresponds to the ratio between the energy E deposited by the
particle and the heat capacity C of the energy absorber, E/C. The time constant is equal to
the ratio between the heat capacity and the thermal conductance G to the bath, C/G. The
most important parameter of the detector is then the heat capacity that has to be small to
achieve big and fast signals: TeO2 is a diamagnetic and dielectric crystals and therefore its
heat capacity depends only on the lattice contribution, as described by the Debye law:
m T
C(T ) = β
M ΘD
3
(1)
where β = 1944 J K −1 mol−1 , m is the absorber mass, M is the molecular weight and ΘD is
the Debye temperature of the material. Operating at temperatures as low as 10mK CUORE
crystals have an heat capacity of about 10−9 J/K leading to a temperature increase of the
crystal of about 0.2 mK / MeV.
The phonon sensor is a device that collects the phonons produced in the absorber and
generates an electrical signal, proportional to the energy contained in the collected phonons.
A simple realization of this device can be accomplished through the use of a thermistor
whose resistance (R) as a function of the temperature (T ) has a steep slope:
γ
Ta
R(T ) = R0 e( T ) .
(2)
CUORE phonon sensors are Neutron Transmutation Doped (NTD) thermistors whose characteristic parameters are R0 = 1.5 Ω, Ta = 3K and γ = 1/2, their working resistance (R(T0 ))
at T0 = 10 mK is about 50 MΩ. In order to measure a resistance variation thermistors are
biased with constant current, thus the voltage across R is directly proportional to it.
The thermal process in real bolometers is more complicated as one has to take into
account other thermal elements like the conductance of the glue that stick the thermistor on
the crystal, the heat capacity of the crystal supports, their conductance to the heat bath,
the heat capacity of the thermistor and the conductance of its wires with the main bath (see
figure 1).
All these elements vary among different bolometers and make the assembly procedures
not well reproducible: the experience made with CUORICINO shown that the 62 available
bolometers are considerably different in signal shape, gain and resolution. Understanding
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Heat bath ~ 10mK
Thermal coupling
thermistor
Absorber Crystal
Figure 1: Sketch of a bolometer (left) and a Cuoricino bolometer (right).
deeply the physics of these detectors could lead to an improvement in assembly setups and
material choices to reach better resolutions and higher reproducibility. Moreover a faithful
modeling of the detector can be a powerful data-analysis tool as well as a useful item to be
inserted in the MonteCarlo simulations.
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Study of the Bolometer Response Function
In order to model the detector response function one has to take into account all the passages
that from the energy release in the crystal contribute to shape the signal sampled and stored
by the ADC. In order to be competitive with the bolometer resolutions, the model will be
built with an accuracy better than 0.5%. Unfortunately not all the detector parameters
are measurable, and those that are measurable often do not have such accuracy: the model
will be then an effective theory of the bolometer, taking advantage of exactly measurable
quantities and collecting those that are not measurable into parameters that will be fitted on
data. The model is being tested on signals generated by 2615 keV γ particles, an energy close
to the energy of the two electrons emitted in the 0νDBD of 130 Te (2530 keV); an example of
recorded signal generated by this particle impinging on the detector is shown in figure 2.
The first step consists on building a thermal model of the bolometer alone. It is mainly
composed by three items: the crystal, the crystal supports and the thermistor. Each of
these items can be represented as a conductance and a capacitance in parallel as heat can
flow through an object and at the same time can be stored by the object itself. Items are
in turn connected by conductances: the crystal-supports contact conductance and the glue
that stick the thermistor on the crystal. Moreover supports and wires have a conductance
to the main bath so that the crystal thermalizes. The thermal circuit is formally equivalent
to an electrical circuit and can be represented by a system of differential equations: with
the initial condition that the crystal is warm at t = 0 one has to look for the solution
describing the temperature variation of the thermistor in time (∆T (t)). Unfortunately values
of conductances and capacitances are not known with the required precision and so they are
not an input to the model. The solution of the differential system, ignoring the dependancies
of conductances and capacitances on temperature can be expressed as:
t
∆T (t) = A − e− τr + αe
3
− τt
1
+ (1 − α)e
− τt
2
(3)
Voltage (mV)
3000
2500
2000
1500
1000
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (s)
Figure 2: Typical pulse generate by a 2615 keV γ particle.
where all the unknown parameters have been collected into five effective parameters: amplitude (A), rise time (τr ), two decay constants (τ1 and τ2 ) and the weight of the two decays
(0 < α < 1).
The second step consist in describing the conversion of the thermistor temperature variation ∆T (t) into resistance variation Rd (t) by means of the relation (2). While the parameter
γ is constant and known, the parameters R0 and Ta are not well measurable. As a consequence also the detector base temperature T0 cannot be measured with high precision. Again
we have to build an effective model. Below a summary of the made approximations follows.
Measurements we did on a test detector shown that the temperature variation of the thermistor when energy is released in the crystal are very small compared to its base temperature
T0 (∆T /T0 ' 0.5%). The relation (2) can then be expanded as follows:
γ
γ
( Ta ) (1−γ ∆TT0(t) )
( Ta )
R[T0 + ∆T (t)] = R0 e T0 +∆T (t) ' R0 e T0
(4)
We are now interested in the resistance variation:
Rd (t) = R[T0 + ∆T (t)] − R(T0 ),
(5)
γ
reminding that R(T0 ) = R0 e
( TTa0 )
one obtain the following expression for Rd (t):
h
γ ∆T (t)
T0
a)
−γ ( T
T
Rd (t) = R(T0 ) e
0
i
−1
(6)
The advantage of this parametrization is that R(T0 ) can be measured with high precision on
the detector, being the resistance when there are no signals, and that the unknown factor
γ( TTa0 )γ T10 is collected to the thermal amplitude of equation (3).
The third step is the effect of the read-out chain on the bolometer signal. The twisted
wires that carry the signal out of the cryostat have a non negligible capacitance that together
with the thermistor resistance make a lowpass filter (cut-off frequency ∼ 10Hz, depending
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on the wires length and on the bolometer resistance). Moreover a 6-pole Bessel filter (cut-off
frequency 12Hz) is applied on the signal to avoid aliasing effects on the ADC. The voltage
corresponding to Rd (t) is modified in the model taking into accounts these two effects.
The described effective model has been tested by fitting signals of a test detector built
and run in winter 07/08, it gave good results and a detector MonteCarlo has been built upon
it.
This winter I will be involved in the Three Towers Run. I will try to improve the model
accuracy measuring detectors parameters, like base resistances and wires capacitances, with
greater precision. Moreover, participating actively in the data analysis of this run, I will test
the model as energy estimator and pulse shape discriminator, comparing its performances
with the present data analysis tools. As final result, the background level in the energy
region of the 0νDBD will be estimated, providing fundamental informations on the discovery
potential of CUORE.
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Optimization of the Signal Filtering and Acquisition
As mentioned before the Cuoricino ADC is preceded by an analogical Bessel filter to prevent
aliasing effects on the acquired signal. The ADC sampling frequency (fs ) has been chosen
in the past as 125Hz in order to have enough samples to describe the pulse shape and to not
compromise the Signal to Noise Ratio (SNR). The Bessel cut-off (fc ) was put at 12Hz in order
to have enough signal and noise dump at the ADC Nyquist frequency (fs /2), therefore its
value depends strictly on fs . These two frequency were chosen equal for all bolometers. As
each bolometer has its own response function and noise this setup could not be the optimal
one for every single bolometer: each of them will have its own optimal cut-off frequency and
sampling frequency.
Once a detector is mounted and is ready for the data acquisition one has to estimate the
optimal sampling and cut-off frequency for each bolometer and adjust them on the setup:
while the sampling frequency can be easily changed on the DAQ system, changing the cutoff frequency of a Bessel filter cannot be always done with the desired precision as it could
involve a new design and new components.
Digital filters can perform better than analogical filters as one can obtain almost any
desired transfer function that is then translated into an algorithm to be applied at the
sampled signal. A big advantage of digital filters is that the algorithm can be implemented
directly in the DAQ software, therefore adjusting the filter to the desired cut-off frequency
does not involve any hardware change.
I will investigate the feasibility of a new filtering system based on digital filters. The
proposed setup will consist on changing the sampling frequency for an higher value (∼ 1KHz)
prepending an analogical low-pass filter with a cut-off frequency higher than the one used
before (∼ 300Hz). The high frequency sampled signal is then digitally cut at the optimal
fc and then subsampled and saved on disk at the optimal fs . At the moment there are no
data sampled at high frequency so I am developing simulations with a signal generated with
the model described before and a random noise. These simulations will define the method
to find the best digital filter and the optimal fs . The new system will then be tested on the
Three Tower Run acquiring signals and noises at high sampling frequency.
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References
[1] “Neutrino masses and mixings and ...” (A. Strumia and F. Vissani), ArXiv:hepph/0606054.
[2] “CUORE: A Cryogenic Underground Observatory for Rare Events” [CUORE Collaboration] (R. Ardito et al.) ArXiv:hep-ex/0501010.
[3] “Results from a search for the 0νDBD decay of 130 Te” [CUORICINO Collaboration]
(C. Arnaboldi et al.) Phys. Rev. C 78 (2008) 035502
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