IN
DEGREE PROJECT
ENGINEERING PHYSICS,
SECOND CYCLE, 30 CREDITS
,
STOCKHOLM SWEDEN 2021
Heat dissipation due to
microvibrations in low temperature
experiments
Heat dissipation due to microvibrations in low
temperature experiments
Julien WITWICKY
Degree Project in Engineering Physics (30 ECTS credits)
Master’s programme in Nuclear Energy Engineering (120 ECTS credits)
KTH Royal Institute of Technology 2021
Date: March 10, 2021
TRITA-SCI-GRU-2021:017
Royal Institute of Technology
School of Engineering Sciences
KTH SCI
Acknowledgements
First of all, I would like to thank Ivan who supervised my master’s project, with a lot of availability and good mood. I enjoyed working and discussing with him and learned a lot from him, both technically and scientifically. His help was also very precious for the writing of this master thesis.
I then warmly thank Alexandre, Laurent and Jean-Louis. It is thanks to their work that the experimental aspects of my master’s project could run in the best conditions. They also taught me about cryogenics and some manipulations related to it.
More generally, thanks to all the people of the low temperature service (DSBT) with whom I had the pleasure to exchange. I also would like to thank the researchers from CNES (France) and SRON (Netherlands) who followed the progress of my master’s project.
Abstract
Ultra-sensitive photodetectors on-board space missions need very low temperatures to keep a good resolution. Cryo-coolers, such as pulse-tubes, help maintaining these conditions within a cryostat. In return however, they generate micro-vibrations. These micro-vibrations dissipate enough heat to cause temperature fluctuations at the detector’s support, thus lowering the de-tector’s resolution. The first objective is to establish a test bench almost from scratch. The test bench includes a dummy representing the detector’s support. The next objectives is to verify that we can measure heat dissipation at the dummy, corresponding to very low values of power ; and finally, to find a link between mechanics and heat dissipation. The dummy consists of a mass suspended by Kevlar chords and is mounted on the cold plate of a cryostat. From the cryostat enclosure, we were able to generate micro-vibrations at the suspended mass and to carry out acceleration and temperature measurements. At 4 K, we were able to measure heat dissipation only around the suspended mass resonance modes. As a first quantitative result, we found that an acceleration of thousands µg (g is the gravitational acceleration) on the cold plate dissipates hundreds of nano-watts. However, these are preliminary results and we will need to improve the test bench for future measurement campaigns.
Sammanfattning
Ultrak¨ansliga fotodetektorer ombord rymduppdrag beh¨over mycket l˚aga temperaturer f¨or att h˚alla en r¨att uppl¨osning. Kryokylare, s˚asom pulse-tubes, hj¨alper att uppr¨atth˚alla dessa f¨orh˚allanden i en kryostat. I geng¨ald genererar de dock mikrovibrationer. Dessa mikrovibra-tioner sl¨apper ut tillr¨ackligt med v¨arme f¨or att orsaka temperatursv¨angningar vid detektorns st¨od, vilket s¨anker detektorns uppl¨osning. Det f¨orsta m˚alet ¨ar att uppr¨atta en testb¨ank fr˚an grunden. Testb¨anken inneh˚aller en dummy som representerar detektorns st¨od. N¨asta m˚al ¨ar att kontrollera att vi kan m¨ata v¨armeavledning vid dummy, vilket motsvarar mycket l˚aga ef-fektv¨arden. Sista m˚al ¨ar att hitta en l¨ank mellan mekanik och v¨armeavledning. Dummy best˚ar av en massa som ¨ar upph¨angd av Kevlar och ¨ar monterad p˚a en kryostats kallplatta. Fr˚an kryostath¨oljet kunde vi generera mikrovibrationer vid den upph¨angda massan och genomf¨ora accelerations- och temperaturm¨atningar. Vid 4 K kunde vi bara m¨ata v¨armeavledning runt upph¨angda massans resonansl¨agen. Som ett f¨orsta kvantitativt resultat, uppt¨ackte vi att en ac-celeration p˚a tusentals µg (g ¨ar tyngdaccelerationen) p˚a kylplattan f¨orsvinner hundratals nano-watt. Detta ¨ar dock prelimin¨ara resultat och vi kommer att beh¨ova f¨orb¨attra testb¨anken f¨or framtida m¨atkampanjer.
Abbreviations
4 K Boiling point of4He, which is more precisely around 4.2 K
77 K Boiling point of nitrogen
300 K Room temperature which is actually between 290 and 300 K
AFG Arbitrary Function Generator
CEA Commissariat `a l’Energie Atomique et aux Energies Alternatives
CNES Centre National d’Etudes Spatiales
PHD Partial Harmonic Distorsion
RMS Root Mean Square
RRR Residual Resistivity Ratio
SRON Space Research Organisation Netherlands
THD Total Harmonic Distorsion
Contents
List of Figures viii
1 Introduction and Theory 1
1.1 Background and objectives . . . 1
1.2 Cryostat operation . . . 1
1.2.1 Principle . . . 1
1.2.2 The cold plate . . . 3
1.2.3 Cooling . . . 3
1.3 Resonance . . . 5
2 Material and Methods 6 2.1 Micro-vibrations . . . 6
2.1.1 Characterisation of the piezoelectric actuator . . . 6
2.1.2 Electrodynamic shaker characterisation . . . 8
2.2 Study object . . . 9
2.3 Test configuration . . . 12
2.3.1 Choosing the configuration . . . 12
2.3.2 The heat switch . . . 13
2.4 Instrumentation . . . 15
2.4.1 Cryogenic sensors and heaters . . . 15
2.4.2 Four-wire measurement . . . 16
2.4.3 Cold plate instrumentation . . . 17
2.5 Mechanical characterisation . . . 19
2.5.1 Mechanical response . . . 19
2.5.2 Modal characterisation . . . 19
2.6 Thermal characterisation . . . 20
2.6.1 Measuring the dissipated power . . . 20
2.6.2 Dissipation as a function of the shaking frequency . . . 21
2.6.3 Dissipation as a function of the acceleration . . . 22
3 Results and Discussion 22 3.1 Shakers characterisation . . . 22
3.1.1 Piezoelectric actuator characterisation . . . 22
3.1.2 Electrodynamic shaker characterisation . . . 24
3.2 Mechanical characterisation . . . 25
3.2.1 Mechanical response . . . 25
3.2.2 Resonances . . . 28
3.2.3 Modal characterisation . . . 29
3.3 Thermal characterisation . . . 30
3.3.1 Dissipation as a function of the shaking frequency . . . 30
3.3.2 Dissipation as a function of the cold plate acceleration . . . 31
3.3.3 Resistance of the copper strap and thermal switch assembly . . . 33
4 Conclusion 35
References 36
List of Figures
1 The cryostat used in this study and its longitudinal section. . . 2
2 The cold plate of the cryostat and its instrumentation. . . 3
3 The elements used for the cooling of the cryostat. . . 4
4 A secondary pump consisting of vanes. . . 4
5 The Cedrat Technologies APA400MML piezoelectric actuator. . . 6
6 The piezoelectric actuator with the added mass, and a cryogenic accelerometer mounted to it. . . 7
7 The characterisation bench of the piezoelectric actuator. . . 7
8 Control and measurement chain for the characterisation of the piezoelectric actuator. 8 9 The PCB Piezotronics K2007E01 electrodynamic shaker. . . 9
10 A 3D model and a photo of the study object. . . 10
11 The suspended mass with the added fins and the accelerometers attached to it. . 11
12 The final study object and the chosen orthonormal marker. . . 11
13 On the left: the cooling curve without adding a copper strap. On the right: the cooling curve with a copper strap (length: 10 cm, diameter: 1 mm, residual resistivity ratio: 50). . . 13
14 The three considered configurations. . . 13
15 A thermal switch made at CEA/Grenoble for the Planck project. . . 14
16 The operation of a thermal switch (Lionel Duband, CEA/Grenoble). . . 14
17 The PCB Piezotronics J351 B41 cryogenic accelerometer. . . 15
18 A LakeShore CX-1030-CU cryogenic thermometer. . . 16
19 The Vishay SFR 25 (402 Ω, mounted on the cold plate and the thermal switch pump) and PTF (5 kΩ, mounted on the suspended mass) resistors, used as heaters. 16 20 The four-wire measurement. . . 17
21 The equipped cold plate, with the chosen marker. . . 17
22 Instrumentation of the cold plate. Each module (numbered from 1 to 9) consists of 3 outlets, each connected to 4 wires (numbered from 1 to 12). . . 18
23 The study object with the thermometer circled in red. The heater is not visible but is fixed underneath the suspended mass as indicated by the red arrow. . . 18
24 The translation mode along X, the rotation mode around Y and their correspond-ing Lissajous curves. . . 20
25 Variation of the suspended mass temperature during measurements. The first variations correspond to periods of micro-vibrations (increase) and rest periods (decrease). The last temperature rise corresponds to a calibration with the heater on the suspended mass. . . 21
26 The piezoelectric actuator response between 50 Hz and 2.7 kHz. . . 22
27 On the left: the maximal PHD of the piezoelectric actuator as a function of the shaking frequency. On the right: the maximal PHD as a function of the acceleration of the piezoelectric actuator, for several frequencies. . . 23
28 Waveform of the piezoelectric actuator shaking at 80 Hz. . . 23
29 The electrodynamic shaker response between 20 Hz and 3.3 kHz. . . 24
30 Maximal partial harmonic distortion rate of the electrodynamic shaker as a func-tion of frequency over a range from 20 Hz to 3.3 kHz for a 37 mV peak-to-peak sinusoidal signal injected by the GBF. . . 25
31 The suspended mass mechanical response between 100 and 400 Hz, at 300 K. . . 26
32 The suspended mass mechanical response between 100 and 400 Hz, at 77 K. . . . 26
34 The suspended mass mechanical responses between 100 and 400 Hz, at 300, 77
and 4 K. . . 27
35 The suspended mass main resonances measured in the X axis. . . 28
36 A lower resonance measured in the X axis. . . 28
37 The three resonances measured in the X axis. . . 29
38 The Lissajous curves for the 185 Hz mode (left) and the 260 Hz mode (right). . . 30
39 The power dissipated at the suspended mass as a function of the shaking frequency. The acceleration on the cold plate is 519 µg around 184 Hz and 1.66 mg around 259 Hz. . . 30
40 The dissipated power and the acceleration on the suspended mass as a function of the shaking frequency. . . 31
41 The power dissipated at the suspended mass as a function of the acceleration on the cold plate. The red point is theoretical: there is no dissipation at rest. . . 32
1
Introduction and Theory
1.1
Background and objectives
The X-IFU instrument (X-ray Integral Field Unit) is an ultra-sensitive detector which aims to measure X-rays from black holes during the Athena space mission (http://x-ifu.irap.omp. eu/). This kind of detector requires very low temperatures to keep a good resolution. This is why we must place it inside a cryostat, where we can drop the temperature down to a few tens of milli-kelvin.
Previous missions used solely liquid nitrogen and helium baths as cold sources [1], but the cryogenic fluids evaporate as they exchange heat. Thus the mission’s lifetime depended only on the volume of cryogenic fluids. Today, this kind of space missions use cryo-coolers to transform electrical power generated by the solar panels of the probe into cooling power, which extends the mission’s lifetime. However, the operation of these cryo-coolers generates micro-vibrations. The micro-vibrations dissipate small amounts of heat close to the detector, lowering the detector’s resolution [2].
This study aims to characterise the link between micro-vibrations and dissipation in a cryo-genic system working at very low temperatures (4 K). This topic is quite new, thus the study is very exploratory and rather bases on measurements than on literature. We made this measure-ments thanks to a test bench we designed from scratch. This test bench relies on a cryostat used by the laboratory for previous researches related to the Herschel mission [3].
1.2
Cryostat operation
1.2.1 Principle
The cryostat we use in this study, lies on a support on which it can pivot, so we can test objects along and against the gravity (this point is not used in the study). This is also useful for modifying the instrumentation of the cold plate when the cryostat is warm and open. The cryostat works with two cryogenic fluids:
- liquid nitrogen, boiling at 77 K at the atmospheric pressure, - liquid helium (4He), boiling at 4.2 K at the atmospheric pressure.
Two separate tanks are filled with those fluids. Each tank is thermally coupled with a screen that protects what is inside from the thermal radiation coming from outside the screen. This is based on Stefan-Boltzmann’s law. The radiation of an emissivity body is proportional to T4 according to Stefan-Boltzmann’s law :
Φ = σT4, (1)
where Φ is the surface heat flux, the emissivity, σ the Stefan-Boltzmann constant, and T the body temperature.
The nitrogen bath (60 L for our cryostat) is thermally coupled with a screen (called ni-trogen, 77 K or 80 K screen). The screen receives radiation in 3004 while what is shielded by the
screen only receives radiation in 774, since the nitrogen screen is at 77 K. Now, Φ(300)/Φ(77) =
3004/774 = 230: there are two orders of magnitude of power received by radiation between the
The helium bath (32 L for our cryostat) is thermally coupled with the cold plate used as a sup-port for the instrumentation and the objects to be tested. It is also coupled with another screen (helium or 4 K screen) used to insulate what is inside the screen from the radiation coming from the nitrogen screen. According to Stefan-Boltzmann’s law, Φ(77)/Φ(4.2) = 774/4.24= 1.13×105
and there are five orders of magnitude of power received by radiation between what is between the two screens and what is inside the helium screen. It allows the test objects to be insulated as much as possible and yields a better measurement.
Figure 1: The cryostat used in this study and its longitudinal section.
The figure above shows that the cryostat actually consists of a succession of thermal barriers:
1.2.2 The cold plate
The cold plate is a thick copper plate inside the cryostat. It is covered with a thin layer of gold, preventing the copper from oxidising and improving the thermal contact with the objects mounted on it. This plate is thermally coupled to the helium bath, as is the 4 K screen. The outer part of the 4 K screen is also covered with gold, and the inner part is covered with a black coating of high emissivity (therefore close to a black body). The function of this black coating is to trap any residual radiation coming from temperatures above 4 K.
Figure 2: The cold plate of the cryostat and its instrumentation.
The cold plate (Figure 2) serves as a support for the study object and the measuring instruments. The cryostat is only a container in which we maintain very cold temperatures for the cold plate and what is mounted on it.
1.2.3 Cooling
It takes several stages to cool the cryostat down:
- making vacuum inside the cryostat, - cooling to 77 K with liquid nitrogen, - cooling to 4 K with liquid helium.
Figure 3: The elements used for the cooling of the cryostat.
Before filling the tanks with the cryogenic fluids, we need to create vacuum inside cryostat in order to insulate it from the outside (stopping convection and gas conduction). To do this, we use a pump which has two operating modes:
- primary pumping (viscous regime): the molecules are in large numbers in the cryostat and interact with each other. They behave like a viscous fluid.
- Secondary pumping (molecular regime) occurs once the pressure is low (about 10−4 mbar), to the point that the molecules become rare and thus rarely interact with each other. The principle is to rely instead on their interactions with the walls of the cryostat and the pump. In order to pump these molecules out of the cryostat, vanes (Figure 1 and Figure 4) rotate very fast (around 104 revolutions per second) at the inlet of the pump pipe, drawing the molecules back towards the primary pump. Otherwise, the molecules would bounce back towards the cryostat.
Figure 4: A secondary pump consisting of vanes.
the cold plate temperature to drop to 77 K.
Once the cold plate is at 77 K, we can finally begin to cool it down to 4 K (actually around 4.2 K which is the boiling temperature of helium-4). To do so, we use a liquid helium vessel to fill the helium tank of the cryostat. A bottle of pressurised helium gas is also connected to the helium vessel to keep the vessel pressurised and ensure a correct flow rate from the vessel to the tank. At the start of the filling, the liquid helium quickly becomes gaseous, for the temperature inside the cryostat is above the its boiling point. Thus it is first helium gas that continues to cool the cryostat down. Once the cryostat is sufficiently cold, the helium stops boiling and the tank begins to fill with liquid helium.
As the first drop of liquid helium appears in the tank, the cold plate temperature brutally drops to 4.2 K. Once the cryostat has dropped to this temperature, we can stop the pump, although molecules are persisting in the cryostat or desorbing from its walls. Indeed, due to its very low temperature, the helium bath acts as a secondary pump by adsorbing the atoms or molecules that are still present in the cryostat. This phenomenon is called cryo-adsorption. It is thanks to this phenomenon that the vacuum within the cryostat is maintained at this level.
In spite of the vacuum within it, the cryostat continues to have slight heat losses by con-duction (support, filling pipe and gas recovery pipe) and by radiation. Thus, the cryogenic liquids are boiling and it is necessary to regularly refill the nitrogen and helium tanks as long as the cryostat must remain cold. Given the volume of the tanks and the rate of consumption of the cryogenic fluids, it is necessary to replenish the tanks with liquid nitrogen every 2-3 days and liquid helium approximately every week.
1.3
Resonance
The physical quantity we use to characterise the intensity of the vibrations is the acceleration. In this study, the acceleration is given in units of standard gravity, noted g, which is equivalent to 9.81 m/s2in France.
At an object’s resonance, the energy accumulates. In other words, the object vibrates much more at resonance frequencies than at other ones. Resonance frequencies are associated with different modes of resonance. There are generally 6 main modes for simple objects: 3 translation modes along the 3 axes and 3 rotation modes around the 3 axes. These resonances are of major importance in this study because we expect to observe most of the heat dissipation at these frequencies.
The resonance frequency fR of an object varies according to the following formula :
fR∝ 1 2π r k m, (2)
where k is the stiffness and m the mass of the object.
2
Material and Methods
Thereafter, every data are given in root mean square (RMS) value, except in exceptional cases, in which case this will be specified. As a reminder, the RMS value of a signal S is the square root of its mean square :
SRM S=
√
< S2>. (3)
2.1
Micro-vibrations
We need to generate vibrations, simulating the very micro-vibrations caused by the cryo-coolers (pulse-tubes, Joule-Thomson cycle machines) during space missions. The choice of the shaker is important: it must be able to induce a low, yet measurable acceleration on the dummy representing the detector (later called the suspended mass). In addition, the signal must be sufficiently pure in terms of harmonic content: in other words, the amplitude of each harmonic must be as low as possible. The shakers we want to use in this study cannot stand cryogenic temperatures and must be mounted outside the cryostat. Thus the vibrations are not generated directly on the dummy but transmit from the cryostat enclosure to the cold plate and finally to the dummy. Two different shakers were tested in order to chose the best candidate: a piezoelectric actuator and an electrodynamic shaker.
2.1.1 Characterisation of the piezoelectric actuator
The piezoelectric actuator is the first shaker we used, since it was available at the beginning of the master’s project. The model is the APA400MML from Cedrat Technologies below.
Figure 5: The Cedrat Technologies APA400MML piezoelectric actuator.
This shaker bases on piezoelectricity, a property of some crystals. A piezoelectric crystal gener-ates an electrical charge as it is under strain: this is called the direct piezoelectric effect. The polarisation of the charge depends on the direction of the strain. This phenomenon coexists with the reverse piezoelectric effect: the same crystal deforms as it is under an electric field. The polarisation of the electric field controls the direction of the deformation. The piezoelectric actu-ator consists of a structure surrounding the piezoelectric crystal, amplifying the motion obtained thanks to the reverse piezoelectric effect.
Figure 6: The piezoelectric actuator with the added mass, and a cryogenic accelerometer mounted to it.
To characterise the piezoelectric actuator response, we attach the piezoelectric actuator to a suspended support, to free it as much as possible from the surrounding (table, floor). A seismic accelerometer (its sensitivity is 1 V/g) is mounted on the piezoelectric actuator (Figure 6). This accelerometer measures the acceleration on the shaker. It gives knowledge of the piezoelectric actuator response to an input signal delivered by the arbitrary function generator (AFG).
Figure 7: The characterisation bench of the piezoelectric actuator.
The measurement bay (Figure 7) contains an oscilloscope and a spectrum analyser. These are two powerful measuring devices. The spectrum analyser yields the Fast Fourier Transform (FFT) of the signal. The spectrum shows all amplitude peaks, including the potential harmonics. It is also possible to read the amplitude of each peak.
The diagram below (Figure 8) shows the control and measurement chain between the various devices and instruments.
Figure 8: Control and measurement chain for the characterisation of the piezoelectric actuator.
An arbitrary function generator (Tektronix AFG 3022) delivers a sinusoidal signal, which is first amplified by a linear amplifier (Cedrat Technologies LA75A), finally inducing a sinusoidal movement to the piezoelectric actuator. This movement generates vibrations on any object in direct or indirect contact with the latter. A conditioner is used as an amplifier to power the accelerometers. In return, the accelerometers send their signal (due to the direct piezoelectric effect described previously) back to the conditioner. We can read this signal at the output of the conditioner via the oscilloscope or the spectrum analyser.
Preliminary measurements revealed harmonics in the piezoelectric actuator response: in other words, the signal is not always purely sinusoidal. The spectrum analyser makes these interference frequencies clearly visible. To characterise this harmonic content, we introduce the partial har-monic distortion rate of the i-th harhar-monic (P HDi), which is the ratio between the i-th harmonic
amplitude and the amplitude of the fundamental (which is by definition the first harmonic):
P HDi(f ) =
hi(f )
h1(f )
, (4)
where hi(f ) is the amplitude of the i-order harmonic of the frequency f .
In order to characterise the harmonic content of the piezoelectric actuator’s response, we record the amplitudes of the fundamental and of the highest harmonic. Then, we use this data to plot the maximal partial harmonic distortion (P HDmax) versus the shaking frequency. We could
have plotted the total harmonic distortion (T HD, by definition the sum of all P HDi), but this
would have been complicated because we wouldn’t have known at which harmonic to stop.
2.1.2 Electrodynamic shaker characterisation
Figure 9: The PCB Piezotronics K2007E01 electrodynamic shaker.
Like the piezoelectric actuator, it is possible to control the intensity of the signal via the arbitrary function generator. The amplifier, however, is directly included in the device. This signal causes the moving part of the shaker to vibrate. We also mount an epoxy glass rod on this moving part to generate the vibrations precisely on what is in contact with the rod. Instead of this rod, it is also possible to mount an accelerometer on the moving part. We use this feature to characterise the electrodynamic shaker.
To characterise this shaker, we carry out the same measurements as for the piezoelectric actuator, with more or less the same measuring bay and chain (Figures 7 and 8). Then we compare the characterisations of both shakers. The measurements are about searching potential resonances between 20 Hz and 3.3 kHz and characterising the harmonic distortion. The frequency range is very wide because we want to find a resonance. Later in the study however, we won’t make measurements with shaking frequencies higher than 500 Hz. The AFG delivers a sinusoidal voltage of 37 mV peak-to-peak to the shaker. It corresponds to the manufacturer’s recommen-dation to start the characterisation with a certain acceleration on the vibrating part at 100 Hz: 500 mg in this case. We record both the fundamental and the highest harmonic amplitudes at several frequencies in the [20 Hz, 3.3 kHz] range. We use this data to plot the electrodynamic shaker response and the maximal partial harmonic distortion, as for the piezoelectric actuator.
2.2
Study object
Figure 10: A 3D model and a photo of the study object.
The model consists of a stainless steel frame and an aluminium barrel suspended from this frame. The mass is suspended by 0.29 mm diameter Kevlar chords, a thermally insulating and highly resistant material. The Kevlar chord is a twist of two strands which are themselves made up of several strands. The diameter of 0.29 mm is actually the effective diameter, i.e. the diameter that a single cylindrical wire would have if it had the same mass as the two twisted strands Kevlar wire. The Kevlar hanging system is made of a single Kevlar thread, although it looks like the mass is suspended by 16 chords. Indeed, return pulleys are used on the suspended mass and on the frame to guide the wire between different return trips (16 in total). Both ends of the wire are hooked onto the frame using capstans. One of the two ends is taut thanks to a screw and a clicking system that allows the Kevlar thread to be put under tension. The pulleys and capstans are made of Ta6V alloy, a titanium alloy containing aluminium and vanadium among others.
The frame serves primarily as an attachment point for the suspended mass. It also acts as an interface between the suspended mass and the cold plate of the cryostat. The suspended mass and the Kevlar however are the core of this study: Kevlar chords play an important role in power dissipation due to micro-vibrations, and we measure the temperature and thus the dissipation on the suspended mass.
Figure 11: The suspended mass with the added fins and the accelerometers attached to it.
Finally, we realised after preliminary tests carried on the cryostat that the resonance frequencies of the suspended mass were likely to fall into a frequency range where the cryostat transmits little vibration. In order to prevent possible difficulties or even the impossibility of carrying out measurements around these resonance frequencies, we decided to ballast the suspended mass, thus lowering its resonance frequencies (Figure 12).
Figure 12: The final study object and the chosen orthonormal marker.
2.3
Test configuration
2.3.1 Choosing the configuration
The micro-vibrations dissipate heat because of the friction at the Kevlar chords (between the strands composing the chord and at the fasteners). If the suspended mass is thermally insulated from the cold plate, it can no longer be cooled effectively and this power dissipation causes a potentially measurable rise in temperature.
In order to carry out heat dissipation measurements properly, we must define a configu-ration which could possibly include other elements in addition to the study object mounted on the cold plate. The challenge is twofold: the suspended mass must be sufficiently thermally insulated to make the slight heat dissipation due to the micro-vibrations measurable. On the other hand, we must be able to cool the suspended mass in a reasonable time. It implies, on the contrary, that there must be a good thermal conduction between the suspended mass and the cold plate.
In the first instance, two configurations were considered:
- the mass suspended by the Kevlar chords,
- the mass suspended by the Kevlar chords and thermally connected to the cold plate by a copper strap.
In the first configuration, the only thermal link between the suspended mass and the cold plate are the Kevlar chords. Kevlar is a very poor thermal conductor, thus insulating the sus-pended mass. This is an advantage to carry out the measurements. However, this configuration also raises major problems of cooling time: it would theoretically take tens of days to cool the suspended mass down from the ambient temperature. This cooling time was estimated thanks to simulations based on a simplified model of the configuration (Figure 13).
Figure 13: On the left: the cooling curve without adding a copper strap. On the right: the cooling curve with a copper strap (length: 10 cm, diameter: 1 mm, residual resistivity ratio: 50).
We want to keep only the advantages of both configurations. Thus the system must operate as the second configuration during the cooling and as the first one during the measurements. We can do this by adding a heat switch between the copper strap and the cold plate (Figure 14). The heat switch can either be a good conductor or a bad one. This is explained further in the next section.
Figure 14: The three considered configurations.
With this system, the cooling time should remain short as the heat switch is turned on. Once the heat switch is turned off, it should conduct much less, but still more than the Kevlar chords. In other words, it should give enough sensitivity for the heat dissipation measurements, but not as much as the configuration with only the Kevlar chords. This new configuration has other disadvantages. The added elements (copper strap and thermal switch) are in direct contact with the suspended mass. Thus, we could measure their resonances and mistake them with the suspended mass resonances. Furthermore, there is also a risk that one of these elements may heat up more than the suspended mass and thus influence the measurement of the suspended mass temperature. However, this configuration is the best compromise we have. We will use it for the measurements and take its disadvantages and risks into account.
2.3.2 The heat switch
is closed and cold, it is no longer possible to manually modify the cold plate instrumentation without reopening it. For instance, it is impossible to place a copper thermal link between the cold plate and the suspended mass and then remove it once the suspended mass has been lowered to 4.2 K. The advantage of the thermal switch is the possibility to change its operating mode without having to intervene manually.
Figure 15: A thermal switch made at CEA/Grenoble for the Planck project.
Figure 16: The operation of a thermal switch (Lionel Duband, CEA/Grenoble).
thermal junction between the two copper parts. The advantage of this thermal switch is that it is possible to control the presence or absence of this gas between the two copper cylinders. The OFF or ON position of the thermal switch is controlled via a heater attached to an adsorption mini-pump. The latter is made of activated carbon which adsorbs helium-3 very well under a certain temperature (cryo-adsorption). At very low temperatures, the activated carbon retains the helium-3 gas: the switch is off. Slightly heated (around 25 K for the heat switch used in this study), the activated carbon releases the previously adsorbed gas and thus re-establishes the thermal link: the switch is on. The conduction ratio between the ON and OFF position can be higher than 6000.
2.4
Instrumentation
2.4.1 Cryogenic sensors and heaters
Most of the accelerometers used in this study are cryogenic accelerometers (Figure 17). They contain a piezoelectric crystal that remains sensitive under cryogenic conditions and are equipped with a cryogenic amplifier, limiting the noise on the measurement chain, thus allowing measure-ments to be under cryogenic conditions. Their sensitivity is 100 mV/g (±10%). Since the noise of these accelerometers, measured with the spectrum analyser, can reach 10 µV, it is possible to measure accelerations down to values of the order of 100 µg.
Figure 17: The PCB Piezotronics J351 B41 cryogenic accelerometer.
Tests were carried out at SRON (Netherlands) to determine whether these accelerometers are capable of measuring properly at very low temperatures (4 K). The results confirmed that these accelerometers can be used at very low temperatures, but with a drop in sensitivity of about 20% [5]. They are therefore capable to operate at 4 K (which is necessary for the purposes of this study), although their data sheet shows a limit of 77 K (Appendix 2). It should be noted that the drop in sensitivity is not taken into account in the measurements since we don’t know it precisely enough. We accept it because the study is principally about qualitative results and orders of magnitude. More knowledge and perhaps a brand new test bench will be necessary to have more quantitative results.
Figure 18: A LakeShore CX-1030-CU cryogenic thermometer.
As we can see on the picture, these thermometers can take the form of a pierced cylinder which can be screwed on what we want to measure the temperature of. We use this kind of thermometer on the cold plate and on the suspended mass.
Heaters are also resistors (Figure 19). However, their resistances are higher and we send a much higher electric intensity through them, which dissipates much more heat by Joule heat-ing. This induces a significant amount of heat that can be measured.
The heater placed on the pump of the thermal switch is simply used to control its ON or OFF position, while the heater placed on the suspended mass is used to dissipate a controlled power to carry out thermal power calibrations.
Figure 19: The Vishay SFR 25 (402 Ω, mounted on the cold plate and the thermal switch pump) and PTF (5 kΩ, mounted on the suspended mass) resistors, used as heaters.
In order to check the power dissipated by these resistors, we can simply measure the current flowing through the resistor as well as the voltage at its terminals. The Joule’s law then gives the dissipated power:
P = U × I = R × I2= U
2
R , (5)
where P is the dissipated power, U the voltage, I the current intensity and R the resistance.
2.4.2 Four-wire measurement
It is necessary to measure the resistance of thermometers and heaters correctly. Indeed, it is this measurement that allows the temperature for thermometers and the dissipated power for heaters to be measured. For this purpose, the four-wire measuring method is used. First of all, a resistance is measured according to the principle of Ohm’s law:
R = U
I, (6)
However, it is not possible to have direct access to the ends of the resistor. Moreover, the wires also have a resistance which should not be taken into account when measuring. This is what the four-wire measurement is meant for (Figure 20).
Figure 20: The four-wire measurement.
The voltage is measured directly across the resistor. Therefore, no current flows through the wires used to measure the voltage, and the measured voltage is thus not affected by the resistance of the wires. We can also measure the current, which is also not affected by the resistance of the wires. Therefore the ratio between these voltage and current measurements gives the correct resistance value.
2.4.3 Cold plate instrumentation
The study object as well as the various instruments are mounted on the cold plate. This section is about the place of the various instruments on the cold plate. The photography (Figure 21) and the diagram (Figure 22) below, show the cold plate and its instrumentation.
Figure 22: Instrumentation of the cold plate. Each module (numbered from 1 to 9) consists of 3 outlets, each connected to 4 wires (numbered from 1 to 12).
The study object is mounted on the cold plate. The heat switch is in indirect contact with the cold plate via a copper support on which it is mounted. The cold plate, the suspended mass and the micro-pump of the heat switch are equipped with thermometers, heaters and accelerometers:
- two cryogenic accelerometers are mounted on the suspended mass along the X axis,
- two cryogenic accelerometers are mounted on the cold plate along the X and Z axes. Due to lack of equipment, we couldn’t measure along all axes. We also decided later to focus solely on the X axis.
- A thermometer and a heater are attached to each of the following: the cold plate, the sus-pended mass, and the micro-pump of the thermal switch. The thermometer and the heater of the suspended mass are arranged as shown below (Figure 23).
We use the thermometers to control or measure the temperature:
- on the cold plate, it gives information about whether the cryostat is warming or cooling. It always must be around 4 K during the dissipation measurements.
- The thermometer on the suspended mass is used to measure the heat dissipation, which is the core of the study. It also gives information about the suspended mass temperature during other measurements.
- The one on the heat switch micro-pump helps to control its ON or OFF position.
The heaters also have different uses:
- the heater on the cold plate was mounted in anticipation but was not used at all.
- The one on the suspended mass is used to dissipate a controlled power in order to calibrate the effect of this dissipation on the temperature variation (2.6.1).
- The heater on the heat switch micro-pump is used to switch it on. Heating the activated carbon contained in the switch to about 25 K is sufficient to desorb the helium-3 gas it stores and to re-establish the thermal link between the cold plate and the suspended mass.
2.5
Mechanical characterisation
2.5.1 Mechanical response
As explained in the introduction, we expect to observe heat dissipation mostly or even solely around the resonance frequencies. In order to find these resonance frequencies, we need to know the suspended mass mechanical response to micro-vibrations.
To do that, we could just measure the acceleration on the suspended mass thanks to the ac-celerometers which are fixed on it. However, this would prove insufficient. The vibrations are generated on the cryostat vacuum vessel, which means that the vibrations are not generated directly on the suspended mass. In other words, the cold plate’s mechanical response could have an influence over the acceleration measured on the suspended mass. We can solve this issue by controlling the acceleration on the cold plate, thanks to the accelerometer mounted on the latter.
We measure the acceleration on the suspended mass for several frequencies with more points around the resonances. Each point is measured as the accelerometer on the cold plate yields a signal of 50 µV (measured with the spectrum analyser). It corresponds to an acceleration of 519 µg on the cold plate since this accelerometer’s sensitivity is 0.0963 V/g.
What we call the mechanical response is simply the plot of the suspended mass acceleration versus the shaking frequency. We will do the measurements in several temperature conditions: ambient (300 K), cooled with nitrogen (77 K) and cooled with helium (4 K).
2.5.2 Modal characterisation
Further studies will certainly include theoretical calculations of the power dissipated through micro-vibrations. However, those calculations require knowledge about the nature of the modes (translation, rotation). This is why the CNES (Toulouse, France) asked us to identify the nature of the modes we found with the mechanical characterisation of the suspended mass.
- a translation mode along the X axis, - a rotation mode along the Y axis.
The diagram below (Figure 24) shows both modes and how we can identify them with two accelerometers and the Lissajous curves.
Figure 24: The translation mode along X, the rotation mode around Y and their corresponding Lissajous curves.
The idea is to measure the amplitude of each accelerometer thanks to an oscilloscope and to look the phase difference between the two signals thanks to the X-Y mode (or Lissajous curves). A curve of equation Y = X (same phase) would highlight a translation mode along the X axis. A curve of equation Y = −X, however, would highlight a rotation mode along the Y axis.
2.6
Thermal characterisation
2.6.1 Measuring the dissipated power
Micro-vibrations on the suspended mass cause its temperature to increase until it reaches a new stabilised temperature. Ideally, we should have used this new equilibrium temperature to get to the dissipated power. However, it takes hours to reach the equilibrium, and we couldn’t afford to wait so long. Therefore, we chose to use the temperature slope (K/s) to get to the dissipated power.
The best approach we found in order to take into account the drift, is to correct the slope by subtracting from it the temperature slope preceding the slope break. For instance, if micro-vibrations are generated during 5 minutes, the corrected temperature slope is the temperature slope measured during these 5 minutes minus the temperature slope measured during the 5 min-utes preceding the micro-vibrations (rest period). Thus, all series of measurements alternate periods of rest and periods of micro-vibrations or heating (Figure 25). The rest periods are only used to correct the temperature slopes measured during micro-vibrations or heating.
Figure 25: Variation of the suspended mass temperature during measurements. The first varia-tions correspond to periods of micro-vibravaria-tions (increase) and rest periods (decrease). The last temperature rise corresponds to a calibration with the heater on the suspended mass.
Now that we have a corrected value of the temperature slope (K/s) we want to find the corre-sponding dissipated power (W). To do that, we use the heater on the suspended mass to dissipate a controlled thermal power into the suspended mass. This heating, like micro-vibrations, causes a change in temperature slope (compared to the drift slope). In other words, we use the corrected temperature slope due to the heating as a calibration. Afterwards, we can get to the dissipated power due to the micro-vibrations through a simple cross-multiplication.
Pvib=
(dT /dt)vib
(dT /dt)cal
× Pcal, (7)
where (dT /dt) are the temperature slopes, P the dissipated powers and ”vib” and ”cal” stand respectively for micro-vibrations and calibration.
2.6.2 Dissipation as a function of the shaking frequency
2.6.3 Dissipation as a function of the acceleration
The second type of measurement consists of measuring heat dissipation at one shaking fre-quency (at the resonance or close) for several values of acceleration on the cold plate. The goal is to plot the dissipated power as a function of the acceleration on the cold plate.
3
Results and Discussion
3.1
Shakers characterisation
3.1.1 Piezoelectric actuator characterisation
The chart below (Figure 26) shows the piezoelectric actuator response to a 100 mV peak-to-peak sine. The frequency range goes from 50 Hz to 2.7 kHz. We made more measurements around the amplitude peaks.
Figure 26: The piezoelectric actuator response between 50 Hz and 2.7 kHz.
The piezoelectric actuator response has a main peak of approximately 10 g at 228 Hz and another of approximately 2.3 g at 793 Hz. Above 2 kHz, the amplitude gradually increases to a peak of about 2.3 g at about 2.64 kHz.
After studying the resonances of the suspended mass (section 3.2), we found that a frequency range going from 100 Hz to 400 Hz was wide enough to characterise the suspended mass. There-fore we want to generate micro-vibrations at the suspended mass in this frequency range above all. The peaks at 790 Hz and 2.64 Hz are outside this frequency range. The main resonance (228 Hz) however, is in the range. This resonance can thus cause difficulties in maintaining a constant level of acceleration on the cold plate. For instance, the lowest acceleration we can achieve at the resonance could still be higher than the highest excitation we can achieve at other frequencies.
Figure 27: On the left: the maximal PHD of the piezoelectric actuator as a function of the shaking frequency. On the right: the maximal PHD as a function of the acceleration of the piezoelectric actuator, for several frequencies.
The value of the maximal partial harmonic distortion is usually below 1% or even 0.1%. However, it reaches higher values around 80 Hz (more than 13%), 120 Hz (almost 8%), which are the sub-frequencies of the main resonance (f /3 and f /2), and 240 Hz (2%).
In addition, the maximal partial harmonic distortion tends to increase with the piezoelectric actuator acceleration, regardless of the shaking frequency. This is probably due to the non-linear behaviour of the mechanical amplifier. Thus, it can even exceed 20%, as at 400 Hz with an acceleration of 900 mg.
When the harmonic distortion is high, it also becomes visible on the time signal. The graph below (Figure 28) is an example of that.
Figure 28: Waveform of the piezoelectric actuator shaking at 80 Hz.
We can notice that the signal is no longer sinusoidal and that the large proportion in third har-monic reveals a secondary frequency of 240 Hz. There are three amplitude peaks in one period corresponding to 80 Hz.
heterogeneous due to its strong resonance. In addition, the signal is highly distorted below 150 Hz and also has significant harmonic distortion around the resonance. It means that the piezo-electric actuator can shake at additional and unwanted frequencies: for instance, shaking at 80 or 120 Hz means to also shake at 240 Hz. Therefore, the piezoelectric actuator is not the ideal shaker for this measurement campaign and we need to find a better alternative.
3.1.2 Electrodynamic shaker characterisation
The response of the electrodynamic shaker to a 37 mV peak-to-peak sine wave is shown in the graph below (Figure 29).
Figure 29: The electrodynamic shaker response between 20 Hz and 3.3 kHz.
Figure 30: Maximal partial harmonic distortion rate of the electrodynamic shaker as a function of frequency over a range from 20 Hz to 3.3 kHz for a 37 mV peak-to-peak sinusoidal signal injected by the GBF.
The maximal PHD always remains below 1% and mostly even below 0.5% over the frequency range of interest. Higher values are measured below 30 Hz. If the maximum partial harmonic distortion exceeds 3% at 20 Hz, it only exceeds 0.5% between 20 and 50 Hz and around 1000 Hz (which is more or less the resonance frequency divided by 3). Between 100 and 400 Hz, on the other hand, it is at its lowest, with an average of 0.12%. This is very low compared to the piezoelectric actuator.
Finally, we expect the electrodynamic shaker to be a better alternative than the piezoelectric actuator, it is less likely to generate vibrations at other frequencies than the one set on the AFG. It also doesn’t have a resonance in the [100-400] Hz range.
3.2
Mechanical characterisation
3.2.1 Mechanical response
The charts below are the suspended mass mechanical responses to micro-vibrations at several temperature conditions. We generated micro-vibrations on the suspended mass with the electro-dynamic shaker with a frequency range of [100-400] Hz. We maintained an acceleration of 519 µg on the cold plate and measured the acceleration on the suspended mass. We measured the mechanical response for each important temperature step: ambient (300 K), 77 K and 4 K.
Figure 31: The suspended mass mechanical response between 100 and 400 Hz, at 300 K.
The acceleration on the suspended mass is between 100 and 10000 µg, but mostly above 519 µg which means that the signal amplifies from the cold plate to the suspended mass. This chart highlights three resonance peaks at 154, 225 and 317 Hz.
The chart below is the suspended mass mechanical response at 77 K. Both the suspended mass and the cold plate are at this temperature and the pump is still running.
Figure 32: The suspended mass mechanical response between 100 and 400 Hz, at 77 K.
The acceleration on the suspended mass is between 30 and 10000 µg, still mostly above 519 µg. This time, we find four resonance peaks at 154, 187, 197 and 257 Hz. The one at 154 Hz remains unchanged. However, the other resonance peaks shifted in frequency. It seems that the peak at 225 Hz shifted to a double peak at 187 and 197 Hz. The one at 317 Hz shifted to 257 Hz.
Figure 33: The suspended mass mechanical response between 100 and 400 Hz, at 4 K.
The acceleration on the suspended mass is between 10 and 20000 µg, but still mostly above 519 µg. There is some missing data in this chart between 200 and 220 Hz because we didn’t manage to maintain an acceleration of 519 µg on the cold plate. In other words, the accelera-tion on the cold plate was very low. This might explain why we don’t find a double peak such as the one at 77 K. Instead, this incomplete chart highlights three resonance peaks at 150, 185 and 260 Hz. The peaks shifted slightly but not as much as from the ambient temperature to 77 K.
The chart below shows the three suspended mass mechanical responses on the same chart, in order to have a better comparison between the temperature conditions.
Figure 34: The suspended mass mechanical responses between 100 and 400 Hz, at 300, 77 and 4 K.
It is easier to see on this chart that the resonance frequencies tend to shift to lower frequencies as the temperature drops. This phenomenon is certainly due to the change in mechanical properties of the materials:
- The Young’s modulus changes.
As a result, there is a change in stiffness. Thus resonance frequencies are shifting, since they depend on the mass and the stiffness. The shift is less important between 77 K and 4 K because the mechanical properties of most materials are changing much less at low temperatures [6].
3.2.2 Resonances
The charts below (Figures 35 and 36) highlight the presumed suspended mass main resonances at 4 K, taken out of Figure 33.
Figure 35: The suspended mass main resonances measured in the X axis.
The first two peaks are found at 185 and 265 Hz. The acceleration peak at 185 Hz reaches almost 70 mg, while it reaches about 120 mg for the peak at 260 Hz.
Figure 36: A lower resonance measured in the X axis.
The graph below (Figure 37) is a synthesis of the three previous graphs to show the resonances in a larger scale and to compare them.
Figure 37: The three resonances measured in the X axis.
The suspended mass mechanical response highlights three resonance frequencies (including a double peak at 77 K we didn’t manage to find at 4 K). In fact, while the first two peaks at 185 and 260 Hz are probably two resonances of the suspended mass, the much lower amplitude of the 150 Hz peak suggests it is another object’s resonance frequency. This is probably the thermal switch, which has a priori a resonance around 150 Hz and is in close contact with the suspended mass. As explained in section 2.3.1, there was a risk that adding new elements close to the suspended mass interferes with the measurement.
3.2.3 Modal characterisation
The screenshots below (Figure 38) show for both frequencies (185 and 260 Hz), the phase between the two accelerometers mounted on the suspended mass (Lissajous curves).
Figure 38: The Lissajous curves for the 185 Hz mode (left) and the 260 Hz mode (right).
These Lissajous curves highlight indeed, that the modes doesn’t have the same natures. At 185 Hz, the equation is Y = X which means that the accelerometers have the same phase. At 260 Hz however, the equation is Y = −X, meaning that the accelerometers have opposite phases. Thus the resonance at 185 Hz should be the translation mode along the X axis while the one at 260 Hz should be the rotation mode around the Y axis.
3.3
Thermal characterisation
3.3.1 Dissipation as a function of the shaking frequency
We measured the heat dissipation around the frequencies corresponding to the ”mechanical” resonances. The two charts below (Figure 37) are plots of the heat dissipation as a function of the shaking frequency, highlighting the ”thermal” resonances.
Figure 39: The power dissipated at the suspended mass as a function of the shaking frequency. The acceleration on the cold plate is 519 µg around 184 Hz and 1.66 mg around 259 Hz.
The dissipated power and the acceleration of the suspended mass are plotted on the same chart below. As a reminder, these thermal and mechanical response measurements were not carried out at the same time. All the graphs are normalised as if the acceleration on the cold plate was 519 µg for each measurement (whereas the dissipation measurement around 259 Hz was actually performed with 1.66 mg on the cold plate). This normalisation treatment is justified by the fact that it has been shown that the level of dissipation is proportional to the acceleration on the cold plate (3.3.2).
Figure 40: The dissipated power and the acceleration on the suspended mass as a function of the shaking frequency.
First of all, the chart shows that the ”thermal” resonance frequencies are not exactly the same as the ”mechanical” resonance frequencies: the mechanical response reveals resonances at 185 and 260 Hz, versus respectively 184 and 259 Hz for the thermal response.The change in temperature between the mechanical and the thermal characterisations can explain this slight frequency shift. The suspended mass temperature is indeed around 20 K for the mechanical characterisation ver-sus 4 K for the thermal characterisation. As a reminder, the mechanical characterisation could only be carried out using the accelerometer attached to the suspended mass. This accelerometer dissipates enough power to raise the temperature of the suspended mass up to more than 20 K. Since the resonance frequencies tends to shift to lower frequencies as the temperature drops (3.2.1), it is possible that this 1 Hz shift is due to the difference in suspended mass temperature between the two types of measurements.
The charts above (Figure 37) suggest that there is, for the same acceleration on the sus-pended mass, more dissipation at 184 Hz than at 259 Hz. This could have several causes:
- The frequency resolution is only 1 Hz, which might be insufficient, since the resonances are so sharp. For instance, the mechanical resonance could very well be found at 260.4 Hz instead of 260 Hz and the thermal resonance at 258.7 Hz instead of 259 Hz. A shift of a few dHz could have a significant impact on the measured amplitude. Thus the measurements should be done with a better resolution (for instance 0.1 Hz instead of 1 Hz) during the next measurement campaign. Of course, the measurements would take much more time.
- Despite the care taken in defining the data processing procedure to convert temperature slopes into dissipated power, some choices remain partly arbitrary.
at the resonances are of different nature (translation along the X axis and rotation around the Y axis).
3.3.2 Dissipation as a function of the cold plate acceleration
The charts below (Figure 41) show the dissipated power as a function of the acceleration on the cold plate. We carried out the measurements for two frequencies: 184 Hz and 260 Hz.
Figure 41: The power dissipated at the suspended mass as a function of the acceleration on the cold plate. The red point is theoretical: there is no dissipation at rest.
We can model both plots with a linear law. The regression coefficients are 0.9925 at 184 Hz and 0.9979 at 260 Hz. The equations are P = 0.2547 × a at 184 Hz and P = 0.069 × a at 260 Hz, where P is the dissipated power (nW) and a the acceleration (µg). The good regression coefficients (r2 is higher than 9.90 in both cases) show that the dissipated power is proportional to the acceleration on the cold plate. These plots don’t prove the proportionality above 2000 µg but it is enough for the previous measurements done with hundreds of µg on the cold plate.
The graph below (Figure 42) shows the dissipated power as a function of the acceleration on the cold plate for two identical tests carried out one day apart (September 30th and October 1st 2020).
The two curves are modelled by a linear law. The regression coefficients are 0.9155 for the first test and 0.9979 for the second. The equations are P = 0.0169 × a for the first and P = 0.069 × a for the second, where P is the dissipated power (nW) and a the acceleration (µg). The regres-sion coefficient is lower for the measurement made on September 30th. We could explain the poor regression coefficient by a significant error in the measurement of the acceleration on the cold plate. Indeed, it can happen that the latter fluctuates during while we are generating the micro-vibrations. Moreover, the values of dissipated power are lower and thus closer to the noise.
Moreover, there is an important difference between the two slopes, which calls into ques-tion the repeatability of the measurements. We could explain this difference in dissipated power by a small frequency shift of the resonance (maybe a few dHz) between the two days. Indeed, we know that the dissipated power can vary by one order of magnitude between a frequency f and a frequency f ± 1 (Figure 39). Thus a shift of a few dHz could be enough to explain this difference. We couldn’t confirm this hypothesis because an operating accelerometer on the suspended mass would heat the latter: we can’t carry out mechanical and thermal measurements at the same time.
3.3.3 Resistance of the copper strap and thermal switch assembly
We could have measured the dissipated power with a static rather than a dynamic approach: in other words, we could have measured the new equilibrium temperature rather than the tem-perature slope. However, we preferred the dynamic approach since it requires a much shorter measurement time, whereas it takes several hours for the temperature to reach a new equilibrium. The measurements presented on the chart below would have allowed the dissipated power to be traced back to the equilibrium temperature.
The thermal link consisting of the copper strap and the heat switch conducts the heat from the suspended mass to the cold plate. The following equation describes the conduction between the suspended mass and the cold plate:
P = Gth× ∆T ⇔ ∆T = Rth× P, (8)
where Gth and Rth are respectively the thermal conductance and resistance of the thermal link
between the suspended mass and the cold plate, P is the power (W) and ∆T a temperature difference between the suspended mass and the cold plate.
Figure 43: Thermal resistance curve of the thermal link consisting of the copper strap and the heat switch.
We can model the curve with a linear law of equation ∆T = 60.09 × P where ∆T is the tem-perature difference (mK) and P the dissipated power (µW). The regression coefficient is 0.9985. The slope (K/W) is the thermal resistance of the thermal link consisting of the copper strap and the thermal switch in OFF position. Its inverse is the thermal conductance Gth (in W/K). We
measured a thermal resistance of 6.009 × 104 K/W or a thermal conductance of 1.664 × 10−5
W/K. These values are close to those of the thermal switch since the thermal resistances add up and the resistance of the thermal switch in the OFF position should be much higher than that of the copper strap.
4
Conclusion
During this master’s project, I contributed to the establishment of a test bench: I helped designing it and installing it, including the elements on the cold plate. Then I carried out and processed most of the measurements. It also implied to watch after the experiment and reinject liquid nitrogen into the cryostat twice in a week. I also shared the advancement of the project with other researchers, including from SRON and CNES. Finally, I presented the results in sev-eral reports, including this master’s thesis, and during the X-IFU consortium.
As a conclusion, we managed to meet the study’s objectives, but this is just the begin-ning of a long line of measurement campaigns. First of all, we established a test bench from scratch, allowing us to measure heat dissipation at a very low temperature (4 K). We were able to measure heat dissipation down to tens of nano-watts, which means that the sensitivity is high. In order of magnitudes, micro-vibrations corresponding to an acceleration of 1 mg on the cold plate dissipate hundreds of nano-watts on the suspended mass, are expected to cause a temperature rise of tens of milli-kelvins.
We also established a link between mechanics (resonances) and thermics (dissipated power). It is one of the most important results of this study. Indeed, measuring dissipation (exceeding 10 nW) was only possible by generating micro-vibrations around the suspended mass resonance frequencies. In other words, mechanical resonances cause peaks of heat dissipation, called ther-mal resonances in this study. If further studies confirm that fact, it would mean that solving this issue is all about mitigating some resonances or frequencies.
In space missions, the micro-vibrations come from the noise of the operating cryo-coolers. If we manage to mitigate target frequencies coming from this noise, we could get rid of the heat dissipation issues. It also might be possible to manufacture a support for the detector, without any disturbing resonances.
This study within the framework of a master’s project, made it possible to establish a test bench and to carry out a first measurement campaign to explore this topic. However, most of the results are either qualitative or not quantitative enough. Thus, we characterised the phenomenon only partially and in orders of magnitude. New measurement campaigns, drawing lessons from the first one, will be necessary to obtain more precise and quantitative results. We would need to characterise the suspended mass in all axes and to identify every mode. If possible, we would also improve the dissipation measurements, since the dynamic approach we have chosen is fast but not optimal.
We can give several suggestions for future measurement campaigns. First of all, we could design a new study object to make the measurements and their processing easier: this object would have a simpler geometry (a sphere for instance) and the suspended mass would be made of a single material, in order to guarantee better temperature homogeneity. We could also au-tomatise the measurements, using Labview, for instance. I would make it possible to carry out more measurements in less time. It means measurements with a better resolution and maybe enough results to calculate an error, among other things.
References
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[2] Takei, Yoh, et al. ”Vibration isolation system for cryocoolers of Soft X-ray Spectrometer (SXS) onboard ASTRO-H (Hitomi).” Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray. Vol. 9905. International Society for Optics and Photonics, 2016. [3] Duband, L., et al. ”Herschel flight models sorption coolers.” Cryogenics 48.3-4 (2008): 95-105.
[4] Catarino, I., G. Bonfait, and L. Duband. ”Neon gas-gap heat switch.” Cryogenics 48.1-2 (2008): 17-25.
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