cryocooler is installed in a cryostat with two thermal copper screens clamped on the two cold stages. A triaxial piezo- accelerometer monitors the second stage ...
An Alternative Strategy for Cooling the Mirrors of the Gravitational Wave Interferometers at Low Temperature ∗
A. Cinelli† , E. Majorana† , P. Puppo†, P. Rapagnani ∗, F. Ricci∗ University of Rome ’La Sapienza’, Physics Department, P.le A. Moro 2, 00185, Roma,Italy † INFN Sezione di Roma, P.le A. Moro 2, 00185, Roma, Italy
Abstract— A new generation of gravitational wave interferometers is under study with the main goal to improve the sensitivity of the detectors which are now starting to take data. One of the dominant noises which limit the actual sensitivity of the interferometers is the thermal noise of the suspended optics. However, reducing the temperature of the test masses without injecting vibration noise from the cooling system is a technological challenge. We present the first results on a new active system to dampen the vibrations from a pulse tube refrigerator coupled to a suspended mirror. Index Terms— Cryogenics, gravitational interferometers.
I. I NTRODUCTION NE of the most challenging goals in the construction of an advanced generation gravitational wave interferometer is cooling the mirrors at low temperature. At the present state of the art of the interferometeric detectors, the dominant noise sources in the most interesting frequency range can be reduced by cooling the mirrors of the Fabry-Perot cavities. Indeed, many noise sources depend directly on temperature or are indirectly related to it by means of the material properties. For these reasons, the choice of the materials is essential in designing a cryogenis interferometer. Among the most important noise sources related to thermal effects there is the thermal noise due to brownian forces which drive the mirror internal modes via the fluctuation-dissipation theorem. Another noise directly related to the temperature is due to the thermoelastic effect given by the temperature fluctuations in the mirror substrate and coating. This noise term is also related to the elastic expansion coefficient of the materials and is proportional to the second power of temperature [1], [2]. Finally another important noise source is the thermal lensing due to the temperature gradients present in the mirror substrate and coating. This noise is related to the thermal conductivities and to the fluctuations of the coating refraction index [3].
O
II. I SSUES TO COOL THE INTERFEROMETER MIRRORS As mentioned in the previous section, in developing a cooling system for the interferometer mirrors, some important issues both in the design of the cryogenic apparatus as well as in the
choice of the materials of the mirror suspensions must be taken into account. One of the main requirements is that the mechanical noise injected during the refrigeration procedure must be negligible. As a consequence a good mechanical isolation between the mirror and the cooler is necessary. Another important element in a cryogenic system is the thermal link with the refrigerator. Taking care of having short thermal links and good thermal couplings is important to have low refrigeration power losses. For instance, the use of a mechanical attenuator as a heat link is a good solution to dampen the vibrations of the cooler, but has the disadvantage to take a part of the refrigeration power. On the other hand the mirror suspension itself must have the required thermal conductivity to reduce thermal gradients and to optimize the cooling time. The requirements we have just described suggest that the overall design of the mirror suspension and control system will be very different from what it is currently used in interferometric antennas (for instance see ref. [4] ). The new system will be the result of a trade off between the necessity to have a strong thermal contact with the refrigeration apparatus and the need to reduce any dissipation source due to the coupling of the suspension with the mirror. III. C RYOGENIC TECHNIQUES IN THE GRAVITATIONAL WAVE RESEARCH
A lot of work has been already done to cool the resonant gravitational wave detectors by using cryogenic fluids. The first cryogenic antenna of 20 kg was successfully cooled down to 4 K by the group headed by Edoardo Amaldi and Guido Pizzella in 1974. The cooling runs were very useful to understand the cryogenic techniques and the behavior of material properties in the range of low temperatures [5]. A second important result was reached when the antenna Explorer, having a mass of 2400 kg was cooled at the temperature of liquid helium in 1982. In this experiment the noise injected by the boiling cryofluid was reduced thanks to the suspension system. However a further improvement of the sensitivity was reached when the boiling of the liquid helium was drastically decreased by working below its λ point [6].
On the other hand the experience with cryogenic resonant antennas teached us that the maintanaince of such a big cryogenic apparatus is difficult and requires a heavy work. For instance, a liquid helium refilling is necessary tipically once per month, with a consequent stop of a few days of the data taking. A cryogenic interferometer would have a similar problem with the added complication of the increased number of systems to be cooled down, four at least. Indeed it must be taken into account that to maximize the duty cycle, all the cryogenic operations should be performed at the same time on all the systems, with an increased need of facilities and man power. IV. U SING CRYOCOOLERS An alternative to the cryofluids is the use of a GiffordMcMahon (GM) cryocooler which is widely used in various fields of science and industries because of its convenient handling. However it provides large vibrations due to the displacer motion. Another possible solution is to use a pulse tube (PT) cryocooler which is expected to be less noisy because it has no moving parts in its cold head. Moreover, it is more reliable and has a 2 to 3 times higher efficiency than GM cryocoolers for loads temperatures between 55 and 120 K. A pulse tube cryocooler seems to be suitable for our purposes. However also this kind of cryocooler can inject mechanical noise because of the gas pulse flowing in its cold head.
Fig. 1. Power Spectral densitiy of vibration of the cryocooler Cryomec PT-407 second cold head in the low frequency range.
A. Vibration measurements on the pulse tube cryocooler We have investigated on the vibrations of a commercial pulse tube double stage cryocooler (Cryomec PT-407). The cryocooler is installed in a cryostat with two thermal copper screens clamped on the two cold stages. A triaxial piezoaccelerometer monitors the second stage vibrations at low temperature. Figures 1 and 2 show the noise measurements of the II cold stage in the low and high frequency ranges. The sharp peak at 1.4 Hz can be explained by the gas pulse flowing in the cold stage, while the noise structure present in the high frequency range which is mainly due to resonances of the cryostat screens. Comparing the results of our vibration measurements with similar ones performed on another commercial cryocooler manufactored by Sumitomo Industries in Japan [7], we found that the latter one is less noisy than the Cryomec one. For this reason the Sumitomo pulse tube seems preferable to the Cryomec one for our applications. B. Cooling tests using a pulse tube on a CaF 2 mirror sample. We have performed a cooling test of a CaF 2 mirror sample using the cryostat equipped with the Cryomec cryocooler. The test was done in order to study the thermal behavior of the a system cooled by a pulse tube. The experimental apparatus is sketched in figure 3. The mirror has a diameter of 100 mm and is 30 mm thick, it is
Fig. 2. Power Spectral densities of vibration of the cryocooler Cryomec PT407 second cold head in the high frequency range.
suspended by two copper wires of 0.5 mm diameter wrapped around its lateral surface and acting also as thermal links. We have monitored the temperatures of the thermal screens,
the mirror suspension clamp and of the center of the CaF 2 sample surface.
Fig. 4. Temperature behavior of the first and second thermal screen and of the CaF2 sample. Fig. 3.
Picture of the experimental setup of the mirror cooling test.
The preliminary results are shown in figure 4. To better understand the thermal behavior of this system, we have built a finite element model 6 where we have included the two thermal screens of the cryostat and the suspended mirror. Moreover, the dependency on temperature of the thermal properties of the materials and of the cooling power of the refrigerator stages were included in the computation. Due to the lack of computing power, we were able to simulate only 4.5 hours of the cooling process of the overall system. The measurements are in agreement with the simulated data (see figure 5,7). On the other hand we have computed the complete behavior of the thermal screens in the cryostat up to the equilibrium temperatures. The results were useful to infer if unaccounted thermal losses were present. In stationary condition, we have observed a difference between the temperature values on the center of the mirror surface and the copper wire contact points. This effect could be due both to the presence of a thermal boundary resistance between the CaF2 mirror and its suspending wires, and to an unexpected thermal input. Thus, we have included in our model also the boundary resistance, and we plan to use the finite element simulation to understand which of these two hypoteses can give the observed temperature gap. In the end, the finite element simulation will be used to optimize a complete mirror cryogenic suspension. C. A vibration free cryostat for mirrors. The Sumitomo pulse tube is preferable to the Cryomec one but it is still noisy. As a consequence, for our purposes it is necessary to design a cooling system which can attenuate the PT cryocooler vibrations. The vibration free cryostat (VFC) we have designed is suitable for coupling such a system to a mirror, according to the issues discussed in section III.
Fig. 5.
Comparison between the measurements and the FEM results.
The principle scheme is sketched in the figure 8. It is based on the idea to attenuate the cryocooler vibrations by directly acting on it and consequently allowing a direct heat link between the cryocooler and the mirror, without using any other attenuation system. This solution permits to preserve the refrigeration power. The active control on the cold head vibration is performed by a feedback system in which the displacement is monitored by a tri-axial accelerometer placed on the second stage and the correction is performed by piezoelectric actuators. The cryocooler cold head is clamped to a platform placed on dampers. The cryocooler is connected to the cryostat by a soft silicon bellow designed to mechanically decouple it from the cryostat. The feedback correction signal is sent to three piezoactuators which are loaded by the platform and can act on it from below. In the cryostat, a first thermal screen is connected to the first 30 K cold stage while a second screen is thermally connected
Fig. 6.
Fig. 7.
Contour plot results of the finite elements model of the cryostat.
Fig. 8.
Principle scheme of our Vibration Free Cryostat.
Finite elements model of the cryostat
to the second 4 K cold stage. The heat links are copper stripes arranged on a ring. They are very soft and provide a mechanical decoupling with the system to be cooled. Figure 9 and 10 show the design of the vibration free cryostat and a picture of the first assembly of the system. V. C ONCLUSION We have designed a cryostat which can actively attenuate the vibrations of a pulse tube cryocooler. The system is suitable for applications in the advanced interferometeric gravitational wave detectors. The system was equipped with a 4K pulse tube of the Japanese industries Sumitomo which seems to be the less noisy among the same kind cryocoolers. We plan to characterize its noise and thermal performances in the next future. The finite element simulation will be used to better understand the system behavior, and will help the set up of the vibration compensation system. The vibration free cryostat will be used to develop a new mirror cryogenic suspension, to study the thermal properties of the materials candidates for the mirrors of a cryogenic interferometer and to set up the new electromagnetic actuators which can be used at low temperatures.
ACKNOWLEDGMENT The authors would like to thank the technician M. Perciballi for his skilfull work in the design of the cryostat and its help in the assembling of the system.
Fig. 9.
Vibration Free Cryostat design.
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Fig. 10.
First assembly of the vibration free cryostat.
