- Email: [email protected]
Application of material damping for gravitational wave detectors
Journal of Alloys and Compounds 355 (2003) 224–229
L
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Application of material damping for gravitational wave detectors K. Tsubono* Department of Physics, University of Tokyo, 7 -3 -1 Hongo, Bunkyo-ku, Tokyo 113 -0033, Japan
Abstract Gravitational waves, predicted by Einstein in the theory of relativity, are expected to open a new window into the Universe. Although worldwide efforts are being made, gravitational waves have not yet been detected directly, since their effect is extremely weak. In gravitational wave detectors, there are several noise sources. One is the resonant peaks in mechanical systems, such as vibration isolation and test mass suspension. Active and passive methods are used to suppress high-Q resonances of mechanical structures. Also, low-loss materials for the mirrors are crucial to reduce thermal noise. We describe these aspects of damping which appear in gravitational wave detectors. 2003 Elsevier Science B.V. All rights reserved. Keywords: Gravitational wave; Damping material; Laser interferometer
1. Introduction In laser interferometric gravitational wave (GW) detectors, two opposite concepts, high damping and low loss, are important to achieve both high sensitivity and high stability. High damping for mirror isolation is desirable to suppress the resonant peaks and residual motion of mirrors. In our TAMA300 laser interferometric GW detector [1], we have used metal-sealed rubber in a stack for vibration isolation to achieve vacuum-compatible isolation with sufficient damping. We have also applied a damping alloy (M2052) in the suspension of the telescope for mode-matching, and confirmed that material damping works effectively in the GW detector. Extremely low-loss materials are crucial for mirrors in order to reduce thermal noise. We have developed a method to measure the intrinsic Q of low-loss materials. With this method, we performed a series of measurements for several fused-silica samples, and found that some kinds of fused silica have very high Q values.
produced by dynamic sources, such as rotating binary stars, the curvature of space will change with time and propagate in all directions with the speed of light. This ripple of space–time is the GW. Hulse and Taylor confirmed the existence of GWs by observing the orbit change of a binary pulsar, SN1913116, in the 1980s [3]. The disturbance in the orbit was caused by energy loss due to the emission of GWs. The existence of GWs was thus confirmed indirectly. However, a direct observation of GWs has not yet been realized, since their effect is extremely weak. GWs are produced by various astronomical sources [4]. The coalescence of binary stars will emit GWs; the stars can be neutron stars or black holes. A supernova is the last stage of life of a massive star and produces strong GWs during its explosion. Cosmic strings made just after the big bang are expected to produce GWs. GWs carry an important piece of information about catastrophic events which cannot be probed through other astronomical observations in the optical, radio, or X-ray bands. GWs are expected to open a new window onto the Universe; this window is gravitational wave astronomy.
2. Gravitational waves (GWs) In 1916, Einstein predicted GWs in the theory of relativity. In his theory, gravity is expressed by the curvature of space–time [2]. If gravity is, therefore, *Tel.: 181-3-5841-4141; fax: 181-3-5841-4279. E-mail address: [email protected] (K. Tsubono).
3. Laser interferometric GW detector How to detect GWs is described here. A GW will change the distance between two free masses. The amplitude of a GW is expressed in terms of h, which is a dimensionless number and is equal to the magnitude of the
0925-8388 / 03 / $ – see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S0925-8388(03)00234-2
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
strain. The typical amplitude of h is |10 221 ; this number is our present target for detection. Even if a GW with this amplitude incidents between the Sun and Earth (the distance is 1.5310 8 km), the change in distance will be only the size of a hydrogen atom. A Michelson-type laser interferometer is used to detect such a tiny effect of GWs. Worldwide efforts are being made to detect GWs. In the US, two 4-km arm-length interferometers have been built in Hanford and Livingston [5]. A French and Italian team is constructing a 3-km arm-length interferometer in Pisa, Italy [6]. A 600-m arm-length detector is under construction in Hannover, Germany, in a collaboration between the UK and Germany [7]. A simplified scheme of a laser interferometric GW detector is shown in Fig. 1. The laser beam is split into two orthogonal directions by a beam-splitter, and the reflected light from the two arms is combined at the photo-detector. Since a GW has a quadrupole pattern, it causes different effects on the two orthogonal lengths. Thus, GW can be detected as the fringe-pattern change in the output of the photo-detector. TAMA is the name of a Japanese project for GW detection [1]. The TAMA300 laser interferometric GW detector has an arm-length of 300 m and is located on the campus of the National Astronomical Observatory in Mitaka. The whole detector was constructed underground so as to reduce disturbances from outside. All of the optics are housed in vacuum chambers and pipes. We started operation of the TAMA300 detector in 2000 ] [8]. The achieved sensitivity, h˜ | 5 3 10 221 /ŒHz from 700 Hz to 1.5 kHz, is sufficient to catch possible gravitational wave events in our galaxy [9]. We can operate the detector for over 24 h stably and continuously. Last summer we performed a 2-month data-taking run and collected over 1000 h of data. We are now analyzing the obtained data, searching for gravitational waves from coalescing binaries using a matched filtering technique with templates of the chirping signal [10]. There are several noise sources in the interferometric GW detector. Laser shot noise, thermal noise, seismic noise, electric noise, and gravity gradient noise are the
Fig. 1. Schematic view of the TAMA300 laser interferometric GW detector. Because the GW has a quadrupole pattern, it causes different effects on two orthogonal 300-m arms. Thus, GW can be detected as a fringe-pattern change in the output of the photo-detector.
225
Fig. 2. Scheme of a typical double-pendulum mirror suspension system. To damp the pendulum motion of the mirror, we use low-Q materials in the suspension frame and the upper-stage wire. Alternatively, we can apply a damping force on the intermediate mass. To reduce thermal noise we use high-Q materials for the lower stage wire and the mirror.
dominant noise sources. Among these noises, thermal and seismic noises are considered in this article.
4. The mirror and its suspension In principle, the detector measures small changes in the distance between two mirrors; hence, the most important parts of the interferometer are the mirrors. They are usually suspended by wires so that they act as free masses and are isolated from ground vibration. The TAMA mirrors are made of fused silica, 10 cm in diameter and are suspended by two-loop tungsten wires from an intermediate mass.
Fig. 3. TAMA300 mirror suspension system incorporating a stack for vibration isolation.
226
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
The mirror and intermediate mass make a double pendulum. Fig. 2 shows a scheme of a typical double-pendulum mirror suspension system. Low-Q and high-Q materials are used in this mirror and its suspension system. First, the pendulum motion of the mirror should be damped to a level, say Dx , 0.1 mm, since the laser light has a wavelength of about 1 mm. Also, we must avoid the resonant peaks in the structure. Therefore, the upper-stage wire and the frame materials should have low Q values. Alternatively, we can apply a damping force on the intermediate mass by some means. The mirror itself and the lower-stage wire should have a high Q in order to reduce the thermal noise. In this way, two contrasting properties appear in the mirror suspension system.
5. Damping for mirror suspension First, we describe the damping of the mirror suspension system. As an example, a schematic view of the TAMA mirror suspension system is shown in Fig. 3. The requirements for the suspension system are sufficient damping, good controllability and sufficient vibration isolation. The damping property is an important factor for the suspension system, as stated above. Damping schemes are divided into two categories, active and passive. An example of active damping is the mirror suspension
Fig. 5. Measured horizontal-to-horizontal transfer function of the stack, without and with a bellows. The two transfer functions were almost the same, showing that the degradation of the isolation ratio due to the bellows was negligible over this frequency range.
of the VIRGO detector [6]. In the VIRGO detector, an inverted pendulum and seven-stage cascaded vibration filters are used for the mirror suspension in order to obtain high isolation at low frequencies. The total length of the
Fig. 4. Cross-section of a three-stage stack for vibration isolation. Vacuum compatibility was achieved by enclosing rubber with a welded bellows.
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
Fig. 6. Telescope for mode-matching used in TAMA300. The optical components are suspended by wires to isolate them from seismic motion. Damping alloy M2052 is used in the suspension wire and the damper for the spring.
227
pendulum is 7.3 m. To stabilize the pendulum motion, they use an active control system consisting of position and acceleration sensors and actuators. With this active scheme, the system is fully adjustable, but very complicated. The other scheme is passive damping. The first example is magnetic eddy-current damping [11]. The pendulum motion is damped by an eddy current induced by strong permanent magnets around an intermediate mass. Using this scheme, all of the pendulum modes are damped. This scheme is used in the TAMA300 detector. This technique is simple and robust, but has little flexibility. A second example of passive damping is using rubber. In GW experiments, all of the optics is in a vacuum so as to avoid any optical and / or acoustic disturbances. Thus we have developed a vacuum-compatible vibration isolation stack comprising alternative layers of heavy mass and metal-sealed rubber [12]. We use chloroprene rubber
Fig. 7. Vibration isolation ratio of the telescope obtained with different configurations, with and without the M2052 material. The lower trace is a magnified view of the spectrum near the frequencies of the wire resonances.
228
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
blocks enclosed by a gas-tight metal bellows. Fig. 4 shows a cross-section of the vibration isolation stack. With this three-stage stack we could obtain 60 db vibration isolation at 100 Hz, as shown in Fig. 5. This method is also simple and robust. A third scheme is material (metal) damping. Here, we introduce a high-performance damping material (M2052). M2052 is a Mn-based twinning-deformation-type alloy. This alloy was invented by Kawahara and his group [13] and evaluated in the GW detector by Mio [14]. They use M2052 in the suspension for the TAMA mode-matching telescope. As shown in Fig. 6, the optics for the telescope is suspended by wires and springs. A damping alloy (M2052) is used in the wire and damper for the spring to suppress wire resonances. With M2052 materials, they achieved a Q of 45 for the wire resonance. The performance of the telescope suspension with damping material can be seen in Fig. 7. The system with M2052 damping material is now operating stably in the TAMA detector.
6. Low-loss materials for mirrors Next, we consider low-loss materials for mirrors. As can be seen from the fluctuation dissipation theorem, the mechanical loss is the origin of the thermal noise [15]. Therefore, the materials of the mirror and final-stage suspension wire should have very high Q values. The following are the results of a low-loss material search performed at the University of Tokyo [16,17]. In order to clarify the loss property of a material, it is necessary to measure the intrinsic Q of the material itself. However, usually the measured Q is dominated by loss due to the support. Hence, we have developed a method to measure the material’s Q using a nodal support technique. In this method, samples are supported at the nodes of the vibrational modes by point contact. Thus, any loss due to the support can be excluded. We used cylindrical samples, of which two center points on the flat surfaces are nodes in higher order modes. Samples are supported at the center points with two small ruby balls, as shown in Fig. 8. The internal resonant modes are excited by an electro-static actuator and the oscillation decay is measured by a Michelson-type laser interferometer. We measured 13 different fused-silica samples. The size was 6 cm in height and 7 cm in diameter. These samples were supplied from various companies (Heraeus, Corning, Tosoh and Shinetsu). With this method, we observed very high Q values. For example, Heraeus samples (Suprasil-311 and -312) have Q values as high as 3.4310 7 . We measured 50 vibrational modes in each sample, and obtained the frequency dependence of the quality factor. In some samples, the quality factor has a weak frequency dependence. Table 1 summa-
Fig. 8. Setup of the nodal support system. A cross-section is shown: (1) ruby balls; (2) sample; (3) spring; (4) adjusters.
rizes the intrinsic loss of 13 fused-silica samples. We found that heat treatment can improve the Q values. The highest Q was 4.3310 7 for a Suprasil-312 sample after annealing. No correlation was found between the optical properties and the intrinsic mechanical Q value.
7. Conclusion In laser interferometric GW detectors, several methods are used to damp the motion of the mechanical system. Among them, passive damping methods are superior in simplicity and reliability compared with active damping methods. The method of material damping using M2052
Table 1 Measured Q values for 13 fused-silica samples before and after annealing Company / trade name
Maximum Q
Q After annealing
Heraeus Suprasil-1 Suprasil-2 Suprasil-311 Suprasil-312 Herasil-1
1.1310 7 1.3310 7 3.4310 7 3.4310 7 7.2310 5
2.1310 7 4.1310 7 4.3310 7 9.7310 5
Corning 7980-0A 7980-0F 7980-5F
1.1310 7 1.1310 7 1.0310 7
2.1310 7 (980 8C) 2.1310 7 (900 8C)
Tosoh ED-A ED-C ES
1.9310 7 8.8310 6 4.6310 6
Shin-etsu Suprasil P-10 Suprasil P-30
3.0310 6 1.0310 6
(900 8C) (900 8C) (980 8C) (900 8C)
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
alloy has been successfully demonstrated in the telescope suspension of the TAMA300 detector. The possibilities of using material damping in other parts of GW detectors should be explored.
Acknowledgements We are indebted to N. Mio for data concerning telescope damping by M2052. We also acknowledge R. Takahashi and N. Numata for discussions on metal-sealed rubber and high-Q materials. This research was supported, in part, by a Grant-in-Aid for Scientific Research on Priority Areas and a Grant-in-Aid for Scientific Research (B) of the Ministry of Education, Culture, Sports, Science and Technology.
References [1] K. Tsubono, in: E. Coccia, G. Pizzella, F. Ronga (Eds.), Gravitational Wave Experiments, World Scientific, Singapore, 1995, p. 112. [2] C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, Freeman, San Francisco, 1973.
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[3] J.H. Taylor, J.M. Weisberg, Astrophys. J. 345 (1989) 434. [4] K.S. Thorne, in: S. Hawking, W. Israel (Eds.), 300 Years of Gravitation, Cambridge University Press, Cambridge, UK, 1987, p. 330. [5] A. Abramovici et al., Science 256 (1992) 325. [6] The VIRGO Collaboration, VIRGO Final Design Report, VIR-TRE1000-13, 1997. ¨ Quantenoptik Report [7] K. Danzmann et al., Max-Planck-Institut fur No. 190, 1994. [8] The TAMA Collaboration, M. Ando, Class. Quantum Grav. 19 (2002) 1409. [9] M. Ando et al., Phys. Rev. Lett. 86 (2001) 3950. [10] H. Tagoshi et al., Phys. Rev. D 63 (2001) 1. [11] K. Tsubono, A. Araya, K. Kawabe, S. Moriwaki, N. Mio, Rev. Sci. Instr. 64 (1993) 2237. [12] R. Takahashi, F. Kuwahara, E. Majorana, M.A. Barton, T. Uchiyama, K. Kuroda, A. Araya, K. Arai, A. Takamori, M. Ando, K. Tsubono, M. Fukushima, Y. Saito, Rev. Sci. Instr. 73 (2002) 2434. [13] F.X. Yin, Y. Ohsawa, A. Sato, K. Kawahara, J. Mater. Sci. Technol. 14 (1998) 299. [14] N. Mio, T. Tanji, S. Moriwaki, Class. Quantum Grav. 19 (2002) 1647. [15] H.B. Callen, R.F. Green, Phys. Rev. 86 (1952) 702. [16] K. Numata, G.B. Bianc, M. Tanaka, S. Otsuka, K. Kawabe, M. Ando, K. Tsubono, Phys. Lett. A 284 (2001) 162. [17] K. Numata, S. Otsuka, M. Ando, K. Tsubono, Class. Quantum Grav. 19 (2002) 1697.
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Application of material damping for gravitational wave detectors K. Tsubono* Department of Physics, University of Tokyo, 7 -3 -1 Hongo, Bunkyo-ku, Tokyo 113 -0033, Japan
Abstract Gravitational waves, predicted by Einstein in the theory of relativity, are expected to open a new window into the Universe. Although worldwide efforts are being made, gravitational waves have not yet been detected directly, since their effect is extremely weak. In gravitational wave detectors, there are several noise sources. One is the resonant peaks in mechanical systems, such as vibration isolation and test mass suspension. Active and passive methods are used to suppress high-Q resonances of mechanical structures. Also, low-loss materials for the mirrors are crucial to reduce thermal noise. We describe these aspects of damping which appear in gravitational wave detectors. 2003 Elsevier Science B.V. All rights reserved. Keywords: Gravitational wave; Damping material; Laser interferometer
1. Introduction In laser interferometric gravitational wave (GW) detectors, two opposite concepts, high damping and low loss, are important to achieve both high sensitivity and high stability. High damping for mirror isolation is desirable to suppress the resonant peaks and residual motion of mirrors. In our TAMA300 laser interferometric GW detector [1], we have used metal-sealed rubber in a stack for vibration isolation to achieve vacuum-compatible isolation with sufficient damping. We have also applied a damping alloy (M2052) in the suspension of the telescope for mode-matching, and confirmed that material damping works effectively in the GW detector. Extremely low-loss materials are crucial for mirrors in order to reduce thermal noise. We have developed a method to measure the intrinsic Q of low-loss materials. With this method, we performed a series of measurements for several fused-silica samples, and found that some kinds of fused silica have very high Q values.
produced by dynamic sources, such as rotating binary stars, the curvature of space will change with time and propagate in all directions with the speed of light. This ripple of space–time is the GW. Hulse and Taylor confirmed the existence of GWs by observing the orbit change of a binary pulsar, SN1913116, in the 1980s [3]. The disturbance in the orbit was caused by energy loss due to the emission of GWs. The existence of GWs was thus confirmed indirectly. However, a direct observation of GWs has not yet been realized, since their effect is extremely weak. GWs are produced by various astronomical sources [4]. The coalescence of binary stars will emit GWs; the stars can be neutron stars or black holes. A supernova is the last stage of life of a massive star and produces strong GWs during its explosion. Cosmic strings made just after the big bang are expected to produce GWs. GWs carry an important piece of information about catastrophic events which cannot be probed through other astronomical observations in the optical, radio, or X-ray bands. GWs are expected to open a new window onto the Universe; this window is gravitational wave astronomy.
2. Gravitational waves (GWs) In 1916, Einstein predicted GWs in the theory of relativity. In his theory, gravity is expressed by the curvature of space–time [2]. If gravity is, therefore, *Tel.: 181-3-5841-4141; fax: 181-3-5841-4279. E-mail address: [email protected] (K. Tsubono).
3. Laser interferometric GW detector How to detect GWs is described here. A GW will change the distance between two free masses. The amplitude of a GW is expressed in terms of h, which is a dimensionless number and is equal to the magnitude of the
0925-8388 / 03 / $ – see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S0925-8388(03)00234-2
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
strain. The typical amplitude of h is |10 221 ; this number is our present target for detection. Even if a GW with this amplitude incidents between the Sun and Earth (the distance is 1.5310 8 km), the change in distance will be only the size of a hydrogen atom. A Michelson-type laser interferometer is used to detect such a tiny effect of GWs. Worldwide efforts are being made to detect GWs. In the US, two 4-km arm-length interferometers have been built in Hanford and Livingston [5]. A French and Italian team is constructing a 3-km arm-length interferometer in Pisa, Italy [6]. A 600-m arm-length detector is under construction in Hannover, Germany, in a collaboration between the UK and Germany [7]. A simplified scheme of a laser interferometric GW detector is shown in Fig. 1. The laser beam is split into two orthogonal directions by a beam-splitter, and the reflected light from the two arms is combined at the photo-detector. Since a GW has a quadrupole pattern, it causes different effects on the two orthogonal lengths. Thus, GW can be detected as the fringe-pattern change in the output of the photo-detector. TAMA is the name of a Japanese project for GW detection [1]. The TAMA300 laser interferometric GW detector has an arm-length of 300 m and is located on the campus of the National Astronomical Observatory in Mitaka. The whole detector was constructed underground so as to reduce disturbances from outside. All of the optics are housed in vacuum chambers and pipes. We started operation of the TAMA300 detector in 2000 ] [8]. The achieved sensitivity, h˜ | 5 3 10 221 /ŒHz from 700 Hz to 1.5 kHz, is sufficient to catch possible gravitational wave events in our galaxy [9]. We can operate the detector for over 24 h stably and continuously. Last summer we performed a 2-month data-taking run and collected over 1000 h of data. We are now analyzing the obtained data, searching for gravitational waves from coalescing binaries using a matched filtering technique with templates of the chirping signal [10]. There are several noise sources in the interferometric GW detector. Laser shot noise, thermal noise, seismic noise, electric noise, and gravity gradient noise are the
Fig. 1. Schematic view of the TAMA300 laser interferometric GW detector. Because the GW has a quadrupole pattern, it causes different effects on two orthogonal 300-m arms. Thus, GW can be detected as a fringe-pattern change in the output of the photo-detector.
225
Fig. 2. Scheme of a typical double-pendulum mirror suspension system. To damp the pendulum motion of the mirror, we use low-Q materials in the suspension frame and the upper-stage wire. Alternatively, we can apply a damping force on the intermediate mass. To reduce thermal noise we use high-Q materials for the lower stage wire and the mirror.
dominant noise sources. Among these noises, thermal and seismic noises are considered in this article.
4. The mirror and its suspension In principle, the detector measures small changes in the distance between two mirrors; hence, the most important parts of the interferometer are the mirrors. They are usually suspended by wires so that they act as free masses and are isolated from ground vibration. The TAMA mirrors are made of fused silica, 10 cm in diameter and are suspended by two-loop tungsten wires from an intermediate mass.
Fig. 3. TAMA300 mirror suspension system incorporating a stack for vibration isolation.
226
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
The mirror and intermediate mass make a double pendulum. Fig. 2 shows a scheme of a typical double-pendulum mirror suspension system. Low-Q and high-Q materials are used in this mirror and its suspension system. First, the pendulum motion of the mirror should be damped to a level, say Dx , 0.1 mm, since the laser light has a wavelength of about 1 mm. Also, we must avoid the resonant peaks in the structure. Therefore, the upper-stage wire and the frame materials should have low Q values. Alternatively, we can apply a damping force on the intermediate mass by some means. The mirror itself and the lower-stage wire should have a high Q in order to reduce the thermal noise. In this way, two contrasting properties appear in the mirror suspension system.
5. Damping for mirror suspension First, we describe the damping of the mirror suspension system. As an example, a schematic view of the TAMA mirror suspension system is shown in Fig. 3. The requirements for the suspension system are sufficient damping, good controllability and sufficient vibration isolation. The damping property is an important factor for the suspension system, as stated above. Damping schemes are divided into two categories, active and passive. An example of active damping is the mirror suspension
Fig. 5. Measured horizontal-to-horizontal transfer function of the stack, without and with a bellows. The two transfer functions were almost the same, showing that the degradation of the isolation ratio due to the bellows was negligible over this frequency range.
of the VIRGO detector [6]. In the VIRGO detector, an inverted pendulum and seven-stage cascaded vibration filters are used for the mirror suspension in order to obtain high isolation at low frequencies. The total length of the
Fig. 4. Cross-section of a three-stage stack for vibration isolation. Vacuum compatibility was achieved by enclosing rubber with a welded bellows.
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
Fig. 6. Telescope for mode-matching used in TAMA300. The optical components are suspended by wires to isolate them from seismic motion. Damping alloy M2052 is used in the suspension wire and the damper for the spring.
227
pendulum is 7.3 m. To stabilize the pendulum motion, they use an active control system consisting of position and acceleration sensors and actuators. With this active scheme, the system is fully adjustable, but very complicated. The other scheme is passive damping. The first example is magnetic eddy-current damping [11]. The pendulum motion is damped by an eddy current induced by strong permanent magnets around an intermediate mass. Using this scheme, all of the pendulum modes are damped. This scheme is used in the TAMA300 detector. This technique is simple and robust, but has little flexibility. A second example of passive damping is using rubber. In GW experiments, all of the optics is in a vacuum so as to avoid any optical and / or acoustic disturbances. Thus we have developed a vacuum-compatible vibration isolation stack comprising alternative layers of heavy mass and metal-sealed rubber [12]. We use chloroprene rubber
Fig. 7. Vibration isolation ratio of the telescope obtained with different configurations, with and without the M2052 material. The lower trace is a magnified view of the spectrum near the frequencies of the wire resonances.
228
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
blocks enclosed by a gas-tight metal bellows. Fig. 4 shows a cross-section of the vibration isolation stack. With this three-stage stack we could obtain 60 db vibration isolation at 100 Hz, as shown in Fig. 5. This method is also simple and robust. A third scheme is material (metal) damping. Here, we introduce a high-performance damping material (M2052). M2052 is a Mn-based twinning-deformation-type alloy. This alloy was invented by Kawahara and his group [13] and evaluated in the GW detector by Mio [14]. They use M2052 in the suspension for the TAMA mode-matching telescope. As shown in Fig. 6, the optics for the telescope is suspended by wires and springs. A damping alloy (M2052) is used in the wire and damper for the spring to suppress wire resonances. With M2052 materials, they achieved a Q of 45 for the wire resonance. The performance of the telescope suspension with damping material can be seen in Fig. 7. The system with M2052 damping material is now operating stably in the TAMA detector.
6. Low-loss materials for mirrors Next, we consider low-loss materials for mirrors. As can be seen from the fluctuation dissipation theorem, the mechanical loss is the origin of the thermal noise [15]. Therefore, the materials of the mirror and final-stage suspension wire should have very high Q values. The following are the results of a low-loss material search performed at the University of Tokyo [16,17]. In order to clarify the loss property of a material, it is necessary to measure the intrinsic Q of the material itself. However, usually the measured Q is dominated by loss due to the support. Hence, we have developed a method to measure the material’s Q using a nodal support technique. In this method, samples are supported at the nodes of the vibrational modes by point contact. Thus, any loss due to the support can be excluded. We used cylindrical samples, of which two center points on the flat surfaces are nodes in higher order modes. Samples are supported at the center points with two small ruby balls, as shown in Fig. 8. The internal resonant modes are excited by an electro-static actuator and the oscillation decay is measured by a Michelson-type laser interferometer. We measured 13 different fused-silica samples. The size was 6 cm in height and 7 cm in diameter. These samples were supplied from various companies (Heraeus, Corning, Tosoh and Shinetsu). With this method, we observed very high Q values. For example, Heraeus samples (Suprasil-311 and -312) have Q values as high as 3.4310 7 . We measured 50 vibrational modes in each sample, and obtained the frequency dependence of the quality factor. In some samples, the quality factor has a weak frequency dependence. Table 1 summa-
Fig. 8. Setup of the nodal support system. A cross-section is shown: (1) ruby balls; (2) sample; (3) spring; (4) adjusters.
rizes the intrinsic loss of 13 fused-silica samples. We found that heat treatment can improve the Q values. The highest Q was 4.3310 7 for a Suprasil-312 sample after annealing. No correlation was found between the optical properties and the intrinsic mechanical Q value.
7. Conclusion In laser interferometric GW detectors, several methods are used to damp the motion of the mechanical system. Among them, passive damping methods are superior in simplicity and reliability compared with active damping methods. The method of material damping using M2052
Table 1 Measured Q values for 13 fused-silica samples before and after annealing Company / trade name
Maximum Q
Q After annealing
Heraeus Suprasil-1 Suprasil-2 Suprasil-311 Suprasil-312 Herasil-1
1.1310 7 1.3310 7 3.4310 7 3.4310 7 7.2310 5
2.1310 7 4.1310 7 4.3310 7 9.7310 5
Corning 7980-0A 7980-0F 7980-5F
1.1310 7 1.1310 7 1.0310 7
2.1310 7 (980 8C) 2.1310 7 (900 8C)
Tosoh ED-A ED-C ES
1.9310 7 8.8310 6 4.6310 6
Shin-etsu Suprasil P-10 Suprasil P-30
3.0310 6 1.0310 6
(900 8C) (900 8C) (980 8C) (900 8C)
K. Tsubono / Journal of Alloys and Compounds 355 (2003) 224–229
alloy has been successfully demonstrated in the telescope suspension of the TAMA300 detector. The possibilities of using material damping in other parts of GW detectors should be explored.
Acknowledgements We are indebted to N. Mio for data concerning telescope damping by M2052. We also acknowledge R. Takahashi and N. Numata for discussions on metal-sealed rubber and high-Q materials. This research was supported, in part, by a Grant-in-Aid for Scientific Research on Priority Areas and a Grant-in-Aid for Scientific Research (B) of the Ministry of Education, Culture, Sports, Science and Technology.
References [1] K. Tsubono, in: E. Coccia, G. Pizzella, F. Ronga (Eds.), Gravitational Wave Experiments, World Scientific, Singapore, 1995, p. 112. [2] C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, Freeman, San Francisco, 1973.
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