Monolithic fused silica suspension for the Virgo gravitational waves detector

Transcription

1 REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 73, NUMBER 9 SEPTEMBER 00 Monolithic fused silica suspension for the Virgo gravitational waves detector P. Amico, L. Bosi, L. Carbone, a) and L. Gammaitoni Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I Perugia, Italy and Dipartimento di Fisica, Università di Perugia, I Perugia, Italy F. Marchesoni Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I Perugia, Italy and Dipartimento di Fisica, Università di Camerino, I-603 Camerino, Italy M. Punturo b) Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I Perugia, Italy F. Travasso and H. Vocca Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I Perugia, Italy and Dipartimento di Fisica, Università di Perugia, I Perugia, Italy Received April 00; accepted for publication 10 June 00 Thermal noise in mirror suspension wires is the most severe limit to the low frequency sensitivity of interferometric gravitational wave detectors presently under construction. The pendulum mode mechanical quality factor of the suspension last stage significantly affects the noise level of the detector output. The monolithic design for this suspension stage, using a low dissipation material, is proposed for Virgo. High mechanical Q s and high breaking strengths have been obtained for monolithic fused silica fibers. A low dissipation and high strength bonding technique using potassium silicate bonding is proposed. 00 American Institute of Physics. DOI: / I. INTRODUCTION Several interferometric gravitational wave detectors are close to being operative in the world: LIGO, 1 GEO600, TAMA, 3 and Virgo. 4,5 The optical cavities of such interferometers are realized by suspending massive fused silica mirrors to a relatively complex chain of seismic attenuation stages. In Virgo, for instance, thermal noise due to the fluctuation of the suspension last stage in the pendulum mode is expected 6 to dominate the antenna sensitivity in the 5 50 Hz range. The power spectrum X() of the mirror surface displacement X(t), due to the pendulum mode of the mirror, is given by the fluctuation-dissipation theorem 7 X 4k BT R 1 Z 4k BT IH, 1 where f, Z() is the mechanical impedence and H() is the force to displacement transfer function of the last stage suspension. Currently, the Virgo mirror a cylinder of fused silica, 0.35 m across and about 0.1 m thick (m1 kg) 8 is suspended by a cradle formed by two parallel wire loops hanging 50 mm apart. The effective length of the resulting pendulum is about 0.7 m. The wires are made of C85 harmonic steel and their diameter is d w 0. mm. 9 Four a Present address: Dipartimento di Fisica, Università di Trento, I Povo, Italy. b Author to whom correspondence should be addressed; electronic mail: michele.punturo@pg.infn.it BK7 borosilicate crown optical glass prisms are inserted as spacers between the mirror lateral surface and the suspension wires. There are three contributions to the detector noise level that are due to the thermal motion of the suspension wires: pendulum and spring vertical oscillations of the suspended mass, violin mode motion of the wires. Let us start considering only the pendulum mode. In this case, it is possible to model the suspension as an ideal oscillator and to use a structure damping model i.e., we assume the loss angle ()const, see below to account for the internal dissipation process. 10 The horizontal force to displacement transfer function is expressed as H h 1 1 m 0 i 0w, where m is the mass of the suspended mirror and () the loss angle of the oscillator. The resonance frequency 0 is given by 0 0w 0g, 0g g, 0w k el m n f p EI 1 m, where k el is the elastic constant of the suspension wire, E is the Young s modulus of the suspension wire material, I /64d 4 w is the moment of inertia of a wire cross section /00/73(9)/3318/6/$ American Institute of Physics Downloaded 15 Oct 00 to Redistribution subject to AIP license or copyright, see

2 Rev. Sci. Instrum., Vol. 73, No. 9, September 00 Monolithic suspension for Virgo 3319 with diameter d w, n is the number of suspension wires in Virgo n4, f p is the number of flexural points in a wire ( f p ), and is the wire tension ( mg/n). The oscillator loss angle has three main components Y 4k BT m vt w H vt, 9 h vt f 0 Y, L arm where h vt ( f ) represents the relevant contribution in the displacement horizontal direction, 0 being the vertical to horizontal coupling angle given by the Earth s curvature in Virgo In effect, a different and larger coupling between the vertical modes and the horizontal displacement is expected because of some asymmetry in the suspension; this effect is hardly modeled a priori and for this reason has been neglected. The violin modes contribution can be expressed as 6,10 w e th, where w is the loss angle due to the wire material itself, e is the excess loss angle due to parasitic dissipation processes like the residual clamping losses 11 and th () is the thermoelastic contribution 9,1 to the dissipation th 1, 4 X viol 4 4k BT i 1 i w d w m h viol L arm X viol, i i i i i, 10 E T c, 5 c d w.16, where c is the specific heat, the linear expansion coefficient and is the conductivity of the wire material. Finally, from Eqs. 1 and, the fluctuation power spectrum can be espressed as X Pend 4k BT m 0w H h, 6 h Pend f X L Pend, arm where h Pend is the amplitude spectral density in terms of equivalent h and L arm is the interferometer arm length (L arm 3000 m in Virgo. For the vertical spring motion we have the vertical force to displacement transfer function represented by H vt 1 1 m vt i vt w, 7 where the vertical oscillation frequency vt is vt d w / E m n. 8 The vertical displacement spectrum is thus where i i w L d 1 w w EI, i i EI 1 i i EI 1 11 and w is the density of the wire material. The low frequency tail ( i ) of this noise contribution is negligible in a detector like Virgo. If B is the tensile breaking strength in Pascal of the wire material, the moment of inertia I can be expressed as I d w C s B mg nc s B, 1 where C s is a safety factor (C s 1) that expresses the percentage of the breaking stress at which the wire is loaded. Finally, using 1 in the pendulum Eq. 6 and in the spring vertical Eq. 9 power spectrum expressions, it is possible to obtain the total relevant displacement power spectrum, which for frequencies higher than the resonance frequencies can be written as X h 4k BT g 1 5 Eg 4nm C s B 0 E w m C s B. 13 This is the noise level expected in a gravitational wave detector like Virgo in the Hz range, where the seismic noise is suppressed by an efficient seismic attenuation chain and the Newtonian noise 13 is comparable in amplitude up to 4 10 Hz. From Eq. 13 the importance of the minimization of the ratio ()/(C s B)] is evident. The optimal material to realize the mirror suspension should be a low dissipation material with a high and reliable C s not too small breaking strength. The search for a material that can satisfy these requirements has been pursued by Braginsky s group in Moscow see, for example, Refs. 14 and 15, who first revealed the promising properties of fused silica fibers in gravitational waves detection. Downloaded 15 Oct 00 to Redistribution subject to AIP license or copyright, see

3 330 Rev. Sci. Instrum., Vol. 73, No. 9, September 00 Amico et al. Fig.. The taper shape and the central wire diameter are related to the length of the part of the rod melted by the flames and to the pulling speed. It is possible to model the shape of the taper as in Ref. 17; in Fig. the wire shape is modeled with an exponential taper dotted line and with an inverse square root taper continuous tick line FIG. 1. Picture of part of the wire production machine. II. EXPERIMENTAL APPARATUS In order to meet these requirements we realized and tested prototypes 16 with different design and material. In the following we will briefly describe the facilities that have been used to build and test a monolithic fused silica suspension system, together with the results obtained. The first apparatus to be described is the machine realized to produce fused silica fibers with large heads, to be used as the test mass suspension wires. The mechanical part of this machine has been developed in collaboration with S. McIntosh, of the Glasgow GEO600 group. It consists of two vertically sliding frames, reported in Fig. 1; that pull a fiber starting from a 5-mm-diam synthetic fused silica rod. The rod is melted in a relatively small region using a concentric crown of flames. The flames are produced from very pure oxygen and hydrogen gas. The fibers produced with this technique have been geometrically characterized with a computerized microscope that reads the fiber profile along its entire length. The fiber presents two large heads connected to the central part at constant diameter through two tapers see FIG.. Typical monolithic fiber profile. Continuous thin line: experimental data; continuous tick line: inverse square root model of the taper; dotted line exponential model of the taper. r 0 rz, 14 1 r 0 1 z r 1 where r(z) is the transvers radius of the taper along the longitudinal z coordinate of the wire, r 0 is the radius of the original fused silica rod, r 1 is the radius of the fiber and z 0 is the taper length. Equation 14 reproduces the taper shape of our fibers. The current version of the production machine, with a simple manual control, is able to produce wires of the Virgo expected length 0.7 m with a fluctuation of about 0.05 m. A new version of the production machine, based on a commercial, motorized, material testing instrument, is under development in the Perugia Labs. A different setup is used to measure the breaking strength of the fused silica fibers. It has been noted that it is extremly easy to underestimate the effective breaking strength of fused silica. In fact, scratches on the fiber surface can reduce the breaking strength by more than one order of magnitude. For brittle materials like fused silica, Griffith s crack theory 18 is valid; if a is the dimension of the largest crack on the surface of the wire, the fracture stress is given by E a, 15 where is is the surface energy per unit area (J/m ). The surface energy is equivalent to the work done when bonds are broken during the process of creating new surfaces. It is extremely important to avoid any contact between the fiber and any hard surface during breaking strength measurement or mirror suspension. For this reason, a breaking strength measurement setup has been realized directly in the production machine itself, in such a way any transportation and handling of the wire has been minimized. The experimental apparatus used for the measurement of the loss angle has been already described in a previous article. 9 Some improvement has been obtained in the recoil losses reduction and in the readout noise. Our sample wires are clamped vertically and left to hang freely. The vibration mode frequencies are given by the relations f 1 1. g, f i i EI l, z 0 16 where l is the mass per unit length and 1.875, , , The suspended wire vibrations are excited by an electrostatic actuator. The resulting motion is read through a shadow sensor made by an infrared Downloaded 15 Oct 00 to Redistribution subject to AIP license or copyright, see

4 Rev. Sci. Instrum., Vol. 73, No. 9, September 00 Monolithic suspension for Virgo 331 light-emitting diode and a two quadrant photodiode. The two current signal are first amplified and then subtracted in such a way that the common mode noise is suppressed. The ringdown of the ith mode is acquired and the corresponding mechanical quality factor is measured online. The mechanical quality factor Q i of the ith mode is related to the decay time i through the formula Q i f i i. 17 The decay time i is measured by fitting the exponential decay of the ring down envelope. The online computation of the decay time is performed using a LabView program that calculates the Hilbert transform see Eq. 18 and Ref. 0 H x(t) of the ring down x(t) and then extracts the envelope function from the analytic signal z(t)x(t)i H x(t): H xt 1 xt tt dt. 18 The last step in order to realize a monolithic suspension, once the fiber is produced, is to attach the fiber head to the mirror. It is pratically impossible to hot weld the fiber directly to the mirror; in fact, because of the high melting temperature and the low thermal conductivity of fused silica, directly welding the fiber to the mirror locally heated causes a large stress on the mirror substrate itself. It is necessary to transform the fiber-to-mirror welding in a fiber-to-fiber welding procedure. For this reason, following the pioneering work of the Glasgow GEO600 group, 1 an intermediate step must be performed; a small fused silica appendix, so-called ear, to which the fiber will be welded, is attached to the mirror. This ear will be attached to a flat strip machined on the lateral surface of the Virgo mirror. The bonding technique to glue the ear to the mirror is a hydroxide catalyzed hydration dehydration chemical process called silicate bonding, developed in the Gravity Probe B project by Dr. J. Gwo. This technology was acquired by the Perugia Labs several years ago through a collaboration project with the Glasgow GEO600 group. The first step of this process is the hydration, with a pure KOH solution or in other cases 3 with a NaOH solution, oftheear and mirror bonding surfaces, that must exhibit a good surface flatness level /10, 633 nm. In this step silanol groups Si OH are formed on the bonding surfaces. The second step is the etching caused by the KOH on the fused silica surfaces. Several Si O bonds are broken and a certain amount of inosilicates and oligosilicates SiO 3 chains are formed in solution through the reaction SiO KOH K SiO 3 H O. 19 The third and last step is the dehydration, caused by KOH, of the Si OH groups with the formation of Si O Si bridges that, connecting to the silicates chains in solution, construct the solid interface between the two bonding surfaces. In the Virgo suspension, the ear attached to the mirror is under a shear and torsion composed stress, because the fused silica fiber is welded a few millimeters apart from the mirror surface. A test bench has been realized to measure the strength of the bonding in operative condition: two small cylindric FIG. 3. Breaking strength of fused silica fibers. White bars: acid solution cleaning procedure. Gray bars: Ethilic alcohol cleaning procedure. Black bars: uncleaned fused silica rods. fused silica samples, attached by silicate bonding, can be stressed with a screw that applies a progressive force at about 5 mm away the bonding surfaces in such a way that a large torsion is applied together with a shear stress. The applied stress is measured through a load cell inserted between the screw and the cylinder lateral surface. A force of several hundred newtons can be exerted with this device. III. EXPERIMENTAL RESULTS Since the strength of fused silica fibers depends on the quality of the surface, the effect of rod surface cleaning procedure on the fiber strength has been investigated. Fused silica rods have been cleaned before fiber pulling using either ethyl alcohol gray bars in Fig. 3 or an acid solution white bars in Fig. 3 made by sulfuric acid, hydrogen peroxide, and potassium bichromate. There is no difference between the cleaned and uncleaned rods black bars in Fig. 3. An average value of B GPa can be extracted from Fig. 3. This must be compared with the breaking strength of C85 wires: B C GPa. The fused silica breaking strength is higher than the C85 value, but shows a larger fluctuation. This is mainly due to the fact that the fused silica breaking strength is dominated by surface defects, as reported by Eq. 15. The fused silica loss angle is shown in Fig. 4 versus the mode frequency. It is clear that the fused silica loss angle is two orders of magnitudes lower than the C85 loss angle. The different frequency behavior is due to the different thermoelastic contribution. In fact, a 00-m-diam C85 wire shows the thermoelastic peak around 680 Hz, while a m-diam fused silica fiber should show the same peak at Hz. In Fig. 4, there are two different curves for fused silica fibers shown. The curve with solid triangles is taken by hanging a fiber with an intermediate massive bob to reduce the suspension recoil losses. 4 Since a small difference is measured between the fused silica with and without Downloaded 15 Oct 00 to Redistribution subject to AIP license or copyright, see

5 33 Rev. Sci. Instrum., Vol. 73, No. 9, September 00 Amico et al. FIG. 4. Loss angle. Squares: C85 wire. Circles: synthetic fused silica. Triangles: synthetic fused silica with isolation bob. an isulating bob, a low recoil loss contribution is expected in our apparatus. The measurements of the silicate bonding strength are reported in Fig. 5, where the stress in MPa is obtained dividing the force applied by the bonding surface. First, it should be noted that, in order to avoid impurities in the bonding surfaces that can be, under stress, the starting point of a fracture, it is necessary to maintain a high cleanliness level during the entire bonding process. For this reason very pure KOH solution has been used and the bonding surfaces have been well cleaned with the acid solution, isopropanol alcohol and pure water. All the bonding processes have been performed under a class 100 laminar flux bench. Several strength tests have been performed on cylindric samples with different flatness levels. Samples with flatness equal to /k with k10,7,4 and 633 nm have been silicate bonded. In Fig. 5, the samples with /10 flatness, tested after 44 days, show too low breaking stress. Under microscope analysis, they showed a poor bonding quality, possibly due to bad cleaning or low solution purity. FIG. 5. Silicate bonding strength: the numbers k10,7,4 close to the symbols indicate the flatness quality of the surface in terms of /k. FIG. 6. Expected sensitivity curve in Virgo: a expected total sensitivity with C85 steel wires; b contribution due to the mirror thermal noise (Q mirror ); c contribution due to the pendulum thermal noise if Q pend 10 9 and Q Eddy ; d contribution due to the pendulum thermal noise if Q pend 10 9 and Q Eddy ; e contribution due to the pendulum thermal noise if Q pend 10 8 and Q Eddy ; f contribution due to the pendulum thermal noise if Q pend 10 7 and Q Eddy. IV. DISCUSSION Fused silica is a promising material for the suspension wires of the optics of a gravitational wave detector like Virgo. From the lower curve in Fig. 4, it is possible to extract the structural loss angle of the fused silica w , which is more than two orders of magnitude lower than the loss angle of the C85 steel. In the present analysis the further distinction between the bulk and surface dissipation contribution to the structural loss angle has been neglected for a more accurate treatment of this point see Refs. 4 and 5. The breaking strength of fused silica fibers is also larger than the corresponding value for C85 steel wires, currently adopted as reference solution. The large spread of the breaking strength measures determines a decrease of the safety factor C s for fused silica. Using fused silica fibers of 300-m-diam to hang the Virgo mirror, a safety factor of C s 15% is obtained; this value must be compared with the 65% adopted for C85 steel wires. The use of potassium silicate bonded ears to attach the suspension wires to the mirror is compatible with the strength of this kind of bonding. The shape of the ears to be used in Virgo is still to be defined, but to have a safety factor about 3, in terms of breaking stress, a contact area larger than 150 mm, is foreseen. The effect of silicate bonding on the pendulum Q for a Virgo-like configuration must be still investigated; previous measurements 16 taken on a smaller mirror realized by the Glasgow GEO600 group and hanged through two suspension fused silica fibers to the low recoil losses facility in Perugia, showed promising results. Previous results by other authors 6 and preliminary measurements on the effect of the silicate bonded ears on the mirror Q in the configuration reported in Ref. 7 show that the substrate quality factor is not affected by the presence of the ears. The feasibility of a full-fused silica suspension for a gravitationl wave detector is confirmed by the fact that, in June 001, the GEO600 collaboration assembled a first Downloaded 15 Oct 00 to Redistribution subject to AIP license or copyright, see

6 Rev. Sci. Instrum., Vol. 73, No. 9, September 00 Monolithic suspension for Virgo 333 monolithic suspension in their interferometer. In that case the mirror was much lighter about 5.6 kg than required by Virgo and the suspension fibers were overdimensioned to be compliant with the local control requirements with respect to actual load; in this configuration the monolithic suspension design proved to work well. If a full fused silica suspension will be realized in Virgo, a great improvement in the sensistivity is expected. In Fig. 6, the different sensitivity scenarios are plotted. The thick continuous line (a) represents the expected sensitivity with the reference Virgo setup 6 and the thin continuous line (b) represents the thermal noise contribution due to the mirror vibration 7 if a substrate Q of about is used. If we use the loss angle value with the Virgo suspension geometry dilution factor, the expected pendulum Q is about The resulting thermal noise contribution to the sensitivity curve is reported in the dotted line (d) in Fig. 6. In this curve and in all the computation reported in this article the effect on the dilution factor 17 of the fiber taper shape has been neglected. Since previous measurements 16 showed a lower Q measured for real pendulum suspended through fused silica suspension, because of the presence of excess losses, the other two curves (e) and ( f ) have been plotted in Fig. 6 using, respectively, Q pendulum 10 8 and Q pendulum In any case, for this class of curves there is a large expected improvement in terms of sensitivity respect to the use of C85 stell wires. In Ref. 8 another source of losses for the pendulum oscillation has been investigated. The eddy currents induced by the mirror magnets on the reference mass limit the pendulum Q in Virgo to about In this case the expected sensitivity with fused silica suspension and conductive reference mass is reported in the dashed line (c) in Fig. 6. This one is a viscous loss and the slope of the pendulum thermal noise contribution to the sensitivity is thus different. 6 The obtained results suggest, for an advanced design for the Virgo interferometer, the use of fused silica suspension wires and a dielectric reference mass. ACKNOWLEDGMENTS This research has been supported by the Istituto Nazionale di Fisica Nucleare INFN under the Virgo Project. 1 A. Abramovici et al., Science 56, K. Danzmann et al., GEO600: Proposal for a 600 m Laser Interferometric Gravitational Wave Antenna. Max-Planck-Institut für Quantenoptik Report No. 190, Garching, Germany, K. Tsubono and the TAMA collaboration in Gravitational Wave Detection, edited by K. Tsubono, M.-K. Fujimoto, and K. Kuroda Universal Academy, A. Giazotto, Phys. Rep. C18, ; C. Bradaschia et al., Nucl. Instrum. Methods Phys. Res. A 89, VIRGO Collaboration, The VIRGO Final Conceptual Design, VIR-TRE- DIR , Virgo Internal Note, M. Punturo, The VIRGO sensitivity curve, VIR-NOT-PER , Virgo Internal Note, 001, and see 7 H. B. Callen and T. A. Welton, Phys. Rev. 83, ; H. B. Callen and R. F. Greene, ibid. 86, G. Cagnoli et al., Rev. Sci. Instrum. 71, G. Cagnoli et al., Phys. Lett. A 55, P. R. Saulson, Phys. Rev. D 4, ; Y.L.HuangandP.R. Saulson, Rev. Sci. Instrum. 69, G. Cagnoli et al., Phys. Lett. A 13, C. Zener, Elasticity and Anelasticity of Metals University of Chicaco Press, Chicago, G. Cella et al., Class. Quantum Grav. 15, V. B. Braginsky et al., Phys. Lett. A 175, V. B. Braginsky et al., Phys. Lett. A 18, G. Cagnoli et al., Phys. Rev. Lett. 85, P. Willems and M. Thattai, Phys. Lett. A 53, R. A. Higgins, Properties of Engineering Materials Arnold, London, 1994 ISBN P. M. Morse, Vibration and Sound McGraw Hill, New York, J. S. Bendat and A. G. Piersol, Random Data-Analysis and Measurement Procedures Wiley, New York, 1986 ISBN N. Robertson et al., Proceedings of the Third E. Amaldi Conference AIP, New York, 000, p S. Buchman et al., Adv. Space Res. 5, H. Y. Wang et al., Sens. Actuators B 45, A. M. Gretarsson et al., Rev. Sci. Instrum. 70, A. M. Gretarsson et al., Phys. Lett. A 70, S. Rowan et al., Phys. Lett. A 46, P. Amico et al., Rev. Sci. Instrum. 73, G. Cagnoli et al., Rev. Sci. Instrum. 69, Downloaded 15 Oct 00 to Redistribution subject to AIP license or copyright, see