The quasi-monolithic suspensions are at the heart of the advanced LIGO interferometers. The suspensions provide the technique for holding the 40 kg test mass optic in a quiet reference frame; minimising seismic noise and also thermal noise arising from thermodynamic fluctuations. The requirements are extremely stringent, requiring no more than 10-19 m of motion at 10 Hz per second of operation (or 10-19 m√Hz). To meet this goal requires state-of-the-art technology, pioneered in GEO 600, which features fused silica fibres to suspend the test mass.
Figure 1 below shows the quadruple pendulum suspension which was a major deliverable from the UK groups. The suspension comprises 4 stages; the upper two are made of metal and the lower two are made of fused silica; an ultra-high purity glass. Metal wires suspend the upper 3 stages while fused silica fibres are used to suspend the test mass. The pendulum stages provide seismic isolation above their resonant frequencies while the final fused silica stage provides seismic isolation and the low thermal noise performance. The suspension also requires isolation from vertical ground motions and this is provided by 3 stages of springs which are housed in the metal masses and the upper support structure. The use of 4 pendulum stages means that if we push the top mass of the suspension, at a frequency of 10 Hz, the motion of the test mass is 100 million times smaller. It is this method by which the ground motion, which is typically picometre (10-12 m√Hz) displacement at the top of the quadruple suspension, can be reduced to the requisite level of 10-19 m√Hz.
A functioning interferometer requires the ability to point the test mass and for this reason a second pendulum suspension hangs behind the main optic chain. This "reaction chain" is used to apply forces onto the optic and because it is also suspended, it does this in as quiet a way as possible. The first 3 masses of the quadruple pendulum have magnets attached onto them, while the reaction chain carries small coils which can be energised with current. This type of voice coil actuator is an efficient method for applying forces onto the optic. Advanced LIGO utilises a technique called hierarchical control whereby the control forces are reduced as we go down the test mass chain, thus smaller magnets are attached to the penultimate mass. At the test mass there are no magnets attached and the forces are applied via an electrostatic drive. The reaction mass has gold quadrant electrodes onto which a high frequency high voltage can be applied. By changing the level of this voltage it is possible to apply tiny forces at the micro-Newton level for final tuning of the interferometer angular alignment and positioning.
The thermal noise of a gravitational wave suspension is made up of Brownian noise (due to internal friction in the material) and thermoelastic noise (due to statistical temperature fluctuations coupling through the thermo-mechanical properties). Ultra-low thermal noise requires the use of a fused silica monolithic suspension for the final stage; a technology that has been developed and characterised in Glasgow for both the work on GEO and Advanced LIGO since 1995. Fused silica is used because its level of internal friction is approximately 1000 times lower than a typical metal such as stainless steel. Figure 2 shows a comparison of the initial LIGO and Advanced LIGO suspension designs. In initial LIGO a single loop of metal wire supported a 10.7 kg optic. This wire was clamped at the upper point using steel clamps. While this suspension provided suitable performance for the initial detectors, improving the broadband sensitivity of Advanced LIGO and pushing the lowest operating frequency down to 10 Hz required a significant increase in suspension performance; driving the new fused silica technology.
Advanced LIGO Suspensions
For Advanced LIGO, techniques have been developed in Glasgow to fabricate the suspension fibres and develop techniques to attach the fibres to the masses. In Figure 2 the "ears" are bonded to the side of the test mass. We utilise a technique called hydroxide-catalysis bonding which enables us to make the ear/mass attachment rigid and low noise. This technique was initially developed in Stanford for the Gravity Probe-B mission and was transferred to Glasgow, where we subsequently developed the process for the ground-based gravitational wave network. The ears have two horns onto which fused silica fibres are welded.
The fibres are produced with a carbon dioxide laser pulling machine shown in figure 3. The pulling machine directs 100 W of 10.6 µm laser light (infra-red radiation) onto the silica stock causing it to heat up to over 1750 °C and become molten (figure 4). The top end of the fibre is pulled out from the melt forming the fibre, with the speed determining the ultimate diameter. In this way we can produce fibres of identical length which are similar to approximately 20 µm in diameter. These machines are the state-of-the-art for producing high quality strong fused silica fibres, and the Glasgow group has built pulling machines for Advanced LIGO and Advanced VIRGO.
The fibre end stock, which is welded to the horns, is 3 mm diameter and it is from this stock that a fibre is pulled. Each fibre is approximately 600 mm long and is 400 µm diameter at its thinnest point. At each end of the fibre, over the last 10mm length, the fibre diameter increases to 800 µm to cancel thermoelastic noise. This noise couples temperature fluctuations into the suspension via the thermal expansion coefficient and also the change in Young's modulus, or fibre stiffness, with temperature. Fused silica has a remarkable property in that at room temperature these two effects can be made to cancel by choosing the appropriate stress in the fibre. It is for this reason that the fibre is thickened at the end, such that the stress is around 200 MPa rather than the 800 MPa in the centre. The fibre must be made thinner in the centre as we require the bouncing mode of the suspension to be below 10 Hz, the lower limit of Advanced LIGO, and also the violin modes, which are analogous to the plucking of a string, above 400 Hz. To demonstrate the remarkable low loss nature of the fibres, a violin mode will only decay in amplitude by 33% after 4 days of oscillation, performing roughly 300 million cycles. It is this remarkable performance that enables Advanced LIGO to reach a sensitivity of 10-19 m√Hz at 10 Hz. There are 4 fibres used to suspend each Advanced LIGO test mass, so each carries a load of 10 kg. This is well below the ultimate tensile strength of fused silica which would suspend approximately 70-80 kg on each fibre. This is equivalent to a stress of 4 GPa, well above the yield point of typical metals like steel.
The suspension is termed a quasi-monolithic structure meaning that it looks like it is fabricated from a single piece of fused silica. The 40 kg mirrors are polished, coated and have ears bonded onto their sides. The test mass/penultimate mass are then inserted into the support structure and aligned to their nominal position. Each fibre is then tested prior to installation by suspending 15 kg (150% of the final operating load) for 5 minutes to ensure robustness. The fibre is then cut to length, installed into a set of ceramic tweezers (figure 5) and brought into the suspension structure. The 4 fibres are welded to the ears using a 2nd carbon dioxide laser. The laser beam is piped to the weld point via an articulated arm, comprising rotatable joints with gold mirrors. Each weld typically takes 15 minutes and a full suspension can be completed in 1-2 days. Once the 8 welds have been performed (2 per fibre) the test mass position and angle is measured. The requirements are that the position should be ±0.1 mm and the angles ±2 mrad. This is achieved via a precision autocollimator and siting telescope. A final critical step is called "destressing", in which the fibres are extended by 5% of their full deflection while a laser beam heats the silica fibre stock. This ensures that the fibres hangs straight and is also used to remove any thermal stress. This is repeated for the top 4 welds and then the 4 bottom welds.
Suspension hanging and characterisation
After destressing the suspension is ready for hanging. The tension is applied to the fibres by lowering the test mass on a jack. Due to the softness of the suspension fibres the 40 kg optics extends approximately 6mm during the application of the full load on the fibres. This entire process is monitored with the siting telescope. The final stage of suspension construction includes measuring the suspension modes and first 4 violin modes of each fibre, which can then be used to build up a complete model of the system. We profile each fibre prior to welding and have bespoke Finite Element codes to predict the thermal noise performance of each suspension for the purpose of characterisation and testing. The lower suspension stage is then mated to the remaining 3 stages of the quadruple pendulum, and the entire system is then bolted onto the underside of the Advanced LIGO seismic isolation system. This entire system is then lifted into the chamber for further characterisation in air. The final stage is to pump the entire vacuum chamber down, perform further in-vacuum tests, then wait for a gravitational wave.