Mechanical loss of fused silica fibres for use in gravitational wave detectors.

This thesis is an account of work carried out at the Institute for Gravitational Research (IGR), in the University of Glasgow between October 2010 and March 2014. The research presented contributes to the design of ultra-low mechanical loss suspensions for use in gravitational wave detectors and other kinds of interferometry. This thesis focuses on measuring the parameters of mechanical loss in fused silica suspensions that will limit the sensitivity of advanced gravitational wave detectors and other kinds of interferometers where fused silica suspensions are used. These investigations were carried out under the supervision of Dr Giles Hammond and Professor Sheila Rowan. Chapter 1 gives an introduction to gravitational wave astronomy and provides an insight into which astrophysical objects are able to emit gravitational radiation. The chapter goes on to describe current and future detection techniques that are used and planned in order to make the first direct detection of gravitational waves, noting some results and limits which have been achieved to date. The chapter also introduces the different noise sources that will limit the sensitivity of gravitational wave detectors. The information detailed in this chapter has all been derived from previously published literature. Chapter 2 introduces the theory of thermal noise and derives the relationship between the mechanical loss and thermal noise in fused silica suspensions via the fluctuation dissipation theorem. Discussion covers how this limits the sensitivity of a gravitational wave detector. The chapter includes the theory of loss mechanisms present in fused silica. Again the information contained in this chapter has all been derived from previously published literature. Chapter 3 contains details and results of an experiment, where the expansion coefficient of fused silica fibres was measured under varying amounts of stress. Results demonstrate that the effective thermal expansion co-efficient of a fused silica fibre can be nulled by placing the fibre under a particular level of stress. This nulling of the effective thermal expansion coefficient should lower the thermoelastic noise contribution in silica suspensions, essential for allowing second generation gravitational wave detectors to reach their target thermal noise sensitivity of below 10^{-19}m/sqrt{Hz} at 10Hz. The experimental work in this chapter was conceived by Professor James Faller with a prototype demonstrated by Dr Stuart Reid. The set-up was then revised and modified by the author and Dr Giles Hammond to achieve the results presented in this thesis. Throughout this experiment Colin Craig helped with the machining of the invar set-up and Dr Kirill Tokmakov with suspending the silica fibres placed under large amounts of stress. Experimental measurements and analysis were carried out by the author. Chapter 4 describes an experiment in which a fused silica fibre was held under tension and the harmonic violin mode losses over a range of frequencies were measured. The fibre was then cut and cantilever modes of the fibre measured. The contributions from excess losses were calculated and shown not to limit the experiment. A theoretical dilution factor was determined along with the modal strain distribution of the violin and cantilever modes from finite element analysis (FEA). The FEA was aided by Dr Rahul Kumar and Dr Alan Cumming. The data measured was then compiled with a loss model to give information about the loss contributions of fused silica such as thermoelastic loss, surface loss and weld loss. Designing of the silica pendulum system used in this experiment was helped by Russell Jones and the machining of the silica mass holders for CO2 welding was done by Steven Craig. Construction of the silica pendulum system was undertaken by Dr Giles Hammond and the author, who carried out the experimental measurements. Analysis of the data presented in this chapter was aided by Dr Matthew Pitkin who contributed a Markov Chain Monte Carlo regression fitting code. Chapter 5 repeats the above experiment; where the author used a modified fused silica fibre to measure violin mode losses. The modified silica fibre allowed loss measurements to be made at a much lower frequency than in the previous violin mode set-up. In an attempt to study the nonlinear thermoelastic loss in more detail. The stress on the silica was also varied to observe the nulling of the effective thermal expansion coefficient directly through measurements of the mechanical loss. This experiment used many of the components described in chapter 4 and so the same people are acknowledged for their contribution. Construction of the silica pendulums used was carried out by Dr Giles Hammond, Dr Kirill Tokmakov and the author. Chapter 6 focuses on measuring the mechanical loss of 20-30micron diameter fused silica fibres, for use in the Hannover AEI 10m prototype interferometer. This chapter illustrates the problems faced when trying to measure the mechanical losses of thin fibres. The mechanical loss data was then compiled with a loss and finite element model to give information about the loss contributions of fused silica such as thermoelastic, surface and weld loss in thin silica fibres. This experiment was constructed initially by Dr Stuart Reid with some of the welding being performed by Dr Kirill Tokmakov. All of the experimental measurements and analysis were the work of the author. Chapter 7 details the conclusions that can be drawn from the various experiments in previous chapters. The results will be be applicable across many areas of research where low mechanical thermal noise is required. More generally the results can be used as a basis for research that requires mechanical systems at room temperatures for example systems needed to produce stable optical cavities. A further important discovery emerging from this thesis is the ability to cancel and reverse the effective thermal expansion coefficient of fused silica by placing the silica under stress. This process allows stressed silica to be used in systems were low thermal expansion coefficient materials are needed. Thus fused silica can be used as an alternative to composite materials such as invar