Once interferometers perform beyond the level of the seismic noise and the shot noise in the ``initial LIGO'' goals, thermal noise from the internal modes of the test masses may dominate the noise budget over a wide band near 100 Hz. This would be the case for test masses with the presently-achieved Q values, if their dissipation is approximately of the ``structural'' form.
At present, the evidence for structural damping in fused silica comes only from combining Q measurements at different frequencies made in different oscillators.[8] What is really desired for such an important noise source is the ability to determine the level of dissipation, as a function of frequency, for actual test masses. The obstacle to obtaining this kind of information has been our reliance, up until now, on determining dissipation by measuring quality factors of resonances; test masses are specifically designed to have no resonances in the frequency band in which LIGO will search for signals.
This obstacle could be overcome if we replaced measurements at resonant
frequencies with measurements of a test mass's response to an impulse or
step function in stress. There are well-developed techniques in anelasticity
theory to interpret such time-domain measurements in the more familiar
frequency-domain language of 
.[10] On various occasions
this technique has proven the most useful way to interrogate physical
systems.[11]
An especially clean version of this kind of measurement is the one called
the anelastic aftereffect. The system under test is prepared by being
subjected to a stress for a long time (compared with the time scales of
interest.) Then the stress is released and the strain of the system is
measured as it evolves toward the relaxed state. If the time evolution of
the system's strain is given by 
, then the loss function can be
shown to be
A system governed by structural damping will exhibit an anelastic
aftereffect with a time dependence proportional to 
.
Following a suggestion from Alex Abramovici of the LIGO group at Caltech, we
shine polarized light through the bulk of the test mass, and determine by measuring the rotation of polarization caused by the
photoelastic effect. From January 1995 through July 1997, postdoctoral
researcher Mark Beilby (Ph.D. 1995, Irvine, with Riley Newman) built and
debugged the apparatus to carry out this measurement. By the time he left
(for a teaching position at Swarthmore College), the apparatus was capable
of resolving losses of structural form with loss angles as small as 
. For lossy glasses such as BK7 it was easy to measure the loss
versus frequency over the range between about 0.1 Hz and 10 Hz; it showed
roughly constant 
, at a level of 
. For fused silica,
the sensitivity is still not quite sufficient. (A paper describing this
apparatus has been drafted, and will be submitted for publication soon.)
A new postdoc, Dr. Steven Penn (Ph.D. 1993 MIT, postdoctoral work at UWash with Blayne Heckel and Eric Adelberger) began working in our group on October 1, 1997. He has been working to improve the performance of the time-domain measuring system, and then to apply it to materials and suspensions for gravitational wave interferometers.
We expect that we should be able to reach the shot noise limited sensitivity in our system, which is more than an order of magnitude better than the present noise. Combining that with more agressive use of averaging multiple measurements, it should prove feasible to measure the dissipation in even the best fused silica. Dr. Penn will also work on extending the upper frequency limit of dissipation measurement beyond the present 10 Hz to 100 Hz or even higher. The present upper limit is set by a deliberately slow release of the squeezing mechanism, which helps keep excitation of the sample's rigid body modes at a low level. (These motions are detected by our optical system because most samples have at least a small level of fixed birefringence.) We will test a variety of other strategies for minimizing this problem: more careful balancing of the vise, fitting out the sinusoidal low frequency motions, and combinations of ``fast'' and ``slow'' runs that will together span a wide frequency range.
Once the sensitivity of the system is sufficient, we will be able to apply it to a variety of samples of interest. Fused silica, the material from which LIGO's test masses will be made, is obviously of prime importance; it may remain the material of choice even for the next-generation suspension slated for installation in LIGO in 2004. Learning the actual level of dissipation in the LIGO signal band (especially in the decade centered on 100 Hz) will be vital to understanding of the thermal noise budget; hunting for ways to make it as low as possible could have a big payoff. Another material that may become useful for the next-generation suspension, or soon thereafter, is sapphire. We will attempt to measure the level of dissipation in a sample of sapphire that will be supplied to us by the Stanford group. Most of these measurements will be made on small samples. But we will soon be installing a new larger vacuum tank that can accomodate LIGO-sized test masses, so we could test full-scale prototypes, or even production items if necessary.