Abstract
Thermal distortion of test masses, as well as thermal drift of their vibrational mode frequencies, present a major challenge for operation of the Advanced LIGO and Advanced VIRGO interferometers, reducing optical efficiency, which limits sensitivity and potentially causing instabilities which reduce duty-cycle. In this paper, we demonstrate that test-mass vibrational mode frequency data can be used to overcome some of these difficulties. First, we derive a general expression for the change in a mode frequency as a function of temperature distribution inside the test mass. Then we show how the mode frequency dependence on temperature distribution can be used to identify the wavefunction of observed vibrational modes. We then show how monitoring the frequencies of multiple vibrational modes allows the temperature distribution inside the test mass to be strongly constrained. Finally, we demonstrate using simulations, the potential to improve the thermal model of the test mass, providing independent and improved estimates of important parameters such as the coating absorption coefficient and the location of point absorbers.
Highlights
During Advanced LIGO’s [1] first and second observing runs, about 100 kW of optical laser power circulated in the Fabry Perot arm cavities of the interferometers [2]
In this paper we provided an efficient method of computation of the vibrational mode frequency response to a temperature perturbation in the test mass
We demonstrated that the method may be inverted, enabling the conversion of vibrational mode frequency measurements into temperature distribution information
Summary
During Advanced LIGO’s [1] first and second observing runs, about 100 kW of optical laser power circulated in the Fabry Perot arm cavities of the interferometers [2]. The heating of mirror surfaces of the test masses associated with this circulating power presents a significant technical challenge, since the thermal deformation of mirror leads to the loss of optical efficiency. The frequency of these modes depends on the temperature distribution inside the test mass Some of these modes are the drivers of parametric instability [8,9], the control of which was limited by thermal transients [10,11]. It is useful to monitor the three-dimensional temperature field inside each test mass for optical efficiency and parametric instability control. It was shown that hundreds of vibrational modes are visible at the interferometer output at quiescent amplitudes These measurements can by extension allow estimates of the thermal distortion of the test-mass mirror surfaces and distortion in thermo-optic lens in transmission of the test mass. VI a Bayesian method for refining testmass thermal model parameters is described
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