Designing arm cavities free of parametric instability for gravitational wave detectors

Abstract

Parametric instability is an intrinsic problem in high power laser interferometer gravitational wave detectors. Optical cavity modes interact with acoustic modes of the test masses, leading to laser power dependent exponential growth of acoustic vibration of the test masses. Future detectors are being planned with designed optical power as high as 5 MW. This increases the requirements for suppressing of parametric instability through various currently available methods. Parametric instabilities could also be alleviated through careful design of the acoustic mode structure and optical mode spacing. Here we study parametric instabilities in future gravitational wave detectors with arm lengths between 6 and 10 km. We show that by careful choice of test mass radii of curvature, dimensions and arm lengths it is possible to design detectors that are free of parametric instability up to 3 MW of intra-cavity power with large enough tolerance on mirror radii of curvature change. We present several case studies and give an example of a design with 6335 m arm cavities and test mass diameter of 52 cm that is parametric instability free. This design is relatively tolerant, staying free of instabilities for a 45 m change in test mass radius of curvature. Maintaining this radius of curvature could easily be done with good design and thermal compensation.