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Advanced laser interferometer gravitational-wave detectors use high laserpower to achieve design sensitivity. A small part of this power is absorbed inthe interferometer cavity mirrors where it creates thermal lenses, causingaberrations in the main laser beam that must be minimized by the actuation of"ring heaters," which are additional heater elements that are aimed to reducethe temperature gradients in the mirrors. In this article we derive the first,to the best of our knowledge, analytical model of the temperature fieldgenerated by an ideal ring heater. We express the resulting optical aberrationcontribution to the main laser beam in this axisymmetric case. Used inconjunction with wavefront measurements, our model provides a more completeunderstanding of the thermal state of the cavity mirrors and will allow a moreefficient use of the ring heaters in the Advanced Laser InterferometerGravitational-wave Observatory.

Analytical model for ring heater thermal compensation in the Advanced Laser Interferometer Gravitational-wave Observatory