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

TL;DR

This paper presents the first analytical model of the temperature field caused by ring heaters in gravitational-wave detectors, enabling better thermal compensation and improved sensitivity.

Contribution

It introduces an analytical model of ring heater thermal effects in LIGO mirrors, enhancing thermal management strategies.

Findings

Model accurately predicts temperature distribution

Optical aberration contributions quantified

Improves thermal compensation efficiency

Abstract

Advanced laser interferometer gravitational-wave detectors use high laser power to achieve design sensitivity. A small part of this power is absorbed in the interferometer cavity mirrors where it creates thermal lenses, causing aberrations in the main laser beam that must be minimized by the actuation of "ring heaters," which are additional heater elements that are aimed to reduce the temperature gradients in the mirrors. In this article we derive the first, to the best of our knowledge, analytical model of the temperature field generated by an ideal ring heater. We express the resulting optical aberration contribution to the main laser beam in this axisymmetric case. Used in conjunction with wavefront measurements, our model provides a more complete understanding of the thermal state of the cavity mirrors and will allow a more efficient use of the ring heaters in the Advanced Laser Interferometer Gravitational-wave Observatory.