  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.
