Thermal Noise modelling for the ET-LF payload in the case of radiative cooling

In the context of the third-generation gravitational wave detector design, several noises must be understood and minimized. One of them is thermal noise, described theoretically by the Fluctuation and Dissipation Theorem (FDT).

This study aims to describe the impact of introducing a radiative heat exchanger in terms of thermal noise. While thermal noise has been assessed for classical conductive cooling of the ET-LF payload, this has never been done for radiative cooling. The radiative cooling of the payload requires adding a significant amount of exchange area and this amount of surface might be a source of thermal noise. Moreover the description of such noise has been mainly analytical and applied to simple systems.

In order to describe higher order models, this study is based on a Finite Element approach, without Levin approximation. Firstly, a comparison between analytical and FEM predictions is performed to validate the approach. Then, a sensitivity analysis is carried out to assess the influence of the radiative heat exchanger fins properties (geometric and material) on thermal noise. In the end, studies of the E-TEST and ET models are performed to evaluate the impact of this radiative heat exchanger.

Results show that this addition of plates not only modifies the inertia of the system but also introduces new resonances that come from the plates modes, leading to a higher thermal noise response.

In addition to having an estimate of the thermal noise in complex systems, this approach is easily adaptable to any model. It offers a valuable tool for design optimization, allowing different configurations to be tested in order to minimize the thermal noise response.