New approach of Thermal Noise Finite Element modelling for the Einstein Telescope cryogenic payload. Centre Spatial de Liège

Abstract

In the context of the third-generation gravitational wave detector design, several noises must be un- derstood and minimized. One of them is thermal noise, described theoretically by the Fluctuation and Dissipation Theorem (FDT). This study aims to mainly describe the impact of introducing a radiative heat exchanger in terms of thermal noise. Although 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 a 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, using the state space matrices rather than using the Levin’s method. 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 fin properties, from the radiative heat exchanger (RHE), on thermal noise. In the end, studies of the E-TEST and ET models are performed to evaluate the impact of considering an RHE. Results show that this addition of fins not only modifies the inertia and mass of the system, but also introduces new resonances that come from the plate modes, leading to a higher local thermal noise response. However, no overall increase in thermal noise was observed. The ET-LF model using a radiative cooling strategy shows that it satisfies the ET-LF requirements for Thermal Noise. The study also highlights the importance of the boundary conditions and the assumption made in the literature. 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.