Cryogenic emissivity enhancement through multi-scale structures for the Einstein Telescope radiative heat exchanger Centre Spatial de Liège

Abstract

The Einstein Telescope is the future European third-generation gravitational-wave observatory. Achieving its target sensitivity requires cooling the silicon mirrors of the low-frequency interferometer below 20 K, so as to suppress thermal noise to acceptable levels. Among the proposed thermal-management strategies, purely radiative cooling is particularly attractive because it extracts heat without any mechanical contact with the mirror. However, conventional black coatings suffer a significant loss of emissive performance at cryogenic temperatures, which limits the effectiveness of radiative heat exchangers.

This thesis investigates how surface structuring of coated metallic substrates can compensate for this degradation. A comprehensive modelling framework was developed, spanning from the electromagnetic foundations of thermal radiation to rigorous wave-optical simulations. As a first step, a spectral model of the Aeroglaze Z306 coating was established using effective-medium theories combined with the scattering-matrix method. The model was calibrated against available calorimetric and spectral radiometric measurements, allowing its optical properties to be extrapolated over the wavelength range relevant to cryogenic temperatures. The resulting predictions indicate a strong emissivity reduction between 10 and 20 K for conventional coating thicknesses, thereby motivating the investigation of alternative design strategies.

Several classes of radiation-trapping cavities were subsequently analysed within the incoherent geometrical-optics framework using Monte Carlo ray tracing. Square grooves, sine grooves and W-grooves were identified as promising geometries, and their performance was evaluated under realistic constraints including coating thickness, wall thickness, fin pitch and minimum feature spacing. The results demonstrate that surface structuring can substantially raise the effective emissivity of coated fins, recovering a significant fraction of the emissivity degradation experienced by conventional flat coatings at cryogenic temperatures.

Because the optimal cavity dimensions fall in the millimetre range, the validity of the geometrical-optics approximation was further examined through rigorous electromagnetic simulations based on the Fourier Modal Method. These analyses confirm that wave-optical effects do not erode the radiative performance predicted by geometrical optics. On the contrary, resonant electromagnetic phenomena can further enhance emissivity over part of the spectral range of interest.

Overall, this work demonstrates that geometrical radiation trapping is a viable route to improving the performance of cryogenic radiative heat exchangers for the Einstein Telescope, and more broadly highlights the potential of combining geometrical and wave-optical design strategies to engineer highly emissive surfaces for cryogenic applications.