Measurement of the thermal accommodation coefficient of helium on a crystalline silicon surface at low-temperatures

Abstract Proposals for next-generation gravitational wave observatories include cryogenically cooled 200 kg test mass mirrors suspended from pendulums and made of a crystalline material such as crystalline silicon. During operation of the observatories, these mirrors undergo heating due to the absorption of laser radiation of up to a watt. Low noise cooling techniques need to be developed. Low-pressure helium exchange gas at 5 K might contribute to the challenging task. Here, we report the measurement of the helium accommodation coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>11</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mi>T</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>30</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , which is the probability that a helium atom thermalises with a surface at a given temperature when reflected from it. We find <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>T</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>&gt;</mml:mo> <mml:mn>0.7</mml:mn> </mml:mrow> </mml:math> for temperatures <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> K, which increases the cooling power compared to recently used assumptions. The idea of free molecular flow helium gas cooling is thus supported and might find application in some observatory concepts.