Abstract
Thin plates with a thicknessd smaller than the phonon mean-free path can be used to increase the heat exchange in 3 He- 4 He refrigerators at very low temperatures. The resistanceR for the heat current density of these plates is theoretically investigated. For plates withd still larger than the dominant thermal-phonon wavelength λ T in the plate,R is given by twice the Kapitza resistance. Ford ≈ λ T the resistanceR decreases due to phonon tunneling. Ford ≪ λ T there exists a region whereR varies asT −1, in contrast to theT −3 dependence for thicker plates. Numerical calculations are carried out for copper plates immersed in pure 4 He. The results show that one obtains a large increase of the heat exchange due to phonon tunneling for plates with a thickness of a few microns at temperatures in the millidegree range.
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