Thermal Conductivity of Superfluid $$^3$$ 3 He-B in a Tubular Channel Down to 0.1 $$T_\mathrm{c}$$ T c at the $$^{4
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Thermal Conductivity of Superfluid 3 He-B in a Tubular Channel Down to 0.1Tc at the 4 He Crystallization Pressure T. S. Riekki1
· J. T. Tuoriniemi1 · A. P. Sebedash2
Received: 12 July 2019 / Accepted: 7 December 2019 © The Author(s) 2019
Abstract We studied the thermal conductivity of superfluid 3 He in a 2.5-mm effective diameter and 0.15-m-long channel connecting the two volumes of our experimental assembly. The main volume contained pure solid 4 He, pure liquid 3 He and saturated liquid 3 He– 4 He mixture at varying proportions, while the separate heat-exchanger volume housed sinter and was filled by liquid 3 He. The system was cooled externally by a copper nuclear demagnetization stage, and, as an option, internally by the adiabatic melting of solid 4 He in the main volume. The counterflow effect of superfluid just below the transition temperature Tc resulted in the highest observed conductivity about five times larger than that of the normal fluid at the Tc . Once the hydrodynamic contribution had practically vanished below 0.5Tc , we first observed almost constant conductivity nearly equal to the normal fluid value at the Tc . Finally, below about 0.3Tc , the conductivity rapidly falls off toward lower temperatures. Keywords Helium-3 · Helium-4 · Helium-3–Helium-4 mixture · Superfluid thermal conductivity
1 Introduction Thermal conductivity of superfluid 3 He consists of two components: diffusive conductivity due to the quasiparticle motion and hydrodynamic conductivity caused by the superfluid–normal fluid counterflow effect [1]. The hydrodynamic conductivity is most important just below the superfluid transition temperature Tc , as it requires the presence of the normal component, whose amount decreases exponentially with temperature. Diffusive conductivity has been discussed in a few theoretical publications
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T. S. Riekki [email protected]
1
Low Temperature Laboratory, School of Science, Aalto University, P.O. BOX 15100, 00076 Aalto, Finland
2
P. L. Kapitza Institute for Physical Problems, RAS, Kosygina 2, Moscow, Russia 119334
123
Journal of Low Temperature Physics
[2–5] and has been measured using a heat-pulse method [6,7]. Measurements of the total thermal conductivity have been made only on a narrow temperature span near the Tc [8,9] at a selection of pressures, and at a single point at the 3 He crystallization pressure in the ballistic quasiparticle regime [10]. Our interest in the matter is related to our adiabatic melting experiment that aims to cool 3 He and saturated 3 He–4 He mixture to ultra-low temperatures at the 4 He crystallization pressure 2.564 MPa [11,12]. The method is capable of reaching temperatures below 0.1 mK by melting solid 4 He and mixing it with liquid 3 He. At the lowest achievable temperatures, our quartz tuning fork thermometers become insensitive [13], and a computational modeling of the system is required to evaluate the temperature. To carry out the simulation, we need good understanding of the thermal couplings within the system, of which one of the key
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