Numerical Cooling Power Predictions for a Dilution Refrigerator via Kinetic Modeling

Dilution refrigeration uses circulating 3He to produce cooling by utilizing the properties of 3He-4He mixtures and is the only technology that provides continuous cooling down to several mK. The mixing process of liquid 3He in liquid 4He is endothermic, thus extracting heat from the surroundings. Applications of this apparatus can be found in various fields of applied physics, e.g., research on novel superconductors, the realization of quantum computers, the search for the hypothesized Majorana particle and in the study of other novel quantum properties. In the present work, the flow of 3He gas inside the vacuum pumping system of a dilution refrigerator is simulated and the estimation of the produced cooling power is performed. The 3He gas flow varies from the hydrodynamic regime inside the dilution refrigeration towards the transition regime outside the device and close to the vacuum pumps. Three-dimensional Navier-Stokes calculations have been performed by using appropriate velocity slip boundary conditions. In addition, due to the fact that close to the vacuum pumps the flow is characterized by high Knudsen numbers, a simplified one-dimensional approach based on the kinetic theory of gases has been applied to estimate the importance of the rarefaction effects on the measured flow quantities. The analysis shows that the one-dimensional approach provides results in good agreement (within 10%) with that obtained by the Navier-Stokes calculations. Several aspects of the flow are examined, including the adiabaticity of the solid walls and the gravitational effects. Overall, the current work provides an in-depth modeling analysis of the dilution refrigeration technology as well as useful practical information that can be used for further improvement of the cooling power of these devices.