Principles and methods of dilution refrigeration

Following a brief introduction in Section I, the properties of pure $H{e}^3$ and of dilute solutions of $H{e}^3$ in superfluid $H{e}^4$ which are relevant to the design and understanding of dilution refrigerators are discussed in Section II. In Section III the basic model for discussing the thermodynamics of the dilution process is developed and applied to both a continuously operating refrigerator and to single-cycle refrigerators using both $H{e}^3$ flow and superfluid $H{e}^4$ flow. The relative merits of $H{e}^3$ flow and superleak operated devices are also mentioned. In Section IV the thermodynamical properties of $H{e}^3$ in the dilute phase of the refrigerator are calculated, including the dependence of concentration on temperature and the effective enthalpy function. The heat exchange problem is discussed in Section V, first by introducing new measurements of the Kapitza resistance for saturated dilute solutions and then by relating these to the concept of a $H{e}^3$-phonon resistance in the dilute solutions. Finally specific design estimates are made for the heat exchangers. In Section VI the physics of the $H{e}^3$ circulation problem is discussed. The effects of circulated $H{e}^4$ and of viscous heating due to $H{e}^3$ flow are also emphasized. Both the effects of thermal conduction and viscosity limit the low temperature attainable in a $H{e}^3$ flow type of dilution refrigerator. There is a lower limit to 'the temperature attainable as a result of these intrinsic factors which is calculated in Section VII.