Dilution Refrigerator - Cooling Power

Cooling Power

At not too low temperatures the cooling power at the mixing chamber is approximately given by

where is the 3He molar circulation rate, T_m is the mixing-chamber temperature, and T_i the temperature of the 3He entering the mixing chamber. In the case of zero heat load there is a fixed ratio between the two temperatures

From this relation it is clear that a low T_m can only be reached if T_i is low. In dilution refrigerators T_i is reduced by using heat exchangers as shown in Fig.2. However, at very low temperatures this becomes more and more difficult due to the so-called Kapitza resistance. This is a heat resistance at the surface between the helium liquids and the solid body of the heat exchanger. It is inversely proportional to T4 and the heat-exchanging surface area A. In other words: to get the same heat resistance one needs to increase the surface by a factor 10,000 if the temperature goes down by a factor 10. In order to get a low thermal resistance at low temperatures (below about 30 mK) a large surface area is needed. The lower the temperature, the larger the area. In practice one uses very fine silver powder.