Theory for the Operation of a Magnetic Refrigerator at Temperatures below 1°K

Abstract

A theory for determining the optimum cycle of a magnetic refrigerator is developed. The refrigerator consists of a helium bath, a paramagnetic working substance, and an isothermal reservoir. The working substance is connected to the bath and to the reservoir via thermal valves. In the theory the valves are presumed to be superconducting wires, but no assumptions are made concerning the characteristics of the working substance. The expected behavior of a refrigerator utilizing both He⁴ and He³ baths is investigated. It is predicted that a magnetic refrigerator operating from a bath temperature of 0.3° or 0.4°K will be able to maintain an isothermal reservoir temperature of 0.05°K or lower with heat inputs of 10–20 ergs/sec, providing the effects of thermal contact resistance can be kept small. The effect of thermal resistance on refrigerator performance is investigated. The same theoretical techniques have been used to predict the behavior of a magnetic refrigerator utilizing a mechanical switch. In the paper the theoretical and experimental results are compared. Moderately good agreement is obtained.