Optimization of helium refrigerators and liquefiers for large superconducting systems

A general method for optimizing ideal Claude cycles with multiple expansion engines is presented for two types of engine arrangements. In one case, the inlet temperature of one engine is equal to the outlet temperature of another engine. In the second case, inlet and outlet temperatures of adjacent engines are independent of each other, the more general case which is sometimes used in practice. The optimizing technique is especially adapted to superconductive systems in which some of the helium vapour is used to cool electrical leads and mechanical support systems. The helium fraction to be returned to the refrigerator-liquefier vs the fraction to be used for other purposes is conventionally entered as a parameter which becomes part of the optimization technique.