Designing efficient Gifford- McMahon (GM) cryocoolers that would allow cooling to temperatures below 4.2 K is considered an important step in the development of helium temperature technologies. Modern two-stage GM machines ensure cold production up to 4.2 K, but with relatively low efficiency, due mainly to the low heat capacity of the material used for the second-stage regenerator packing of GM machines. Two urgent problems are solved, in order to create 4 K GM cryocoolers: the non-stationary heat exchange processes in GM regenerators are described; the efficiency indicators of a GM second-stage regenerator based on cenospheres filled with helium are identified. A comparative analysis of the various types of regenerator packing, which make it possible to obtain temperatures below 4.2 K, is performed, and the advantages of helium-filled cenosphere packing are substantiated. The operation of a two-stage GM cryorefrigerator with a cooling capacity of 0.2 W at a temperature level of 4.2 K is analyzed using the wave approach to regenerator modeling. It is shown that the GM machine can be improved by using a regenerator filled with cenospheres in its second stage.

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