The use of high temperature superconductors (HTS) in very long power transmission lines requires a reliable and effective cooling. Since the use of cryocoolers does not seem feasible for very long distances, an efficient cryogenic refrigeration cycle needs to be developed. For cooling superconducting cables based on MgB2 liquid hydrogen or high pressure helium gas are the possible cooling agents. For re-cooling the cooling agent, one would need a refrigeration cycle for the temperature range 20 to 25 K. For this purpose the state of the art is a refrigeration cycle using pure helium as refrigerant. But the very low molecular weight of helium restricts the use of turbo compressors, which limits the overall efficiency. In order to increase the molecular weight of the refrigerant an addition of neon to the helium has been considered, which would allow the use of a turbo compressor. But the use of this two-component mixture is limited in temperature by the freezing line of neon. The freezing line can be lowered in temperature by the addition of hydrogen to the mixture. Liquid hydrogen acts as absorbent for the neon preventing it to freeze. The resultant refrigeration cycle is a hybrid of the well-known mixed refrigerant Klimenko cycle with the Brayton cycle or a kind of mixed refrigerant Claude cycle.