Within the conceptual design study for the Future Circular Hadron Collider (FCC-hh) it was shown, that a large part of the total cryogenic heat load falls into the 40 to 60 K temperature level. Thus, additional cryogenic refrigerators for this temperature level are specified for each of the 10 foreseen cryoplants. Such cryogenic system was developed at the TU Dresden and is based on a Brayton cycle working with a neon-helium mixture as refrigerant and using multistage centrifugal compressors. The duty requirements comprise a 5.8 MW total heat load at 40 to 60 K for beam screens and shielding, additional 2.7 MW at 300 to 40 K for the pre-cooling of the Helium-cycle and a turndown ratio of up to 3.8. The optimisation of the referenced system was performed in order to obtain a high efficiency of the cryogenic cycle and tolerable costs for system components at the same time. An analysis of the mixture composition influence on the components and on the total gas mass was performed, including calculations for different operational modes. Restrictions for industrially existing hardware were taken into consideration. Updated cycle parameters are subsequently described.