Thermo-magnetic refrigeration as applied to hydrogen liquefaction I. Fundamentals and type-II superconductors

Gas liquefaction utilizing the entropy transport by flux lines (FLs) in the mixed state of type-II superconductors has been proposed. Refrigerating power and the Joulian heat generated by FL current are proportional to and to the square of the superconducting (super-) current, respectively. The optimum super-current, the corresponding field strength, and the net refrigerating power ( q n ) are expressed by the elemental parameters. Introducing the well-defined FL-flow viscosity coefficient, we show that the maximum q n appears at the field with 1 9 of the upper critical field under the corresponding super-current density, and we expect the optimum refrigeration power density of about 15.8 j 0 * and 4.49 j 0 * W / m 2 (where j 0 * is the critical super-current density) for Nb 3 Ge ( T 0 = 23.2 K , B C 2 = 14.5 T at T 0 ) and MgB 2 ( T 0 = 40.0 K , B C 2 = 16 T , at T 0 ), respectively.