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 (qn)(qn) are expressed by the elemental parameters. Introducing the well-defined FL-flow viscosity coefficient, we show that the maximum qnqn appears at the field with 19 of the upper critical field under the corresponding super-current density, and we expect the optimum refrigeration power density of about 15.8j0* and 4.49j0*W/m2 (where j0* is the critical super-current density) for Nb3GeNb3Ge (T0=23.2K, BC2=14.5T at T0T0) and MgB2MgB2 (T0=40.0K,BC2=16T, at T0T0), respectively.