Magnetic properties and critical currents of MgB2

This review focuses on the superconducting properties of MgB2 that are relevant for power applications. The reversible mixed state parameters are the most important, since they define the limiting conditions for loss-free currents: the transition temperature, the upper critical field and the depairing current. They also determine the flux pinning energy, the pinning force and the elastic properties of the flux line lattice and, therefore, strongly influence the critical current densities. The magnetic properties of magnesium diboride are anisotropic and influenced by the two different energy gaps of the σ- and π-bands. Whereas the transition temperature could not be enhanced significantly during the past five years, the upper critical field was considerably increased by impurity scattering or doping. Flux pinning is very weak in MgB2 single crystals and was only improved by irradiation techniques so far. In polycrystalline samples, grain boundary pinning seems to play the dominant role. High critical currents close to the theoretical limit were found in c-axis oriented thin films. The anisotropy of the upper critical field strongly reduces the critical currents in untextured MgB2 at high magnetic fields, where the supercurrents become highly percolative, since not all grains are superconducting anymore. The performance of polycrystalline wires and tapes was significantly improved during the past few years by increasing the upper critical field and by reducing its anisotropy. Pinning seems to be nearly optimized in many forms of this material, but the connectivity between the grains might be further improved. (topical review)