Analytical approach to AC loss calculation in high-T_c superconductors

Using a linear spline approximation for the E-J characteristic of a superconductor and representing the solution in form of series, analytical expressions for AC losses have been obtained. The expression explains experimentally observed frequency and magnetic field dependencies of AC losses. Cases of complete and incomplete magnetic field penetration have been distinguished. AC losses per cycle decrease with increasing frequency in the case of incomplete penetration, the case relevant to thick slabs and low amplitude magnetic fields, while in thin slabs and large magnetic fields they increase with increasing frequency, the case of complete penetration. The analysis of the analytical solutions obtained has given a simple criterion for the applicability of the critical state model (CSM) to the calculations. This criterion involves characteristics of both superconductor and applied magnetic field. The physical meaning of the criterion in terms of ratios between the characteristic decay times of magnetic field energy in a superconductor and the period of applied magnetic field has been established. It has been shown that the analytical solutions can be applied for various forms of E-J characteristics by means of defining effective critical current density and flux flow resistivity.