Analytic expressions for critical-state ac susceptibility of rectangular superconducting films in perpendicular magnetic field

A set of analytic expressions for the critical-state magnetization and ac susceptibility χ′-jχ″χ′-jχ″ curves of rectangular superconducting films of arbitrary aspect ratio in perpendicular field is obtained. They are formulated based on the exact/accurate high/low-field limits for rectangular films together with the exact analytic formulas for thin circular disks. Thus, the accuracy of the expressions is very high in high and low fields. At a characteristic intermediate field amplitude, where χ″χ″ takes its maximum, the error is checked by direct numerical calculations to be well below 1%. Thus, the provided expressions can be conveniently and satisfactorily used for practical and theoretical researches of superconducting materials, such as coated conductors.