AC Energy Losses Above and Below H c1 in Niobium and Niobium-25 At.% Zirconium

Abstract

Calorimetrically determined energy losses for a series of niobium and niobium-25 at.% zirconium samples carrying an af transport current agreed with those calculated from hysteresis loops determined by dc magnetization measurements. The results of this study showed that the energy losses in ultra-high-purity annealed Nb are less than those for any of the other samples studied at magnetic fields less than 1500 G. The magnetic field dependence of the energy losses in all of the samples studied is given by EL = E12hm, where EL is the energy dissipated per unit surface area per cycle and is independent of frequency, E12 is a constant which depends on the material and surface finish, and h = Hp/Hc1, where Hp is the peak ac field amplitude, and Hc1 is the lower critical magnetic field; m = n1 when h≤1, and m = n2 when h≥1. For both highly reversible and highly irreversible samples, n1 ≈ 3. For the least reversible samples, n2 ≈ 4, increasing to ∼8 for the most reversible samples studied. E12 generally increased with decreasing reversibility and was strongly dependent on the surface finish of the sample, increasing as the surface roughness increased. The power loss PL per unit surface area is given by PL = (EL)f. This linear frequency dependence is consistent with a hysteretic loss mechanism as is the agreement between the calorimetrically determined losses and those calculated from the measured hysteresis loops.