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.

Loss measurements were made at 60 Hz on 6-m lengths of 1- and 3-cm-diam superconducting niobium tubes used as the inner conductor of a coaxial line. These tubes carried transport currents up to 1700 and 5300 A, respectively. The losses were found to fit the relation P=fAEc1(H/Hc1)n,where f is the frequency, A is the surface area, Ec1 is the energy loss per unit surface area per cycle at Hc1, the lower critical magnetic field, and H is the peak magnetic field at the surface of the superconductor. The exponent n equals 3 for H≤Hc1 and n≥4 for H≥Hc1. The ac losses showed a 25% linear increase with temperature from 4.2 to 5 K. For the case of an eccentric coaxial line, where the current and magnetic field vary about the circumference of the superconductor, the ac losses were found to agree with those predicted from calculated values of the current and magnetic field distributions. In particular, when the peak surface field is less than Hc1 and R is the ratio of the maximum to minimum surface magnetic fields about the circumference of the superconductor, the losses were a factor (3R2+2R+3)/4R greater than those found at an equivalent current for a concentric configuration.