Higher harmonics in the voltage on a superconducting wire carrying AC electrical current

The problem of determining the harmonic content in the voltage that appears on a superconducting wire carrying cosine-like AC current was resolved theoretically, using two approaches. First, the Fourier components of the voltage spectrum were found by numerical integration. Importance of individual terms was established, leading to two conclusions: a) it is the cosine component of the 3rd harmonic that represents the bulk of harmonic distortion, b) for the practical purposes it is sufficient to consider higher harmonics with n ≤ 7. Then, the analytical formulas were derived. While for the sine components a general expression containing an infinite series was found, closed-form formulas were derived for the cosine components of the harmonics 1, 3, 5, 7. Consequences of the results to the experimental technique used to study the AC transport properties of superconductors are discussed.