Origin of dc voltage in type II superconducting flux pumps: field, field rate of change, and current density dependence of resistivity

Superconducting flux pumps are the kind of devices which can generate direct current into superconducting circuit using external magnetic field. The key point is how to induce a dc voltage across the superconducting load by ac fields. Giaever (1966 IEEE Spectr. 3 117) pointed out flux motion in superconductors will induce a dc voltage, and demonstrated a rectifier model which depended on breaking superconductivity. van de Klundert et al (1981 Cryogenics 21 195, 267) in their review(s) described various configurations for flux pumps all of which relied on inducing the normal state in at least part of the superconductor. In this letter, following their work, we reveal that a variation in the resistivity of type II superconductors is sufficient to induce a dc voltage in flux pumps and it is not necessary to break superconductivity. This variation in resistivity is due to the fact that flux flow is influenced by current density, field intensity, and field rate of change. We propose a general circuit analogy for travelling wave flux pumps, and provide a mathematical analysis to explain the dc voltage. Several existing superconducting flux pumps which rely on the use of a travelling magnetic wave can be explained using the analysis enclosed. This work can also throw light on the design and optimization of flux pumps.