Theory of Flux Motion in Non-Ideal Type-II Superconductors

TLDR

The model incorporates pinning‑force and distribution parameters, generalizing Bean‑London, Silcox‑Rollins, and Yasukōchi formulations. The study proposes a phenomenological pinning‑force density expression and a force‑balance equation to describe magnetic fluxoid motion in non‑ideal type‑II superconductors, coupled with magnetic flux continuity. The authors derive equations for fluxoid dynamics, calculate hysteresis and a.c. loss hysteresis, and model field‑dependent critical current and flux‑penetration relaxation, providing analytical expressions for these phenomena.

Abstract

A phenomenological expression of the pinning force density is proposed, and the equation of force balance including this expression is shown to describe well the motion of magnetic fluxoids in non-ideal type-II super-conductors in cooperation with the equation describing the continuity of magnetic flux flow. The parameters related to an individual pinning force and pin distribution are included in the present expression which contains those from the models of Bean-London, Silcox-Rollins and Yasukōchi as its special cases. The calculated magnetizations agree well with observed data by adjusting the parameters. The hysteresis losses in the course of magnetization are calculated and the field dependence of the a.c. losses are explained. The formulas of the a.c. dynamic losses are also shown. The field dependence of the critical current in the resistive state and the relaxation time of flux penetration are calculated and compared with observed data.