Finite Element Simulation of Temperature and Current Distribution in a Superconductor, and a Cell Model for Flux Flow Resistivity—Interim Results

Abstract

A critical problem arises when current distribution in a high-temperature superconductor and its stability against quench shall be predicted: is it correct to assume homogeneous temperature distribution in superconductors, in general or only in LHe-cooled devices? The finite element analysis presented in this paper shows that during the very first instants following a disturbance, like single Dirac or periodic heat pulses, or large fault currents, temperature distribution in a BSCCO 2223 conductor is highly inhomogeneous. This is because disturbances, of transient or continuous, isolated or extended types in conductor volumes, create hot spots of comparatively long life cycle. As a consequence, separation between Ohmic and flux flow current limiter types, or decisions on the mechanism that initialises current sharing, cannot be made definitely. A semi-empirical cell model is presented in this paper to estimate flux flow resistivity in multi-filamentary superconductors in a successive approximation approach. Weak links are modelled, as nano- and microscopic surface irregularities and corresponding resistances, in analogy to thermal transport. Though the model requests input of a large amount of data (dimensions, porosities, field-dependent quantities) that still have to be verified experimentally, it is by its flexibility superior to ideas relying on, for example, imagination of separate, non-interacting chains of strong and weak links switched in parallel. In particular, and in contrast to the standard expression to calculate flux flow resistivity, the cell model suggests to replace solid conduction by an effective resistivity, a method that is more appropriate for multi-filamentary conductors. The paper also discusses integration time steps in numerical simulations that have to be selected in conformity with several characteristic times of current and thermal transport.