Critical Current Distribution in Composite Superconductors

Abstract

It has long been known that for the description of the E(I)-characteristics of composite superconductors a distribution function can be used instead of a power law relation. With this approach, the conductor is represented by a serial connection of short subsections where the electrical resistance of each subsection is given by a parallel connection of the flux flow resistance of the superconductor and the resistance of the normal conducting matrix. Furthermore the local critical currents are assumed to be normally distributed around a mean value with a standard deviation . If the local critical current in a subsection is exceeded a voltage is generated. The current distribution function is then given by the second derivative of the E (I)-characteristics divided by R/L with R being the overall resistance and L the measuring length. In general only the lower part of the distribution function is apparent. By soldering the conductor in a copper bar the whole distribution can be made visible. In this paper we will give examples of the suitability of the description with Gaussian distribution functions for the low temperature superconductors NbTi and Nb 3 Sn as well as for a Bi2223 tape. A comparison will be made between measurements with and without additional copper.

Critical Current Distributions of Recent Bi-2212 Round Wires

“…The relative standard deviation (σ/µ) is a significant parameter which considers both the breadth and the mean of the I c distribution. Previous investigations of the I c distribution of technological conductors yielded σ/µ ∼ 0.02 -0.50 for Nb 3 Sn, Nb − Ti, and Bi-2223 [11], [13]. However, Warnes et al also reported an enhanced σ/µ ∼ 0.14 for a severely sausaged Nb − Ti wire at 4 T (reduced field, H/H irr ∼ 0.36) which increased to ∼ 0.33 at 10 T [11], thus correlates a high σ/µ value with strong filament sausaging.…”

“…In analyzing the data we take the common view [12], [21], [22], [24] that the local I c along the wire is controlled by multiple independent factors that justify a Gaussian approximation consistent with the central limit theorem [18]. Gaussian distributions have earlier been measured in Nb 3 Sn [13], [18], [19] with σ/µ values of 0.15 at 15 T, about 0.6 H irr . Here we show that a high-J c Nb − Ti has a significantly smaller σ/µ of ∼ 0.05 at 5 T (∼ 0.5 H irr ), although it does rise significantly above 0.1 at 8 T close to H irr .…”

“…An early method that was successfully used to characterize the I c distribution of Nb − Ti and Nb 3 Sn wires used a substantial normal metal shunt to avoid conductor burn out [11], [18]. The method models the I c distribution as a series array of many short longitudinal sections of varying I c [13], [19]. As the applied current exceeds the local critical current (i c ) of a section, the section transitions from a pinned to a flux flow state.…”

“…The 7 -15 point comb size was kept low to avoid smoothing out subtle features of the distribution curve shape. Since the factors that affect local critical current are thought to be randomly distributed and uncorrelated, the distribution of i c plausibly converges to a Gaussian as predicted by the central limit theorem [13], [18], [21], [22] enabling extraction of distribution parameters, such as the mean I c (µ in ( 4)) and the standard deviation (σ).…”

“…Recently, a transition to finer powder made by Engi-Mat has more than doubled J c in state-of-the-art Bi-2212 wires [4] compared to earlier wires made with Nexans granulate powder. To extract the I c distribution of our wires, we employed the method previously employed to characterize the I c distribution from V − I characteristics of Nb − Ti and Nb 3 Sn wires using a normal shunt to make d 2 V/dI 2 analysis possible [10]- [13].…”