FEM Analysis of Current Sharing in REBCO Coated Conductor Cables for Particle Accelerator Applications

Abstract

Current sharing is an important self-protection mechanism in rare earth barium copper oxide (REBCO) coated conductor (CC) tapes and cables that are intended for the construction of high field magnets. Because of the slower quench propagation rate of such cables, we expect that cooling is also required to facilitate the current sharing. We explored this idea by constructing FEM models that include liquid helium cooling and inter-strand contact properties. The results showed that given metallic inter-strand contact, a three-layer tape stack with a defective central tape could carry at least 3.05 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> (where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> is defined for an individual tape). When the inter-strand electrical contact efficiency, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η</i> = inter-strand contact resistance ∗ contact area), was adjusted to be 5400 µΩ*cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and the inter-strand thermal insulance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</i> = inter-strand thermal resistance ∗ contact area), was 5.54 K*m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /W, the maximum current that could flow through the defective tape was 0.6 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> with negligible current sharing to neighboring tapes. After reducing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η</i> to 10 µΩ*cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</i> to 0.01 K*m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /W respectively, current sharing to neighboring tapes increased by 800 times, and the hot spot temperature was reduced. However, if the inter-strand thermal contact was insulating, regardless of the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η,</i> the same tape stack exhibited thermal runaway. Hence, current sharing in REBCO coated conductors is determined by both the inter-strand contact resistance (ICR) and the inter-strand thermal resistance (ITR).