Fractal-based analysis of the void microstructure of Bi2Sr2CaCu2Ox superconducting filaments and the caused anomalous thermal diffusion

Abstract High- T c multifilamentary composites Bi 2 Sr 2 CaCu 2 O x /Ag/Ag-alloy (Bi2212) are the only round wires (RWs) to be potential candidates for fabricating high field magnets. However, the complicated microstructure of Bi2212 RWs, and especially the Bi2212 filaments, makes deep understanding of the correlation between macroscopic electrothermal behaviors and the microstructure a challenge. Building on our previous work of fractal-based analysis of the Bi2212/Ag interface, in this paper we focus on the void (gas bubble or pore) structure of individual Bi2212 filaments, taking a fractal-based analysis of the void structure and the resulting anomalous thermal diffusion. For fractal characterization of the void structure of Bi2212 filaments, we developed a fractal-based reconstruction model, and further derived a one-dimensional fractional order differential equation with the exponent α (0  ϕ  ≤ 1) and fractal dimension (2  D