Simulations of high-field superconductors using time-dependent Ginzburg–Landau theory with accurate material parameters

This thesis investigates the mechanisms which limit the critical current density in high-field superconductors using simulations based on time-dependent Ginzburg–Landau (TDGL) theory. The primary contributions are a fast and general method for solving the TDGL equations in large three-dimensional systems, a preliminary study of an anisotropic coated conductor with nanorod artificial pinning centres, and a study of niobium–titanium using a material model with Ginzburg–Landau (GL) coefficients which are derived from the measured properties of single-phase samples.

The solver uses a geometric multigrid method to solve the backward Euler discretised TDGL equations in the London gauge. It does not assume the frozen-field limit, all of the coefficients can vary in space, and the simulation time scales well with system size and does not depend strongly on the parameters. This allows a wider class of materials to be studied than previous solvers.

In the preliminary study of a system representing a REBCO coated conductor, it was assumed that the pinning landscape consists of resistive cylinders representing nanorod artificial pinning centres embedded in an anisotropic superconducting matrix. The effects of the density, resistivity, and splay of the nanorods were investigated. It was concluded that surface effects in the vicinity of matrix-pin interfaces can play an important role for dense, highly resistive nanorods, and that this might affect the observed critical fields in real materials.

For the model of niobium–titanium, the ratios of the GL coefficients α and β were calculated for the two phases using the measured properties of single-phase samples and GLAG theory. Microstructures were generated procedurally to match the precipitate thicknesses and titanium volume fractions seen in transmission electron microscope images of real wires. Critical field anisotropy simulations were run with a range of effective mass values and a comparison with experimental data implied that the ratio of the effective mass in the titanium precipitates to that of the niobium–titanium matrix is about 2.

Critical current simulations were also run over a range of effective mass values. The magnitude of the high-field critical current density indicated that the effective mass ratio is closer to 4 than 2, but this comparison is sensitive to the precise values of the GL coefficients in a way that the critical field anisotropy is not. Given a 10% error in the calculated penetration depth for niobium–titanium, the critical current data are consistent with an effective mass of 2. It is concluded that the conventional understanding of pinning in niobium–titanium, that fluxons are pinned primarily by ribbon-shaped titanium precipitates, is consistent with a Ginzburg–Landau theoretic model where the pinning force primarily arises due to the higher carrier effective mass in titanium compared with that of niobium–titanium.

This work demonstrates that simulations based on TDGL theory can be used to study industrial superconducting materials, that using accurate coefficients is essential for properly capturing the mechanisms which limit the critical current, and that the carrier effective mass, which has been historically neglected in theoretical and computational studies of pinning, is a key parameter in niobium–titanium. This is a step in making TDGL simulations a more quantitative tool for critical current prediction.