A mathematical approach to simulating electromagnetic field of ReBCO superconductors

Electromagnetic field and alternating current loss in high-temperature ReBCO superconductors can be obtained by treating their complex electromagnetic interactions as a convex optimisation problem

New York | Heidelberg, 15 November 2024

Rare-earth barium copper oxides (ReBCO) are a family of superconducting materials that allow electrical currents to flow with zero resistance, even at temperatures well above absolute zero. This allows them to sustain stronger magnetic fields than other type of superconductors. However, these materials often host a complex nonlinear electromagnetic response. So far, it is a challenge to deal with the electromagnetic problem of ReBCO superconductors accurately and efficiently.

Through new research published in EPJ Special Topics (EPJ ST), Huadong Yong and colleagues at Lanzhou University, China, show that the electromagnetic problem with power law relation can be approached as a mathematical challenge known as a ‘convex optimisation problem’. By applying this problem-solving method, the team was able to accurately calculate the electromagnetic field and alternating current loss for a variety of real-life superconducting structures.

In their study, Yong’s team began by using a mathematical technique called the ‘infeasible start Newton’s method’: an advanced approach to solving optimisation problems, even when starting with imperfect assumptions. Based on previous research, their analysis revealed that the true electromagnetic field distribution in ReBCO superconductors is the solution that minimises a convex functional with linear equality constraints.

The team solved this problem for various superconducting structures: including stacked cables and insulated ‘pancake’ coils. They also extended their method to account for the different electromagnetic behaviours of non-insulated pancake coils. Just as they hoped, their results closely matched those from conventional methods. To make the method faster and more efficient, the team will now aim to simplify their algorithms to simulate the practical ReBCO superconductors in a wide range of technologies.

Reference: Tang, Y., Liu, D., Li, D. et al. Numerical solution of nonlinear electromagnetic field problem of superconducting tape using convex optimization. Eur. Phys. J. Spec. Top. (2024). https://doi.org/10.1140/epjs/s11734-024-01350-9