Continuum modeling of radiation-induced degradation in superconductors

Abstract

Realizing the promise of nuclear fusion requires confining plasma at millions of degrees, a feat achievable only through high-field superconducting magnets. However, the fusion reaction itself generates a relentless flux of high-energy neutrons that degrades these critical and prohibitively expensive coils, limiting the operational lifetime of the reactor and compromising its economic viability. While radiation damage is well-documented experimentally, a predictive theoretical framework that links microscale defects to macroscopic magnetic failure has remained elusive. Here, we bridge this gap with a homogenized continuum damage model based on Ginzburg–Landau theory. By treating radiation-induced defects as “quantized” normal-phase inclusions, we map the degradation of the superconducting order parameter to an equivalent homogenization problem. This approach yields closed-form analytical expressions for the critical current as a function of neutron fluence, magnetic field, and temperature. We calibrate and validate the model against experimental data in the literature on rare-earth barium copper oxide (REBCO) tapes, demonstrating that the complex evolution of superconducting properties, including the counterintuitive “peak effect”, can be captured by a few effective material parameters that need to be calibrated just once. This work provides a design tool for engineering radiation-tolerant magnets, a critical step toward sustainable fusion energy.