Inverse analysis of critical current density in a bulk high-temperature superconducting undulator

Abstract

In order to optimize the design of undulators using high-temperature superconductor (HTS) bulks we have developed a method to estimate the critical current density (${J}_{c}$) of each bulk from the overall measured magnetic field of an undulator. The vertical magnetic field was measured along the electron-beam axis in a HTS bulk-based undulator consisting of twenty Gd-Ba-Cu-O (GdBCO) bulks inserted in a 12-T solenoid. The ${J}_{c}$ values of the bulks were estimated by an inverse analysis approach in which the magnetic field was calculated by the forward simulation of the shielding currents in each HTS bulk with a given ${J}_{c}$. Subsequently the ${J}_{c}$ values were iteratively updated using the precalculated response matrix of the undulator magnetic field to ${J}_{c}$. We demonstrate that it is possible to determine the ${J}_{c}$ of each HTS bulk with sufficient accuracy for practical application within around 10 iterations. The precalculated response matrix, created in advance, enables the inverse analysis to be performed within a practically short time, on the order of several hours. The measurement error, which destroys the uniqueness of the solution, was investigated and the points to be noted for future magnetic field measurements were clarified. The results show that this inverse-analysis method allows the estimation of the ${J}_{c}$ of each bulk comprising an HTS bulk undulator.