A Numerical Method to Calculate Spatial Harmonic Coefficients of Magnetic Fields Generated by Screening Currents in an HTS Magnet

This paper presents a numerical method, named “Segmentation” method, to calculate spatial harmonic coefficients of magnetic fields generated by both transport and screening currents in a high temperature superconductor (HTS) magnet. Once screening current distributions in the individual turn of an HTS magnet are obtained using finite element analysis (FEA) based on the edge-element H-formulation and the domain homogenization technique, the current flowing domain is divided into multiple “segments” and an equivalent loop current in each segment is calculated using an equivalent current transformation technique. Then, harmonic coefficients of magnetic fields by the individual loop currents are calculated analytically and the final harmonic coefficients are obtained by superposition. To verify the proposed segmentation method, an HTS magnet comprising a stack of 12 single pancake coils was assumed and its field gradients without consideration of screening current were calculated up to the 10
^th
order by the so-called “Garrett” method (proven), a numerical analysis based “Inverse” method, and the proposed “Segmentation” method. Good agreement between the three different methods validates feasibility of the proposed method. Then, field gradients of magnetic fields of the same magnet generated by given non-uniform current densities with consideration of screening current were calculated using the proposed method and “Inverse” method. The “Segmentation” method delivers reasonable values of field gradients when compared with “Inverse” method. The results demonstrate that the proposed segmentation method may be used to calculate field gradients of an HTS magnet with the non-uniform screening current distribution considered.