Fast computation method of magnetic field homogeneity for NMR/MRI REBCO pancake coils

Recently, multiple-stacked pancake coils wound with rare-earth barium copper oxide (REBCO) tapes are expected to apply for nuclear magnetic resonance (NMR)/MRI magnets. Since REBCO tapes are very expensive, REBCO magnets should be optimally designed so as to minimize the winding volume. Surely, a highly homogeneous magnetic field is also required for NMR/MRI magnets. To achieve the accurate homogeneity of REBCO magnets, it is necessary to compute the contribution of all REBCO layers one by one, because currents carry over very thin area compared with a whole magnet cross section. However, NMR/MRI magnets generating high-magnetic field usually consist of multiple-stacked REBCO pancake coils, and each pancake coil has >300 turns. To evaluate the field homogeneity contributed by every REBCO layer, therefore, it is necessary to repeatedly compute more than ten thousand times as one magnet shape. In a conventional optimization algorithm, it is necessary to iterate more than one million times for the optimal design of an NMR or MRI magnet. Such an iterative computation is not realistic. Based on the backgrounds, we present a fast computation method using the shift operator of spherical harmonics. In addition, to confirm the validity of the proposed method, it was applied to the shape optimization of 1.5-T MRI magnet. In this paper, the optimization result and computation time are also shown.