An accelerated computation method of Legendre polynomial coefficients for MRI REBCO magnet design

When designing an MRI magnet, its field homogeneity is evaluated by higher-order coefficients of the Legendre polynomial expression than 0th. Recently, the development of ultra-high-field (~10 T) MRI magnet wound with REBCO tapes is underway. REBCO tapes are flat, and its current-carrying region is very narrow compared to its cross section. However, to compute the higher-order coefficients for MRI REBCO magnet is a labor task because the current-carrying region is discretely arranged. In this paper, we propose an accelerated method of computing the higher-order coefficients of the Legendre polynomials for MRI REBCO magnet design using a shift operator.