Development of a decision method for optimum ferromagnetic board arrangements to reduce toroidal magnetic field ripple

A new decision method for ferromagnetic board (FB) arrangements was developed to obtain the desired toroidal magnetic field (TF) distribution. An approximation, in which the magnetization vector is only pointed in the toroidal direction and its magnitude is magnetically saturated, was introduced to allow treatment as a linear problem. The desired thickness distribution of FBs could be obtained by calculating a generalized inverse matrix which transforms from the thickness distribution to the TF distribution due to FBs. We employed a singular value decomposition (SVD) method to calculate the generalized inverse matrix. The final TF distribution was confirmed by the general-purpose 3D non-linear magnetostatic field analysis code. This method was applied to the TF coils of JFT-2M. The maximum TF ripple in the whole plasma region could be reduced from 2.1% to 0.1%.