Static Magnetic Field Shimming Calculation Using TSVD Regularization With Constraints of Iron Piece Placements

A new shimming calculation method for a static magnetic field in cylindrical magnets has been developed and the feasibility was confirmed by a test shimming. The calculation is based on truncated singular value decomposition regularization to solve a linear system of equations with a response matrix from iron piece volumes in shim-pockets to the magnetic field distribution. Singular value decomposition obtains eigenmodes which are numbered in a descending sequence of the singular. Low-ordered (large singular value) eigenmodes are chosen and summed to get the iron piece placements, considering the number of the main coil blocks in the magnet and tuning their eigenmodes strengths. High-ordered (small singular value) eigenmodes, which have a small magnetic field, are utilized to make the iron volumes within constraints in each pocket using iterative calculations. During the test shimming, iron pieces were placed according to the calculation and good homogeneities were obtained. The shimmed magnetic field agreed well with the field predicted by the calculation. These results have shown that the developed shimming calculation method works well to get homogeneous magnetic field.