Slanted-gap quadrupole magnet and its field distribution function

A quadrupole magnet is proposed whose gap is not constant, but depends on the position along the symmetry axis. We were able to formulate a magnetic field distribution function that can reproduce the three-dimensional field distribution of any slanted-gap quadrupole magnet with seven parameters. The relative gain in the focusing power by the slanted-gap quadrupole magnet was estimated to be 0.3-0.7 times the gap difference divided by the mean gap, depending on the field strength. The slanted-gap quadrupole magnet will be useful when we need as high a field gradient and as large a gap as possible under tight spatial and electrical power restrictions.