Principle of Harmonic Shim and Application for Conventional Accelerator Magnets

The harmonic field errors are an evaluation criterion for field quality of accelerator magnets. The limited magnetic pole width and length of conventional magnets will lead to systemic multipole errors. Also the tolerances of machining and material will bring on random multipole errors. Those multipole errors cause the field quality to be bad. The harmonic shims can counteract each multipole error through the change of pole profile, and it improves the field quality radically. The principle of the harmonic shims was analysed and its applications for dipole and quadrupole magnet were discussed in detail.