Magnetic field error analysis of a low- $\beta$ quadrupole magnet

A good field quality is always requested to achieve for the low- beta quadrupole magnet being used in the accelerator projects. To meet the requirement, people are always managing to reduce the field errors from its magnetic design and construction. In order to obtain a basic understanding for various known multipolar field errors, some calculation evaluations have been performed. Based on the results, the possible origins and corresponding correction methods of the deviation were briefly discussed in the paper. (6 refs)