Simulation study for the effects of non-linear magnetic field

The effects of non-linear magnetic field involve a set of non-linear differential equations, which is difficlt to be solved analytically. A computer simulation method is described. Taking the advantage of Monte Carlo technique, it can be applied to determine the tolerance of magnet field, and incorporated with magnet measurement data, the tracking study can be carried out in a imperfect ring. The method has successfully found its application in the BEPC magnet tolerance study as well as field quality evaluation of the magnet prototypes