Pure permanent magnet harmonics corrector ring

A concept for creating any desired harmonics mix in a pure permanent magnet (PM) corrector ring is presented. Useful for nulling various harmonics simultaneously, such a device is versatile for many accelerator applications. The harmonic mix can be changed without redesign or replacement by a new ring or parts and, if desired, can be accomplished in situ via remote control of cylinder motors. Harmonics suppression of greater than a factor of 100 or even 1000 are possible; exact functional dependencies of harmonics suppresion capability versus magnet geometry are given. Sensitivity to positioning and corrector ring PM errors are given, and shown to be themselves nullable.