Multipole correction in synchrotrons

Novel methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron are discussed. In simplest form, correction elements are placed at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson´s rule. The F, C, and D correctors permit direct control of horizontal, coupled, and vertical motion. For example, second-order sextupole nonlinearities can be corrected with F, C, and D octupoles. Generalizations and variations of the methods are described, and applications to the SCC (Superconducting Super Collider), LHC (Large Hadron Collider) AHF, and HERA (Hadron-Electron Ring Accelerator) projects are discussed. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in synchrotrons are demonstrated