Design for Fermilab Main Injector magnet ramps which account for hysteresis

Although the dominant fields in accelerator electromagnets are proportional to the excitation current, precise control of accelerator parameters requires a detailed understanding of the fields in Main Injector magnets including contribution from eddy currents, magnet saturation, and hysteresis. Operation for decelerating beam makes such considerations particularly significant. Analysis of magnet measurements and design of control system software is presented. Field saturation and its effects on low field hysteresis are accounted for in specifying the field ramps for dipole, quadrupole and sextupole magnets. Some simplifying assumptions are made which are accepted as limitations on the required ramp sequences. Specifications are provided for relating desired field ramps to required current ramps for the momentum, tune, and chromaticity control.