Global compensation of magnetic field errors with minimization of nonlinearities in Poincaré map of a circular accelerator

The presence of unavoidable multipole field errors in superconducting magnets is one of the main causes for limiting the dynamic aperture of large accelerators. Global compensation of the field errors based on the minimization of nonlinearities in a one-turn map was found to be very effective in reducing the detrimental effects of the field errors. With a few groups of correctors, nonlinear terms in the one-turn map can be minimized order by order and, consequently, the nonlinearity of the system is significantly reduced. This global compensation of the field errors was tested on the LHC collision lattice. It was found that a few low-order correctors can substantially increase the dynamic aperture and improve the linearity of phase-space region occupied by beams. If there is a significant uncertainty in the field measurement, a global compensation based on the measured field may be optimized with a measurement of the one-turn map.