Simultaneous correction of high order geometrical driving terms with octupoles in synchrotron light sources

As the next generation of light sources is pushing toward high-brightness storage rings with ultralow emittance, the control of the beam nonlinear dynamics becomes increasingly challenging. Nonlinear perturbations, arising from sextupole cross talks, set the limit to the achievable dynamic performance of the machine. Octupoles can be an efficient mean to tackle the remaining resonant driving terms generated to the second order by the lattice sextupoles. However, they have been used sparingly in light sources because of a lack of control on higher order effects. In this paper, we discuss the optimal positioning of octupoles, with respect to the sextupoles present in the lattice, for a local and simultaneous compensation of all fourth order on-momentum phase and amplitude dependent driving terms, using only three families of octupoles. In addition, higher order geometrical terms are also minimized, including among others, second-order tune shift with amplitude. This study is a continuation of past research made on the optimal use of octupoles for the operation of future light sources. The correction method was built on observations made on a simple model, then applied to a realistic low-emittance lattice, designed in the framework of the upgrade of the National Synchrotron Light Source II, to demonstrate its potential.