Abstract
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.
Highlights
Finding the right balance between low-emittance lattices and the control of the stronger nonlinear effects, is one of the most challenging task faced by new generations of light sources
Our nonlinear scheme uses three families of octupoles, powered to control the linear amplitude dependent tune shift (ADTS) and for which their location is optimized with respect to the lattice sextupoles, to produce octupole-like resonant driving terms (RDTs) that systematically counteract the ones generated to the second order by the sextupoles with similar amplitudes
The fourth-order RDTs generated to the first order by the octupoles systematically counteract the ones generated to the second order by the sextupoles with similar amplitudes
Summary
Finding the right balance between low-emittance lattices and the control of the stronger nonlinear effects, is one of the most challenging task faced by new generations of light sources. The cross talks between the firstorder sextupole RDTs generate amplitude dependent tune shift (ADTS), fourth (see the Appendix) and higher order phase-dependent terms affecting the overall efficiency of the machine. Cross talks among octupole RDTs, produce important higher order terms, contributing to the more chaotic behavior of the particles These additional unfavorable effects from octupoles have been discussed in past studies in Refs. Our nonlinear scheme uses three families of octupoles, powered to control the linear ADTS and for which their location is optimized with respect to the lattice sextupoles, to produce octupole-like RDTs that systematically counteract the ones generated to the second order by the sextupoles with similar amplitudes. The impact on chromatic effects and possible use of this scheme features on future light source designs are discussed as well
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