Avoiding beam instabilities and resonances with circular modes

Beam instabilities and resonances affect the transverse dynamics in particle accelerators and, when encountered, can trigger emittance growth and beam loss. Resonance lines originate from nonlinear elements and effects in the lattice,and impose strict constraints on the choice of working points and narrow the available tune space. Circular modes—intrinsically coupled, flat-round eigenmodes—provide an alternative beam motion and dynamics. In this study we derive the third-order sextupole resonance conditions in the coupled (normal-mode) parametrization and show that, with circular-mode lattice design and beam operation, most of these resonance lines are naturally suppressed thanks to the mode’s inherent flatness.