Skew chromaticity in large accelerators

The 2-D ''skew chromaticity'' vector k is introduced when the standard on-momentum description of linear coupling is extended to include off-momentum particles. A lattice that is well decoupled on-momentum may be badly decoupled off-momentum, inside the natural momentum spread of the beam. There are two general areas of concern: (1) the free space in the tune plane is decreased; (2) collective phenomena may be destabilized. Two strong new criteria for head-tail stability in the presence of off-momentum coupling are derived, which are consistent with experimental and operational observations at the Tevatron, and with tracking data from RHIC