Second order chromaticity of the interaction regions in the collider

The collider in the SSC has large second order chromaticity (ξ ₂) With the interaction regions (IRs) contributing substantially to it. We calculate the general expression for ξ₂ in a storage ring and find that it is driven by the first order chromatic beta wave. Specializing to the interaction regions, we show that ξ₂ is a minimum when the phase advance (Δμ _IP-IP) between adjacent interaction points is an odd multiple of π/2 and both IRs are identical. In this case the first order chromatic beta wave is confined within the IRs. Conversely, ξ₂ is large either if Δμ_IP-IP=(2n+1)π/2 and the two IRs are very far from equality or if the two IRs are equal but Δμ_IP-IP=nπ