Second order chromaticity of the interaction regions in the collider

The collider in the SSC has large second order chromaticity (/spl xisub 2/) With the interaction regions (IRs) contributing substantially to it. We calculate the general expression for /spl xisub 2/ 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 /spl xisub 2/ is a minimum when the phase advance (/spl Deltaspl musub IP-IP/) between adjacent interaction points is an odd multiple of /spl pi2 and both IRs are identical. In this case the first order chromatic beta wave is confined within the IRs. Conversely, /spl xisub 2/ is large either if /spl Deltaspl musub IP-IP/=(2n+1)/spl pi2 and the two IRs are very far from equality or if the two IRs are equal but /spl Deltaspl musub IP-IP/=n/spl pi/.<
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