On the Evolution of the chromatic Functions around an IP computed by MAD-X

The chromatic functions W defined by Montague are computed by MAD-X. Contrary to statements made by Montague, the values computed by MAD-X are not constant along a drift space. The reason is that MAD-X uses canonical variables to describe particle trajectories leading to a momentum dependence of the transfer matrix. Simple expressions describing the variations of the chromatic functions around a collider Interaction Point with MAD-X conventions are derived and shown to agree numerically with MAD-X results for a particular case. Derivations of parameters describing betatron mismatch and of chromatic functions are given in the appendix and are expected to provide a better insight on the meaning of these quantities.