Isochronicity Adjustments Using Multipoles in Rings and Transfer Lines

The orbit length dependence of the momentum error can be modified by adjusting the strength of multipole magnets. The present note proposes simple expressions for the change of the length derivatives which are based only on the strength increment and on the local dispersion value in quadrupoles, sextupoles or octupoles. This approach is useful to identify the most effective existing or potential magnet locations, for example in the design of isochronous optics. The formalism may be applied both in rings and in transfer lines. The example of the EPA machine is used to show the accuracy of the expressions.