Abstract

As the size of storage rings proposed and under construction increases, the chromaticity reaches values which require correction schemes with a new order of sophistication involving sextupoles. The very large chromaticities encountered in storage rings like PEP, PETRA and the ''Very Big Storage Rings'' produce a new set of undesirable characteristics in the beam dynamics which require a more complicated means of correction. The method of attack used at PEP to solve the problem of both satisfactory chromaticity correction and stable non-linear motion is discussed. The analytic expressions developed for calculating the dispersion function through second order in delta and for the tune shifts through third order in delta, agree well with the results of the matrix multiplication method over the range in delta of interest. Analytic expressions for the tune shift with betatron amplitude agree well with the results from the tracking programs and can be used to determine for which amplitudes the tune will be shifted to a resonance.

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