Cyclic Motion of Heavy Ions with Charge Spread

A non-linear theory of multicharged ion cyclic motion is presented in the report, the charge q, being considered a discretely changing parameter. Expressions for ion closed orbits are found to an accuracy of ~(Δq/qo)2, where |Δq| is the charge spread near the mean value qo. Conditions of magnetic structure chromaticity compensations are also formulated to the same approximation. The study is made in an easy-to-use form, which may be directly applied to studying monocharged beam dynamics at high momentum spreads.