Analytical expression for betatron tune shift due to field errors in lump quadrupole

摘要

The integrated gradient of a quadrupole will be deviated by a close neighboring sextupole, and this is called the effect of fringe field interference. Using the Lie algebra techniques, an analytical expression for the betatron tune shift due to this effect has been derived. The process does not depend on the supposition of the thin-lens quadrupoles. It can be used to estimate the tune shift differences between the designed lattice and the one including the fringe field interference. More generally, the method can be applied to other kinds of fringe field interference.