Analytic Estimation of the Non-Linear Tune Shift due to the Quadrupole Magnet Fringe Field

摘要

Analytic expressions for the amplitude-dependent tune shift driven by thequadrupole magnet fringe field have been obtained. The magnitude of the effectis compared with other sources of non-linearity such as chromatic sextupoles,octupole errors of the main quadrupole magnetic field and kinematic terms. Anumerical example was the calculation on the lattice of the VEPP-4M e+e-collider.