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

TL;DR

This paper derives analytic formulas for the non-linear tune shift caused by quadrupole magnet fringe fields and compares its significance with other non-linear effects in particle accelerators.

Contribution

It provides the first analytic expressions for the amplitude-dependent tune shift due to quadrupole fringe fields and evaluates their impact in a real collider lattice.

Findings

Fringe field effects can be comparable to other non-linearities.

Analytic formulas enable quick estimation of fringe field impacts.

Application to VEPP-4M collider demonstrates practical relevance.

Abstract

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