The nonlinear effects of fringe fields in HLS

Abstract

The main body of HLS (Hefei Light Source) is an 800MeV electron storage ring, whose circumference is about 66m. As a typical small ring, although the sextupole fields for correction of chromaticities are relatively weak, there still exist strong nonlinear fields coming from fringe fields of dipole and quadrupole magnets. In this paper, the effects of fringe fields on chromaticities and tune shifts with amplitude were discussed and calculated for HLS storage ring. Under the low injection energy, the tune shifts with amplitude coming from fringe fields are one of important sources of transverse Landau damping, which is main stabilizing mechanism for HLS ring.

Analytical transfer matrix of a quadrupole fringe

“…There is an approximation linear map for a linear fringe in SAD [3]. Recently, there have been many studies about quadrupole fringes in high order maps [4,5]. In this paper, we will deduce the analytical linear transfer matrix for quadratic, shifted higher order and exponential fringes.…”