Intrinsic nonlinear effects of dipole magnets in small rings

We find that dynamic aperture depends significantly on the bending radii of dipole magnets when designing a small storage ring for Tsinghua Thomson scattering X-ray source (TTX) mainly because of the nonlinearity of the dipole field. In this paper, we present systematic studies on the intrinsic-geometric nonlinearity of dipole magnets. The Hamiltonian approach is used to determine the expressions of the geometric nonlinear potential and the corresponding third-order resonance strengths. Simulations are conducted to study these resonances. Our analysis results agree well with the tracking results at the third-order resonances 3 nu(x) = l and nu(x) +/- 2 nu(z) = l, where l's are the integer multiple of the number of superperiods.