Physical Review Accelerators and Beams (Jun 2016)
Intrinsic nonlinear effects of dipole magnets in small rings
Abstract
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 3ν_{x}=ℓ and ν_{x}±2ν_{z}=ℓ, where ℓ’s are the integer multiple of the number of superperiods.