Abstract
In the analysis of particle tracking for small circular storage rings, the equation of motion with perturbation terms up to the second order in betatron amplitude is derived by assuming a one-dimensional simple model and the effects are estimated in this paper. The difference of betatron number between the equation of motion with perturbation terms up to the second order and that up to the first order becomes increase, when the magnetic field index is larger than 0.6.
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