Electron storage ring distributions near linear resonance (Q760974)

The standard formula for the shape of a beam in a collisionless electron storage ring can require substantial correction when the (linear) equations of motion have solutions that are nearly periodic or antiperiodic in time. How to calculate approximations to beam shapes in such cases in a simple way is explained. A similar analysis is also applied to the storage ring dispersion (or off-energy function). This technique is similar in its logic to the ''two-time'' and ''smoothing'' methods of Keller.