Nonlinear evolution of the equilibrium electron orbits in a helical wiggler with a positive axial guide magnetic field at magnetoresonance

A model of the coupled nonlinear evolution equations is presented for the slow-varying amplitude and phase of the electron perpendicular velocities in a helical wiggler with positive axial guide magnetic field at magnetoresonance. The transverse motion is dominated by the nonlinear effect, which arises from the correlation between the longitudinal and perpendicular velocities. The analytical results are in very good agreement with numerical calculations.