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

Abstract

Coupled nonlinear evolution equations are derived for the transverse velocity in a helical wiggler with positive axial guide magnetic field at magnetoresonance. The nonlinear oscillator representation is adopted, without having to impose the usual restriction of the slow variation on the amplitude and the phase. Numerical calculations show that the evolution equations are quite appropriate to describe the envelope of the transverse velocity amplitude. The maximum transverse velocity and the maximum axial velocity spread can be estimated straightforwardly from the evolution equations.