Electron orbit in a combined plasma wave wiggler and an axial guide magnetic field free electron laser near magnetoresonance

The nonlinear electron orbit dynamics is presented for a combined electrostatic plasma wave wiggler and an axial guide magnetic field free electron laser near magnetoresonance. The perpendicular orbit equation is derived and simplified identical to the wave-driven nonlinear oscillator equation but with different expressions of parameters. The nonlinear effect induced by the inclusion of β_⊥² in the relativistic factor γ is dominant in governing the perpendicular wiggling velocity and the orbit excursion even in the case of β_⊥²≪β_||² , where γ=(1-β₁²-β_|| ²)^-1/2. The dependence of the maximum perpendicular wiggling velocity and the orbit excursion on the wiggler constant, the wiggler frequency, and the initial parameters of motion is given analytically