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 beta /sub perpendicular to //sup 2/ in the relativistic factor gamma is dominant in governing the perpendicular wiggling velocity and the orbit excursion even in the case of beta /sub perpendicular to //sup 2/<< beta /sub ////sup 2/, where gamma =(1- beta /sub 1//sup 2/- beta /sub ////sup 2/)/sup -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.<
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