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 elec trostatic plasma wave wiggler and an axial guide magnetic field free e lectron laser near magnetoresonance. The perpendicular orbit equation is derived and simplified identical to the wave-driven nonlinear oscil lator equation [8] but with different expressions of parameters. The n onlinear effect induced by the inclusion of beta(perpendicular-to)2 in the relativistic factor gamma is dominant in governing the perpendicu lar wiggling velocity and the orbit excursion even in the case of beta (perpendicular-to)2 much less than beta(parallel-to)2, where gamma = ( 1 - beta(perpendicular-to)2-beta(parallel-to)2-1/2. The dependence of the maximum perpendicular wiggling velocity and the orbit excursion of the wiggler constant. the wiggler frequency, and the initial paramete rs of motion is given analytically.