Chaotic behavior of relativistic electron motion in a free-electron laser with realizable helical wiggler and axial magnetic field is investigated by using Pioncaré maps and Liapunov exponents. It is shown that in the presence of low to medium axial magnetic field, the motion of the electron may be chaotic. The effect of high axial magnetic field on electron dynamics causes the motion to become regular and nonchaotic. The chaotic behavior of electron motion in the absence of self-fields and axial magnetic field is due to the spatial inhomogeneities of the realizable helical wiggler magnetic field.
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