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Nonlinear simulations are devoted to the comparative study of the equilibrium electrons’ motion and stability in the combination of a three-dimensional helical wiggler and a positive or reversed guide magnetic field, where effects of the self-field, off-axis guiding center and adiabatic magnetic field are included. It is shown that a reversed guide magnetic field configuration brings the electron motion much smaller Larmor radius and transverse displacement span than a positive guide magnetic field does, and consequently, provides better transportation quality of the electron beam. Although the electron motion far from the resonance and antiresonance is stable in both the positive and the reversed guide magnetic field configurations, fluctuation induced by a reversed guide magnetic field is smaller than that by a positive guide magnetic field, especially in the adiabatic region of the wiggler. In a certain parameters domain, the self-field of the electron beam is advantageous to confine the electrons’ motion at antiresonance

Equilibrium electrons in free-electron lasers with a 3D helical wiggler and a guide magnetic field: Nonlinear simulations