The Hamiltonian for an electron travelling through a large-amplitude backward electromagnetic wave, an axial guide magnetic field and radiation field is formulated. Poincare surface-of-section plots show that this Hamiltonian is non-integrable, and leads to chaotic trajectories. Equilibrium conditions are derived in the limit where the radiation field approaches zero. Compared to conventional FEL, the total energy of the system at pondermotive resonance E(c) is large, while the electron's critical energy gamma(c) is low for electromagnetic wiggler FEL. Moreover, the threshold wave amplitude (A(r) = A(c)) of beam chaoticity is found at lower values of the radiation field amplitude compared to magnetostatic wiggler FEL. Previous features confirmed that electromagnetic wiggler FEL can operate more coherently and more efficiently at moderated particle's energy compared to magnetostatic wiggler FEL.