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Chaotic electron trajectories in quadrupole wiggler free electron laser

The motion of an individual electron in a FEL in a field configuration consisting of an ideal quadrupole-wiggler field and uniform axial-guide field, is shown to be nonintegrable in Hamiltonian formulations and can become chaotic for certain initial conditions. The presence of chaos, which is induced by the transverse spatial inhomogenieties in the wiggler field; and the self-fields produced by the space charge and current, poses limits on the wiggler field amplitude and the beam size for beam propagation in Free-Electron Laser operation. Upon plotting Poincaré surface-of-section maps, it is shown that the electron dynamics is chaotic.