Abstract
The principles of free-electron laser (FEL) are explained. The motion of an individual electron in a FEL in a field configuration consisting of a quadrupole wiggler magnetic field is investigated. The general formulation of the dynamical problem is given. The Hamiltonian and Hamilton's equations of motion are derived. The problem of integrability and the Hamiltonian chaos is discussed. Upon plotting the Poincare' surface-of-section maps, the sensitivity for the initial conditions is shown. It has been confirmed that the presence of chaos is induced by the equilibrium self-electric and self-magnetic fields produced by the space charge and current of the electron beam. In this paper, the chaotic electron trajectories are modified by the effect of the ion-channel guiding. It is found that the effect of the ion-channel guiding is much better than the use of the axial guide magnetic field in which the motion is still chaotic when the self fields were taken into account.
Key words: Free-electron laser (FEL), wigglers, chaos, quadrupole.
