Chaotic behavior of an electron motion in combined backward propagating electromagnetic wiggler and ion-channel electrostatic fields is studied. The Poincaré surface-of-sections are employed to investigate chaotic behavior of electron motion. It is shown that the electron motion can exhibit chaotic behavior when the ion-channel density is low or medium, while for sufficiently high ion-channel density, the electron motion becomes regular (nonchaotic). Also, the chaotic trajectories decrease when the effects of self-fields of electron beam are taken into account and under Budker condition all trajectories become regular. The above result is in contrast with magnetostatic helical wiggler with axial magnetic field in which chaotic motion is produced by self-fields of electron beam. The chaotic and nonchaotic electron trajectories are confirmed by calculating Liapunov exponents.

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.

An analysis of relativistic electron trajectories in a free-electron laser with a helical magnetic wiggler and an ion channel is presented. The wiggler field amplitude and the ion number density are taken to be uniform. Also included are the self-electric and self-magnetic fields of the electron beam, which is assumed to be of constant velocity and electron number density. The Hamiltonian, which is a constant of the motion, is first expressed in cartesian coordinates and momenta. A second constant of the motion is obtained by canonical transformation. The steadystate orbits, Poincaré maps, and Liapunov exponents are employed to investigate the chaotic motion in the presence of the ion channel. Numerical calculations reveal conditions under which chaotic and non-chaotic orbits exist.

Chaotic electron dynamics in a free-electron laser with realizable helical wiggler and reversed axial magnetic field is investigated. Poincaré maps are employed to investigate the chaotic electron motion. Numerical calculations show that all trajectories become regular (nonchaotic) for high enough axial magnetic field.

No abstract