Nonintegrable Hamiltonian and Chaotic Electron Motion in Dual-Wiggler Free-Electron Laser with Axial Guiding Field

Abstract

A free-electron laser is a laser that has the same optical properties as a conventional laser, such as emitting beams of coherent electromagnetic radiation, which can reach high powers, but uses some very different principles of operation to form the beams. The chaotic motion of electrons causes a considerable decrease in the gain and efficiency of free-electron lasers. In this paper, the Hamiltonian of the dual-wiggler free-electron laser with and without axial guide magnetic field is constructed. Hamilton's equations of motion were derived exactly for both cases. The steady-state solution is also derived and investigated so that the initial conditions of the system are clear. The Poincaré surface-of-section maps were plotted after solving Hamilton's equations of motion numerically, where the chaotic behavior of the system was obvious when the axial field was included while the motion became regular and the Hamiltonian is integrable in the absence of the axial guide magnetic field. Regular orbits are observed clearly for large values of the axial field.