Self-field-induced chaoticity in the electron orbits in a helical-wiggler free-electron laser with axial guide field

The motion of a relativistic electron is analyzed in the field configuration consisting of a constant-amplitude helical wiggler magnetic field, a uniform axial magnetic field, and the equilibrium self-electric and self-magnetic fields produced by the non-neutral electron beam. By generating Poincaré surface-of-section maps, it is shown that the equilibrium self-fields destroy the integrability of the motion, and consequently part of phase space becomes chaotic. In particular, the Group I and Group II orbits can be fully chaotic if the self-fields are sufficiently strong. The threshold value of the self-field parameter ε=ω2pb/4Ω2c for the onset of beam chaoticity is determined numerically for parameter regimes corresponding to moderately high beam current (and density). It is found that the characteristic time scale for self-field-induced changes in the electron orbit is of the order of the time required for the beam to transit one wiggler period. An analysis of the first-order, self-field-induced resonances is carried out, and the resonance conditions and scaling relations for the resonance width are derived. The analytical estimates are in good qualitative agreement with the numerical simulations.