The Effect of Ion-Channel Guiding on the Chaotic Electron Trajectories in a Free Electron Laser

It has been confirmed that when the equilibrium self-fields were taken into account, the motion of an electron in a helical wiggler with axial magnetic field may be chaotic. In this paper, the effect of an ion-channel guiding on the chaotic electron trajectories is analyzed. It is shown that the ion-channel guiding may modify the chaotic electron trajectories. It is also found that when the parameter ε, i.e. ε=ω$\text{}_{pb}^{2}$/4ω$\text{}_{c}^{2}$, is increased, the density of the ion-channel guiding, i.e. α$\text{}_{i}$=ω$\text{}_{pi}^{2}$/4ω$\text{}_{c}^{2}$, must be increased to keep the modification of the chaotic motion. The chaotic trajectories for constant parameter ε and increased density of the ion-channel guiding are presented. Numerical calculations are used to find the intersection between steady state group I and group II and resonance curves. Poincaré surface-of-section maps are generated to demonstrate the chaotic electron trajectories with axial magnetic field and its modification in the presence of an ion-channel guiding.