The stability of electron orbits due to the wiggler field amplitude in free-electron laser

The relativistic electron orbits have been studied in the helical–wiggler field, which included self-field effect in free-electron laser. The equations of motion are derived from the Hamiltonian which includes self-field, and the steady-state orbit solutions were found from the equations of motion. We have analyzed the stability of electron orbits due to the wiggler field amplitude by numerical simulations. We have estimated the maximal Lyapunov exponents, which required estimation of the threshold value of the wiggler field amplitude for the onset of chaos in electron orbits.