The dispersion relation for the harmonic generating mode in dual wiggler free electron lasers

الملخص EN

The unperturbed velocity of electrons moving through free-electron lasers with dual wiggler is obtained.

Then, by writing all of the first order components of the magnetic field, velocity and first order energy in terms of the first order components of the electric field we were able to obtain the dispersion relation for the longitudinal oscillation of electrons.

Finally, to compare our results with previous works in the Eel field, the wiggler field strength was let to be zero, then it was found that the dispersion relation for the longitudinal oscillation of electrons reduce to the dispersion relation for the longitudinal mode in a cold, relativistic streaming plasma