THE EFFECTS OF WEAK SELF-FIELDS ON ELECTRON ORBITS FOR A FREE ELECTRON LASER

A set of coupled equations for electron motion and the dispersion relation of electromagnetic wave (wiggler) in electron beam are studied. The instability of steady-state electron orbits is reduced to the problem of the fourth-order and fifth-order linear ordinary differential equations. It is found that the presence of self-fields plays an important role in determining the behaviour of stable electron orbits.