• B. Farokhi
  IPM, Tehran

A linear theory for a fully relativistic free electron laser with a one dimensional helical wiggler and axial magnetic field in the collective regime is presented. The configuration consists of a cylindrical waveguide with arbitrary ratio of electron beam radius to waveguide inner radius . Transverse and longitudinal components of the velocity are treated as relativistic. Parametric decay of the wiggler pump wave, in the beam frame, in to a relativistic space-charge wave and a relativistic electric-magnetic waveguide mode is analyzed in three dimensions. A relativistic non-linear wave equation is derived in a form which includes the coupling of and modes and employed to obtain a formula for the spatial growth rate of the excited eigenmodes. It was found that the relativistic treatment of the electron oscillations in the wiggler field destroys the cyclotron resonance which appears in the nonrelativistic case. Nevertheless, appreciable amplification was found. Numerical analysis is conducted to study the growth rate, radiation wavelength, and required relativistic factor as a function of axial magnetic field and radius ratio .

• B. Farokhi
  IPM, Tehran

A theory of ion-channel guiding in a planar wiggler is presented. The self-electric and self magnetic fields of a relativistic electron beam passing through a wiggler and ion-channel are analyzed. A numerical study shows that for Lorentz factor and the self-fields can produce very large effects. Also, we have followed the self-consistent method for the analysis of self-magnetic field. The equilibrium orbits and their stability, under the influence of self-electric and self-magnetic fields, are analyzed. New unstable orbits, in the first part of the group I orbits and in the resonance region of the group II orbits are found.