• F. Jafari Bahman, B. Maraghechi
  AUT, Tehran

Three-Dimensional simulation of Free-Electron Laser amplifiers at the presence of helical wiggler and ion-channel has been reported. The electromagnetic field is assumed to express in terms of the TE modes of a cylindrical waveguide in the absence of the electron beam. The final form of dynamical equations for the evolution of the slowly varying amplitude and wavenumber of TE mode is obtained by substitution of the vector potentials in to Maxwell’s equations. A cold, uniform, axisymmetric electron beam with a flat-top density profile has been considered for modeling the initial injection of the electron beam. The three-dimensional Lorentz force equation in the presence of a realistic helical magnetostatic wiggler, ion-channel electrostatic field and electromagnetic fields describes the electron dynamics. A set of coupled nonlinear first order differential equations is derived and solved numerically by Runge-Kutta method. The 10th-order Gussian quaderature technique is used for calculation of averages in the field equations. Finally, evolution of the radiation power and growth rate of the TE11 mode is shown.

• B. Maraghechi, M.H. Rouhani, E. Salehi
  AUT, Tehran

The dynamical stability of electron trajectories in a free-electron laser with planar wiggler is studied. The analysis is based on the numerical simulation of Kolmogorov entropy to investigate how the separation of the trajectories of two neighboring electrons in the six-dimensional phase space evolves along the undulator. Self-electric and self-magnetic fields are taken into account and an adiabatically tapered wiggler magnetic field is used in order to inject the electrons into the wiggler. A considerable decrease in the dynamical stability of electron trajectories was found near the resonance region. It was found that self-fields decrease the dynamical stability of electron trajectories in group I orbits and increase it in group II orbits. Furthermore, the electromagnetic radiation weakens the dynamical stability of electrons as it grows exponentially and become very intense near the saturation point.

• B. Maraghechi, M. Olumi, M.H. Rouhani
  AUT, Tehran

The relativistic cold fluid model is used to study the propagation of the nonlinear traveling wave in a free electron laser (FEL) with electromagnetic wiggler. It is convenient to transform the relevant equations to the frame of reference rotating with the wiggler. The traveling-wave ansatz is employed to obtain three coupled, nonlinear ordinary differential equations that describe the nonlinear propagation of the coupled wave. Saturation and solitary waves in FELs with electromagnetic wiggler may be investigated using these equations. In the small signal limit, the wave equations are linearized and the dispersion relation for the traveling wave is obtained. The numerical solution of the traveling-wave dispersion relation reveals the range of parameters for its unstable solutions. Instability curves with two peaks are found, for which the phase velocity is smaller and larger than the beam velocity.