Anatoliy Opanasenko

FEL dispersion equation with account for relativistic space-charge effects

We give a qualitative derivation of a free-electron laser (FEL) dispersion equation, which takes into account not only non-relativistic (potential) but also relativistic (rotational) space-charge effects. The derivation is based on a generalisation of a dispersion equation for a Compton FEL obtained by us earlier, a certain weakly-relativistic quasistatic approximation of the space-charge field (the Darwin model), and uses an analogy between FEL and a travel wave tube (TWT). An analysis of the obtained linear growth rates is presented.

Free-electron laser with resonant pumping

We find the boundaries of regular and chaotic dynamics zones around the magnetoresonance for a hybrid planar free-electron laser amplifier. For the zones of regular dynamics the maximal magnetoresonant gain is calculated analytically and is shown to be in a good agreement with non-linear numerical simulations. It is also analytically demonstrated that in the vicinity of magnetoresonance the gain is independent of the spatial amplitude of undulator magnetic field. Moreover, we find that in the zone of regular dynamics above the magnetoresonance the efficiency of amplification achieves its maximal value and is less prone to the influence of space-charge effects.

Magnetostatic Resonance in Hybrid Planar Ubitron

In the linear approximation the dispersion relation for an arbitrary waveguide loaded with a thin electron beam moving in magnetic field of a hybrid planar ubitron is obtained. We have calculated the amplification band, spatial growth rate and carried out efficiency estimation taking into account conditions of magnetostatic resonance

Synchronism conditions for a hybrid weakly-relativistic FEL

We propose an analytical technique of twofold perturbation expansion to solve the nonlinear equations of motion of weakly-relativistic electrons moving in the magnetostatic pump field of a hybrid planar free electron laser (FEL) and apply it to obtain linear corrections to the electron trajectories caused by interaction with given propagating modes of a circular waveguide. In a single-particle approximation conditions of the most efficient interaction between an electron beam and propagating modes of a circular waveguide (resonant conditions) are derived analytically using small-signal theory in the microwave field.