Vitaliy A. Goryashko

Dispersion Equation of Hybrid Planar Ubitron

In the linear in the microwave field approximation the dispersion relation for an arbitrary waveguide loaded with a thing electron beam moving in external spatially-periodic magnetostatic field of a planar ubitron and uniform guide magnetic field is obtained. Non-perturbed electron trajectories are found as solutions to a non-linear system of equations via an asymptotic expansion in the small ratio of the amplitude of the undulator magnetic field to the magnitude of the guide magnetic field. As solutions to the travelling wave amplification problem, we calculated the amplification band, spatial growth rate and made an efficiency estimate taking into account magnetostatic resonance.

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.

Numerical simulation of amplification in hybrid planar ubitron

We accomplish numerical simulation of microwave amplification in a hybrid planar ubitron (free electron maser). Results are compared to those obtained in the linear theory.

Dynamical chaos and magnetoresonant gain in hybrid planar ubitron

We study the magnetoresonant amplification regime, formulate a criterion of chaotic dynamics and find the maximal gain under the undulator synchronism for a weakly-relativistic hybrid planar ubitron/ free-electron maser.

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.