Hybrid planar free-electron maser in the magnetoresonance regime

Abstract

We study the operation regime of a hybrid planar free-electron maser (FEM) amplifier near the magnetoresonant value of the uniform longitudinal (guide) magnetic field. Using analytical expressions for individual test electron trajectories and normal frequencies of their three-dimensional oscillations in the magnetostatic field of the hybrid planar FEM, an analytical condition of chaotization of motion is established and shown to be given by the Chirikov resonance-overlap criterion applied to the normal undulator and cyclotron frequencies with respect to the coupling induced by the undulator magnetic field. It is also shown analytically that, in spite of the well-known drop for the exact magnetoresonance, the gain attains its maximal value in the zone of regular dynamics slightly above the magnetoresonant value of the guide magnetic field. Under the condition of undulator resonance, it is practically independent of the amplitude of the undulator magnetic field and the wavelength of amplified signal. To account for space-charge effects, we propose a theoretical model of a weakly relativistic FEM, which accommodates not only potential but also rotational parts of the nonradiated electromagnetic field of a moving charged particle. It turns out that the rotational part of nonradiated field diminishes the defocusing influence of the potential part on the beam bunching. Numeric simulation of the nonlinear stage of amplification is fulfilled, taking into consideration adiabatic entrance of the electron beam to the interaction region and initial electron velocity spread. We find that nonradiated field and initial electron velocity spread do not influence essentially the efficiency of hybrid planar FEM amplification if parameters of the beam-microwave interaction correspond to the operational regime in the zone of regular dynamics near the magnetoresonance.