Hybrid Planar FEM in Magnetoresonance Regime: Control of Dynamical Chaos
  We establish the influence of nonlinear electron dynamics in the magnetostatic field of a hybrid planar free-electron maser on its gain and interaction efficiency. Even for the `ideal' undulator magnetic field the presence of uniform longitudinal (guide) magnetic field potentially leads to the existence of chaotic zone around certain (magnetoresonant) value of the guide magnetic field. The width of the chaotic zone is 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. Using analytical asymptotically exact solutions for trajectories of individual test electrons, we show that the magnetoresonant multiplier in electron trajectories is also present in the expression for the gain. The same Chirikov resonance-overlap criterion allows us to estimate analytically the maximal magnetoresonant gain of a hybrid planar free-electron maser showing that, in spite of the well-known drop in the gain for the exact magnetoresonance, the operation regime in the zone of regular dynamics slightly above the magnetoresonant value of the guide magnetic field is the preferable one. 
Vitaliy A. Goryashko, Kostyantyn Ilyenko, Anatoliy Opanasenko