  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.
