Hybrid Planar FEM in Magnetoresonance Regime: Control of Dynamical Chaos

TL;DR

This paper analyzes how nonlinear electron dynamics in a hybrid planar free-electron maser affect its gain, revealing that operating slightly above the magnetoresonant magnetic field minimizes chaos and optimizes performance.

Contribution

It introduces an analytical approach using the Chirikov resonance-overlap criterion to estimate the maximal gain and identify optimal operation regimes in hybrid free-electron masers.

Findings

Chaotic zones around magnetoresonant fields influence gain.

Operating slightly above magnetoresonance enhances stability and gain.

Analytical estimates align with numerical results for optimal regimes.

Abstract

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.