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 spacecharge 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 beammicrowave interaction correspond to the operational regime in the zone of regular dynamics near the magnetoresonance.

Analysis and optimization of a free-electron laser with an irregular waveguide

“…2 and 3 gives a clear indication that the adiabatic undulator entrance "improve integrability" of the nonlinear dynamical system (15) and reduce the width of chaotic regions. In [17] it was found that the initial positive value for the x-component of the velocity leads to the suppression of the chaotic region. A test electron acquires such a positive average correction to v x passing through the region of the adiabatic entrance.…”

“…Since the relativistic electron-wave interaction is being studied, the nonradiated fields (space-charge fields) are supposed to be negligible. The relativistic effects result in that the force f m caused by the nonradiated magnetic field partially suppresses the defocusing action of the transversal part of the force f caused by the rotational part of the nonradiated electric field (see [17] for details).…”

“…We start our analysis with the integration of the equation of motion generated by the unperturbed Hamiltonian (9). The above integration is the nontrivial problem because the nonlinear dynamical system (9) is not globally integrable [18] and exhibits chaotic behavior if the absolute value of the difference between the normal undulator and normal cyclotron frequencies is less than the betatron frequency [17]. The dynamics of electrons in an ideal undulator and an axial magnetic field was studied in details in Ref.…”

“…The dynamics of electrons in an ideal undulator and an axial magnetic field was studied in details in Ref. [17] using Lindshtedt's perturbation method in configuration space. This allowed one to build a linear microwave theory and analyze the electron-wave interaction in the magnetoresonance regime.…”

Higher-order harmonic effect of a three-dimensional helical wiggler on the Larmor rotation of the equilibrium electrons in a free-electron laser with a positive or a reversed guide magnetic field

“…9 Hitherto, enthusiasm for the FEL configuration with a positive or a reversed guide magnetic field is in continuance. [10][11][12][13] Since the amplified wave energy in a FEL comes from the kinetic energy of the electron beam, motion of the equilibrium electrons substantially affects both the transportation quality of the electron beam and consequently the gain and output power of the wave. Although a great deal of literature has been devoted to this subject and achievements have been made, to the present day there still exist some fundamental questions suspending.…”