• Alexander Lysenko Head of the Department of Applied Mathematics and Complex Systems Modeling, Sumy State University,
  • Iurii Volk PhD student, junior researcher, Department of Applied Mathematics and Complex Systems Modeling, Sumy State University,
  • Anastasia Serozhko Student, Department of Applied Mathematics and Complex Systems Modeling, Sumy State University,
  • Oleksandr Rybalko Postdoc, Department of Electrical Engineering, Technical University of Denmark,



two-stream superheterodyne free-electron laser, two-stream instability, helical electron beams, three-wave resonances.


Background. A powerful terahertz radiation sources creation is one of the perspective tendencies in relativistic plasma electronics. Nowadays there are few devices able to create powerful radiation in millimeter-infrared waveband (even in the part of this band). Therefore, theoretical research of novel powerful terahertz radiation sources, that are also characterized by broad frequency spectrum, is an actual problem.
Objective. The aim of the paper is a study of the influence of multiple three-wave resonant interactions in the klystron type two-stream superheterodyne free-electron laser (TSFEL) with helical electron beam on the forming effectiveness of the powerful waves with broad frequency spectrum.
Methods. In order to theoretically analyze multiple resonances of wave harmonics, as initial, we use quasihydrodynamic equation, the continuity equation and Maxwell’s equations. We apply the hierarchic approach to the theory of oscillations and waves to the equations of motion and continuity, Maxwell’s equations are solved by means of the slowly varying amplitude
method. As a result, we derive a system of differential equations for complex amplitudes of SCW electric field strength harmonics which we analyze by standard methods.
Results. It was shown that in the two-stream superheterodyne FELs, utilizing the two-stream instability in helical electron beams as an additional electromagnetic wave amplification mechanism, the powerful multiharmonic space charge wave
with broad frequency spectrum forms due to multiple resonant interactions. The spectrum width of such wave is larger compared to the spectrum width in TSFELs utilizing straight electron beams. It is also found out that amplification rates in such TSFELs are higher.
Conclusions. An application of helical electron beams in multiharmonic TSFELs using multiple resonant interactions leads to the improvement of their amplification characteristics, frequency spectrum widening in multiharmonic signal generation mode, and to overall geometric dimensions decreasing compared to TSFELs utilizing straight beams.
Keywords: two-stream superheterodyne free-electron laser; two-stream instability; helical electron beams; three-wave resonances.


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