Multiharmonic cubic-nonlinear theory of plasma-beam superheterodyne free-electron lasers of the dopplertron type
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Multiharmonic CubicNonlinear Theory of Plasma–Beam Superheterodyne FreeElectron Lasers of the Dopplertron Type V. V. Kulish, A. V. Lysenko, and V. V. Koval Sumy State University, ul. RimskogoKorsakova 2, Sumy, 40007 Ukraine Received February 3, 2009
Abstract—A multiharmonic cubicnonlinear theory of a plasma–beam superheterodyne freeelectron laser of the dopplertron type is constructed. A retarded electromagnetic wave propagating in the magnetized plasma–beam system toward the electron beam is used for pumping. The multiharmonic interaction of waves which plays an important role is taken into account. Saturation levels and mechanisms are analyzed. The promising application of such systems for generating highpower electromagnetic radiation in the millimeter wavelength range is demonstrated. DOI: 10.1134/S1063780X10130167
1. INTRODUCTION The development and fabrication of new sources of intense electromagnetic radiation in millimeter and submillimeter wavelength ranges is one of the priority problems of modern relativistic plasma microwave electronics. This paper is devoted to the theoretical study of such a source, i.e., the plasma–beam super heterodyne freeelectron laser (PBSFEL) [1]. The fundamental idea of the PBSFEL pumped by a retarded electromagnetic wave propagating in a mag netized plasma–beam system was first proposed in [1], where the parameters of the studied device were esti mated and it was shown that this system can be used as a source of intense electromagnetic radiation in milli meter and submillimeter wavelength ranges. The study was continued in [2], where the quadraticnonlinear theory was constructed, and in [3], where some results of the cubicnonlinear theory of the PBSFEL were presented. This paper is devoted to the discussion of the results of further studies in this direction. Unlike [1–3], the main emphasis is made on the study of cubicnonlin ear effects associated with the consideration of signif icant multiharmonicity of the basic working mecha nism, in particular, saturation levels and mechanisms are analyzed. The studies allowed the conclusion that the use of these systems can be very promising for developing highpower amplifiers and generators of electromagnetic radiation in the millimeter wave length range.
beam system is placed in a longitudinal focusing mag netic field with strength H0. We chose pumping as a retarded electromagnetic wave [4] with frequency ω2 and wavenumber k2, which propagates toward the electron beam. An electromagnetic signal with fre quency ω1 and wavenumber k1 is also fed to the system input. The parametric resonance between the signal wave {ω1, k1} and the pump wave {ω2, k2} results in that a space charge wave (SCW) with frequency ω3 and wavenumber k3 is excited in the plasma–beam system. The frequencies and wavenumbers of these waves in the system under study are related by the parametric resonance condition p3 = p1 – p2 or ω3 = ω1 – ω2 ,
k3 = k1 + k2 ,
where p1 = ω1t – k1z is the phase of the signal electro magnetic w
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