Higher Harmonics in the Output Spectrum of Microwave Sources Based on Nonlaminar Electron Beams (Analysis of the Effect of Transverse and Longitudinal Bunches of the Space Charge)

Nowadays one of the actual problems of modern vacuum electronic devices is moving the operating frequencies towards the millimeter-wave and THz regime. Operation at the n-th harmonic could be one of the possible and well-known approaches to increase the operating frequency of vacuum electronic devices. Devices based on the nonlaminar electron beams (vircator-type devices) employ an intrinsic complicated dynamics of the electron beam and may serve as compact microwave sources owing to the simplicity of design and simple tunability of working regimes. In this work, we study the dependence of higher harmonics excitations on the transverse and longitudinal distribution of current density in nonlaminar electron beams. We have considered two types of spatial form of space charge bunches: solid and hollow (quasi-hollow). Fourier-analysis of these spatial forms of electrons bunches has shown that the hollow (quasi-hollow) form is most suitable for higher harmonics excitation. We have also revealed several factors that exert influence on the spatial form of electrons bunches: a considerable amount of electron velocity scatter, a convergence of electron beam, the presence of reflected electrons in the electron beam, a magnitude of the periodic magnetic field. Experimental studies were carried out with the help of a demountable vacuum setup. Experimental studies have shown that there was an excitation of 15-th harmonic (the main frequency was near the 1 GHz) in the case of hollow (quasi-hollow) electron bunches. We have formulated several recommendations for the excitation of higher harmonics in vacuum electronic devices based on the nonrelativistic nonlaminar electron beams.