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New types of beam-plasma devices generating intense stochastic microwave radiation in the interaction of electron beams with hybrid plasma waveguides were developed and put into operation at the National Science Center Kharkov Institute of Physics and Technology (Ukraine). The objective of the paper is to discuss the results of theoretical and experimental studies and numerical simulations of the normal and oblique incidence of linearly polarized electromagnetic waves on an interface between a vacuum and an overcritical plasma. The main results of the reported investigations are as follows: (i) for the parameter values under analysis, the transmission coefficient for microwaves with a stochastically jumping phase is one order of magnitude greater than that for a broadband regular electromagnetic wave with the same spectral density; (ii) the electrons are heated most efficiently by obliquely incident waves with a stochastically jumping phase and, in addition, the electron distribution function has a high-energy tail; and (iii) necessary conditions for gas breakdown and for the initiation of a microwave discharge in stochastic fields in a light source are determined. The anomalously large transmission coefficient for microwaves, the anomalous character of the breakdown conditions, the anomalous behavior of microwave gas discharges, and the anomalous nature of collisionless electron heating, are attributed to stochastic jumps in the phase of microwave radiation

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