Self-similar character of short pulse generation during the Cherenkov-type electron-wave interaction in a backward wave oscillator

Abstract

The ultrashort high-power pulses of microwave radiation are of interest to a number of scientific and practical applications, for example, in the nanosecond high-resolution radar, spectroscopy, etc. A promising method for generating such pulses is provided by the phenomenon of superradiance of electron bunches during the interaction of a rectilinear electron beam with a backward electromagnetic wave in backward wave oscillators (BWOs). This paper reports the results of studies of self-similar character of pulse propagation within this process.
Using the Lie symmetry analysis, it is shown that the well-known equations of nonlinear nonstationary theory of relativistic O-type BWOs admit a self-similar solution describing an amplifying and compressing pulse. By numerical simulation, it is demonstrated that this solution corresponds to the generation of a short superradiance pulse at the initial stage of the transient process. It is shown that, after a while, the numerical solution reaches the self-similar stage, where the pulse amplitude and the inverse of its squared width grow linearly with time in accordance with the analytical conclusions. Effects limiting the peak power of output pulses are discussed.
The found self-similar solution is also generalized to the case of spatially inhomogeneous BWO, in which the coupling impedance varies along the system. This makes it possible to substantiate the coupling impedance profiling law found by other authors from heuristic considerations. The use of such profiling to increase the peak amplitude of generated pulse in comparison with homogeneous BWO is considered.


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Alena A. Rostuntsova
Saratov State University, Institute of Applied Physics RAS
Russia

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