turbulence

The article deals with the bases of fractal geometry and fates of its creators. The biographies and the discoveries of Felix Hausdorff and Abram Besicovitch – the main characters of the great play called fractal geometry – are presented with the possible degree of detail. There is no doubt that the author and director of this play was Benoit Mandelbrot.

A review of the current state of different theoretical approaches to the description of turbulence in electron beams and electronic devices at microwave frequencies is shown. A three types of turbulent (nonlaminar) electron beams were considered. The first type of turbulent electron beam is caused by the intersection of electronic trajectories (e.g., due to thermal velocity) and it is common to the flow of electrons at all.

The paper presents the results of theoretical and experimental studies of multispeed electron beams. Theoretical and experimental studies of the structure of such beams are considered. It is shown that turbulence forms in such electron beams. It leads to the formation of multiple bunches of space charge, which are sources of broadband noise-like fluctuations. The results of  experimental studies of small-sized laboratory model of the generator based on the principles of  formation and use of multispeed turbulent electron beams are shown.