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Formation of electron bunch in extended stream in crossed fields


E.A. Shamov – Post-graduate Students, Volgograd State Technical University. E-mail:
A.G. Shein – Dr.Sc. (Phys.-Math.), Professor, Volgograd State Technical University. E-mail:

Modern world is inconceivable without microwave devices, which are used in consumer, industrial, medical, aerospace, military and other purposes. At the moment, although the dynamics of the streams is different from the dynamics of a single electron due to the presence of space charge, it is rather trivial and well understood. However, some features of the behavior of streams and most importantly the presence of high noise levels especially in high-power devices remain unclear. Hence designing devices with well-known characteristics is extremely problematic. Models discussed in this article take into account the three-dimensionality of space and the correct configuration of static electromagnetic fields. Electron stream is represented as amalgamated particles on a method of «large particles». The space charge is taken into account using a special hierarchical method of space optimization of interactions similar to the well-known fast multipole method. The laws of distribution of the velocity vector of the particles and their modules, as well as the continuity of entry of particles in the interaction space and prehistory of stream are taken into account. It is particularly noteworthy that the hardware and software system of modeling allows a high level of efficiency to make calculations on computer clusters with graphics processing devices, which made it possible to calculate the dynamics of the streams, consisting of a large number of «large particles». The research resulted in first obtained reliable information on the formation of separate bunches of electrons in the extended electron streams with static crossed fields that define the behavior of stream and its noise properties. The main physical factors of electron bunches formation are: the presence of high density of space electron charge and as a result, significant influence of space charge forces leads to a periodic disturbance synchronism conditions for different parts of the stream of electrons in the plane of rotation perpendicular to the vector of magnetic field (plane xy), synchronizing their trajectories promotes bunch formation, and the interaction between still unformed bunches, that promotes their isolation and retention of the electron density in them; the presence of crossed fields, retaining form and contributing to the rotation of the bunch; restricting the availability of plates along the axis coincides with the magnetic field vector (axis z), which kept the stream, not allowing fall sharply space-charge density, and thus prevent «disintegrating» of the stream; the presence of an extended system of interaction that allows bunches to form. Having the available data synthesized, we can draw an important conclusion that the formation of bunches in stream in crossed fields takes place in any space-charge density, and the difference will be mainly in the speed of their formation. It is especially worth noting that the cyclotron, plasma frequency, and their relations do not predetermine the formation of bunches. As a result, for the first time in the investigation of the dynamics of the extended electron streams in static crossed fields revealed the formation of separate bunches which determined the behavior of the stream and its noise properties. Furthermore, stream behavior of characteristics was investigated, in which bunches with variations of the basic parameters of the system were formed.

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