Mathematical model of calculation of parameters of electron beam of the field electron cathode, applied to the study of morphology of blood cells

Mamaeva S.N., Maksimov G.V.1, Neustroev E.P., Antonov S.R., Pavlov A.N.

North-Eastern Federal University (NEFU), Institute of Physics and Technologies, 677000, Russia, Republic of Sakha (Yakutia), Yakutsk, 48 Kulakovskogo street, Phone: +7 (4112) 49-68-32, E-mail:

11Lomonosov Moscow State University, Faculty of Biology, 119991, Russia, Moscow, GSP-1, Leninskie Gory, Phone: (095) 939-11-16, fax: (095) 939-11-15, E-mail:

At present, it is necessary to formulate approaches of the study of the morphology of blood erythrocytes by using traditional physical equipment, such as an electron microscope, to construct new methods for the differential diagnosis of difficultly diagnosed diseases [1].

To obtain images of the surface of biological objects with high resolution at low accelerating voltages, electron sources with field emission are usually used. Carrying out numerical experiments for calculating the current-voltage characteristics of electron beams of field electron emitters, which makes it possible to select the parameters of the emitter itself, the values of the accelerating voltage, the energy of the primary beam in interrelation with each other, is necessary to obtain the most complete information about the surface and is the least expensive in comparison with full-scale experiment.

In this paper, a physics and mathematical model of the main emission characteristics of the field electronic cathode (FEC) under the influence of an external electric field is constructed and solved, including the following equations: the electron motion equation; Einstein's equation for the photoelectric effect; equations for the current density; law of energy conservation; Maxwell's equations.

As a result of the solution of the presented model, using the numerical Runge-Kutta method of 4th order, the values of the basic emission characteristics of the FEC are obtained to select the mode for carrying out full-scale studies of blood samples, which makes it possible to reveal the information most fully revealed in the objects under investigation.


1. Maksimov G.V., Mamaeva S.N., Antonov S.R., Munkhalova Ya.A., Kononova I.V., Sheikin I.Yu. Measuring Erythrocyte Morphology by Electron Microscopy to Diagnose Hematuria // Measurement Techniques volume 59 (3), June 2016. Pp. 327-330.

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