Abstract
A paraxial solution is constructed for the problem of calculation of forming electrodes for non-paraxial cuts from converging and diverging flows in a spherical diode and a Meltzer flow with circular paths. The solution is expressed in elementary functions for the case of a cone. For example, computations for a square on a sphere (the first approximation of the approximation of a contour) and a toroid with a circular cross section are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Syrovoi, Zh. Tekh. Fiz. 41, 2607 (1971).
V. A. Syrovoi, J. Commun. Techn. Electron. 50, 927 (2005).
B. Meltzer, J. Electr. Contr. 2, 118 (1956).
V. A. Syrovoi, Prikl. Mat. Mekh. 34(1), 4 (1970).
V. A. Syrovoi, Radiotekh. Elektron. (Moscow) 19, 1955 (1974).
V. A. Syrovoi, Radiotekh. Elektron. (Moscow) 39, 1190 (1994).
V. N. Danilov and V. A. Syrovoi, Radiotekh. Elektron. (Moscow) 22, 1473 (1977).
V. N. Danilov and V. A. Syrovoi, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 20, 1727 (1977).
V. T. Ovcharov, Radiotekh. Elektron. (Moscow) 12, 2156 (1967).
V. A. Syrovoi, A Theory of Intense Charged-Particle Beams (Energoatomizdat, Moscow, 2004) [in Russian].
V. L. Kan, Zh. Tekh. Fiz. 18, 483 (1948).
R. P. Poplavskii, Zh. Tekh. Fiz. 20, 149 (1950).
J. Itzkan, J. Appl. Phys. 31, 652 (1960).
V. A. Syrovoi, Introduction to a Theory of Intense Charged-Particle Beams (Energoatomizdat, Moscow, 2004) [in Russian].
V. N. Danilov, in Methods of Calculation of Electron-Optic Systems (Nauka, Moscow, 1977), p. 61 [in Russian].
A. V. Vashkovskii and V. A. Syrovoi, J. Commun. Techn. Electron. 53, 833 (2008).
V. A. Syrovoi, J. Commun. Techn. Electron. 52, 218 (2007).
A. J. MacConnell Application of Tensor Analysis (Dower, New York, 1957; Fizmatgiz, Moscow, 1963).
V. A. Syrovoi, J. Commun. Techn. Electron. 53, 467 (2008).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Nauka, Moscow, 1971; Academic, New York, 1980).
N. N. Lebedev, Special Functions and Their Applications (Fizmatgiz, Moscow, 1963) [in Russian].
Additional information
Original Russian Text © T.M. Sapronova, V.A. Syrovoi, 2012, published in Radiotekhnika i Elektronika, 2012, Vol. 57, No. 8, pp. 893–909.
Rights and permissions
About this article
Cite this article
Sapronova, T.M., Syrovoi, V.A. A Paraxial approximation of the problem of formation of nonparaxial conical and toroidal electron beams of an arbitrary cross section. J. Commun. Technol. Electron. 57, 818–833 (2012). https://doi.org/10.1134/S1064226912070108
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064226912070108