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Field emission triode system with paraboloidal electrodes mathematical modeling. / Егоров, Николай Васильевич; Виноградова, Екатерина Михайловна; Вараюнь, Марина Ивановна; Антонов, Андрей Юрьевич.

In: ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ, Vol. 21, No. 2, 10.07.2025, p. 188-194.

Research output: Contribution to journal › Article › peer-review

Harvard

Егоров, НВ, Виноградова, ЕМ, Вараюнь, МИ & Антонов, АЮ 2025, 'Field emission triode system with paraboloidal electrodes mathematical modeling', ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ, vol. 21, no. 2, pp. 188-194. https://doi.org/10.21638/spbu10.2025.202

APA

Егоров, Н. В., Виноградова, Е. М., Вараюнь, М. И., & Антонов, А. Ю. (2025). Field emission triode system with paraboloidal electrodes mathematical modeling. ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ, 21(2), 188-194. https://doi.org/10.21638/spbu10.2025.202

Vancouver

Егоров НВ, Виноградова ЕМ, Вараюнь МИ, Антонов АЮ. Field emission triode system with paraboloidal electrodes mathematical modeling. ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ. 2025 Jul 10;21(2):188-194. https://doi.org/10.21638/spbu10.2025.202

Author

Егоров, Николай Васильевич ; Виноградова, Екатерина Михайловна ; Вараюнь, Марина Ивановна ; Антонов, Андрей Юрьевич. / Field emission triode system with paraboloidal electrodes mathematical modeling. In: ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ. 2025 ; Vol. 21, No. 2. pp. 188-194.

BibTeX

@article{03679a8097304ae1964e31f1eb9c120b,
title = "Field emission triode system with paraboloidal electrodes mathematical modeling",
abstract = "In this paper the field emission triode system with the axially symmetric electrodes is considered. The field emitter and anode are the confocal paraboloidal surfaces of revolution, modulator is a part of the confocal paraboloidal surface of revolution. To solve the boundary-value problem for the Laplace{\textquoteright}s equation with the boundary conditions of the first kind the paraboloidal coordinates are used. Dual integral equations method is applied to calculate the axisymmetric electrostatic field. The electrostatic potential distribution over the entire region of the triode field system is found in the form of expansions in Bessel functions. Unknown expansion coefficients determination is reduced to solving the Fredholm equation of the second kind. All geometrical dimensions of the system are the parameters of the problem.",
keywords = "boundary-value problem, electrostatic potential distribution, field emitter, mathematical modeling, microelectronics and nanoelectronics",
author = "Егоров, {Николай Васильевич} and Виноградова, {Екатерина Михайловна} and Вараюнь, {Марина Ивановна} and Антонов, {Андрей Юрьевич}",
year = "2025",
month = jul,
day = "10",
doi = "10.21638/spbu10.2025.202",
language = "English",
volume = "21",
pages = "188--194",
journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1811-9905",
publisher = "Издательство Санкт-Петербургского университета",
number = "2",

}

RIS

TY - JOUR

T1 - Field emission triode system with paraboloidal electrodes mathematical modeling

AU - Егоров, Николай Васильевич

AU - Виноградова, Екатерина Михайловна

AU - Вараюнь, Марина Ивановна

AU - Антонов, Андрей Юрьевич

PY - 2025/7/10

Y1 - 2025/7/10

N2 - In this paper the field emission triode system with the axially symmetric electrodes is considered. The field emitter and anode are the confocal paraboloidal surfaces of revolution, modulator is a part of the confocal paraboloidal surface of revolution. To solve the boundary-value problem for the Laplace’s equation with the boundary conditions of the first kind the paraboloidal coordinates are used. Dual integral equations method is applied to calculate the axisymmetric electrostatic field. The electrostatic potential distribution over the entire region of the triode field system is found in the form of expansions in Bessel functions. Unknown expansion coefficients determination is reduced to solving the Fredholm equation of the second kind. All geometrical dimensions of the system are the parameters of the problem.

AB - In this paper the field emission triode system with the axially symmetric electrodes is considered. The field emitter and anode are the confocal paraboloidal surfaces of revolution, modulator is a part of the confocal paraboloidal surface of revolution. To solve the boundary-value problem for the Laplace’s equation with the boundary conditions of the first kind the paraboloidal coordinates are used. Dual integral equations method is applied to calculate the axisymmetric electrostatic field. The electrostatic potential distribution over the entire region of the triode field system is found in the form of expansions in Bessel functions. Unknown expansion coefficients determination is reduced to solving the Fredholm equation of the second kind. All geometrical dimensions of the system are the parameters of the problem.

KW - boundary-value problem

KW - electrostatic potential distribution

KW - field emitter

KW - mathematical modeling

KW - microelectronics and nanoelectronics

UR - https://www.mendeley.com/catalogue/2ce9d85e-f133-32c9-a7fb-45ab5d8afc79/

U2 - 10.21638/spbu10.2025.202

DO - 10.21638/spbu10.2025.202

M3 - Article

VL - 21

SP - 188

EP - 194

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 2

ER -

ID: 136120407