МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПОЛЕВОЙ ЭМИССИОННОЙ СИСТЕМЫ С ПРОИЗВОЛЬНЫМ ЧИСЛОМ ЭМИТТЕРОВ ЛЕЗВИЙНОЙ ФОРМЫ

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МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПОЛЕВОЙ ЭМИССИОННОЙ СИСТЕМЫ С ПРОИЗВОЛЬНЫМ ЧИСЛОМ ЭМИТТЕРОВ ЛЕЗВИЙНОЙ ФОРМЫ. / Виноградова, Екатерина Михайловна ; Егоров, Николай Васильевич ; Доронин, Григорий Геннадьевич ; Фан, Чжоу.

в: Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления, Том 22, № 2, 04.08.2026, стр. 196-204.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{be2797ff03e24a46b0a2f7a07c7d0f18,

title = "МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПОЛЕВОЙ ЭМИССИОННОЙ СИСТЕМЫ С ПРОИЗВОЛЬНЫМ ЧИСЛОМ ЭМИТТЕРОВ ЛЕЗВИЙНОЙ ФОРМЫ",

abstract = "This paper presents the results of mathematical modeling of a two-dimensional field emission system based on an arbitrary number of blade-shaped field emitters. The emitters are located on a flat substrate. The anode is a plane parallel to the substrate plane. Since the surface of each emitter can be considered a corresponding equipotential surface, the influence of the emitters is replaced by the influence of charged filaments to calculate the electrostatic potential distribution throughout the entire emission system. The Poisson{\textquoteright}s equation solution with the boundary conditions of the first kind is found as a series of eigenfunctions, with the coefficients of the series explicitly defined. All geometric dimensions of the system and the potentials at the electrodes are the parameters of the problem.",

keywords = "Poisson equation, boundary value problem, electrostatic potential, field emission, field emitter, mathematical modeling, micro-and nanoelectronics",

author = "Виноградова, {Екатерина Михайловна} and Егоров, {Николай Васильевич} and Доронин, {Григорий Геннадьевич} and Чжоу Фан",

year = "2026",

month = aug,

day = "4",

doi = "10.21638/spbu10.2026.202",

language = "русский",

volume = "22",

pages = "196--204",

journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1811-9905",

publisher = "Издательство Санкт-Петербургского университета",

number = "2",

}

RIS

TY - JOUR

T1 - МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПОЛЕВОЙ ЭМИССИОННОЙ СИСТЕМЫ С ПРОИЗВОЛЬНЫМ ЧИСЛОМ ЭМИТТЕРОВ ЛЕЗВИЙНОЙ ФОРМЫ

AU - Виноградова, Екатерина Михайловна

AU - Егоров, Николай Васильевич

AU - Доронин, Григорий Геннадьевич

AU - Фан, Чжоу

PY - 2026/8/4

Y1 - 2026/8/4

N2 - This paper presents the results of mathematical modeling of a two-dimensional field emission system based on an arbitrary number of blade-shaped field emitters. The emitters are located on a flat substrate. The anode is a plane parallel to the substrate plane. Since the surface of each emitter can be considered a corresponding equipotential surface, the influence of the emitters is replaced by the influence of charged filaments to calculate the electrostatic potential distribution throughout the entire emission system. The Poisson’s equation solution with the boundary conditions of the first kind is found as a series of eigenfunctions, with the coefficients of the series explicitly defined. All geometric dimensions of the system and the potentials at the electrodes are the parameters of the problem.

AB - This paper presents the results of mathematical modeling of a two-dimensional field emission system based on an arbitrary number of blade-shaped field emitters. The emitters are located on a flat substrate. The anode is a plane parallel to the substrate plane. Since the surface of each emitter can be considered a corresponding equipotential surface, the influence of the emitters is replaced by the influence of charged filaments to calculate the electrostatic potential distribution throughout the entire emission system. The Poisson’s equation solution with the boundary conditions of the first kind is found as a series of eigenfunctions, with the coefficients of the series explicitly defined. All geometric dimensions of the system and the potentials at the electrodes are the parameters of the problem.

KW - Poisson equation

KW - boundary value problem

KW - electrostatic potential

KW - field emission

KW - field emitter

KW - mathematical modeling

KW - micro-and nanoelectronics

UR - https://www.mendeley.com/catalogue/f351f28b-8056-3aee-856b-56b1e265efe0/

U2 - 10.21638/spbu10.2026.202

DO - 10.21638/spbu10.2026.202

M3 - статья

VL - 22

SP - 196

EP - 204

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: 160917169