TY - JOUR

T1 - Mathematical modeling of triode system on the basis of field emitter with ellipsoid shape

AU - Egorov, N. V.

AU - Vinogradova, E. M.

N1 - Publisher Copyright: © St. Petersburg State University, 2021.

PY - 2021

Y1 - 2021

N2 - In this paper the mathematical modeling of the triode emission axially symmetric system on the basis of field emitter is considered. Emitter is an ellipsoid of revolution, anode is a confocal ellipsoidal surface of revolution. Modulator is a part of the ellipsoidal surface of revolution, confocal with the cathode and anode surfaces. The boundary-value problem for the Laplace's equation in the prolate spheroidal coordinates with the boundary conditions of the first kind is solved. The variable separation method is applied to calculate the axisymmetrical electrostatic potential distribution. The potential distribution is represented as the Legendre functions expansion. The expansion coefficients are the solution of the system of linear equations. All geometrical dimensions of the system are the parameters of the problem.

AB - In this paper the mathematical modeling of the triode emission axially symmetric system on the basis of field emitter is considered. Emitter is an ellipsoid of revolution, anode is a confocal ellipsoidal surface of revolution. Modulator is a part of the ellipsoidal surface of revolution, confocal with the cathode and anode surfaces. The boundary-value problem for the Laplace's equation in the prolate spheroidal coordinates with the boundary conditions of the first kind is solved. The variable separation method is applied to calculate the axisymmetrical electrostatic potential distribution. The potential distribution is represented as the Legendre functions expansion. The expansion coefficients are the solution of the system of linear equations. All geometrical dimensions of the system are the parameters of the problem.

KW - Boundary-value problem

KW - Electrostatic potential

KW - Field emission

KW - Field emitter

KW - Legendre functions

KW - Mathematical modeling

KW - Micro- and nanoelectronics

KW - electrostatic potential

KW - field emission

KW - boundary-value problem

KW - micro- and nanoelectronics

KW - field emitter

KW - mathematical modeling

UR - http://www.scopus.com/inward/record.url?scp=85111963203&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/efc6ec2a-0ccd-3009-b6b7-bfd93a597a3d/

U2 - 10.21638/11701/SPBU10.2021.203

DO - 10.21638/11701/SPBU10.2021.203

M3 - Article

AN - SCOPUS:85111963203

VL - 17

SP - 131

EP - 136

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 -