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In this paper the mathematical modeling of the electrostatic octupole lens is presented. The octupole lens consist of eight electrodes of the same shape. Each of these electrodes is a part of the circular cylinder of an infinite length. To solve the boundary-value problem for the Laplace equation the variable separation method is used in plane polar coordinates.
In this paper the mathematical modeling of the diode field emission system on the basis of field emitter as a semi-ellipsoid on a flat-surface substrate is considered. The anode is a semi-ellipsoidal surface. The internal area of the system is contained with two layers of different dielectrics. The boundaryvalue problem for the Laplace’s equation in the prolate spheroidal coordinates is solved to...
The rotationally symmetric diode system with a field cathode is under investigation. The shape of the field cathode is sphere-on-cone. The anode is a part of a sphere. In this paper two cases are considered, when the interior of system’s domain is filled with two and three different dielectrics. To calculate the electrostatic potential distribution the method of separation of variables is used. The...
This paper is devoted to the mathematical modeling of the field emission diode system. The diode system is consists of the infinitely thin field emitter as a cathode and a plane anode. The emitter substrate is a plane. The interior of system domain is filled with two different dielectrics. The electrostatic potential distribution is found by the method of separation of variables for the Laplace’s...
This article is devoted to the field emitter of the arbitrary shape mathematical modeling. The axially symmetrical diode system with a field cathode on a plane substrate and a plane anode is under investigation. The effect of the field emitter is simulated using the charged circular lines to solve the boundaryvalue problem so that the zero electrostatic equipotential coincided with the cathode surface...
In this work the axially symmetrical diode system based on a sharp-edged field cathode on a plane substrate is under investigation. Anode is a plane. All interior area of the system is filled with two dielectrics. To solve the boundary-value problem the variable separation method is used and an effect of the field cathode is simulated using the charged circular lines. The electrostatic potential distribution...
Generation and control system for the electron beam modeling and optimization is presented in this paper. The system is considered as the field emission gun. A mathematical model is presented to describe the axially-symmetrical electron gun with a thin emitter on a flat substrate as a field emission cathode and a system of circular apertures as the focusing electrodes. The effect of space charge is...
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