Toshimi Ohye

Improved 3D boundary charge method for high-accuracy electric field calculation

In this paper we propose an improved 3-D boundary charge method for high accuracy calculation of the electric field distribution, where differentiation of the coefficient matrix element (equals the potential coefficient) with respect to each coordinate component is needed. The differentiated potential coefficient, which is called the field coefficient, is expressed as a double integral. We have found that the first integral of the field coefficient can be done analytically in much the same ways as that of the potential coefficient, thereby greatly improving the computation time of the electric field distribution without any loss of accuracy. As a practical application of the method to field analysis, we have treated the misaligned diode system of a field emission gun.

Improved 3D boundary charge method for high-accuracy calculation of potential and electric field in composite dielectric system

In this paper we propose an improved three-dimensional (3D) boundary charge method (BCM) for a composite dielectric system in which insulators, i.e., dielectric materials exist together with conducting electrodes. The method is based on the idea that the composite dielectric system can equivalently be replaced with a conductor system in vacuum by introducing an apparent surface charge density (=true surface charge density + polarization surface charge density), on every conductor-to-dielectric interface and every dielectric-to-dielectric interface. In calculating the apparent surface charge density, whole interfaces are divided into n small surface elements, and the apparent surface (or boundary) charge density on each small surface element is obtained by solving a set of n-dimensional simultaneous linear equations, where the coefficient matrix elements is expressed as a double integral and the diagonal matrix element becomes a singular or nearly singular integral. A high-accuracy and high-speed calculation of the double integral is the key point of the method, and we have succeeded in great improvement of both numerical accuracy and computation time.

Computer simulation of electric field analysis for vertically aligned carbon nanotubes: I. Simulation method and computing model

This paper describes a computer simulation method and a computing model for electric field analysis of a vertically- aligned carbon nanotube (VACNT) system by means of an improved three-dimensional boundary charge method (3-D BCM). A real VACNT system where the number of CNTs is as large as ten millions per 1 mm2 is modeled by 9x9 CNTs standing vertically on the cathode substrate. The whole conducting surface consisting of CNTs, the cathode substrate and the anode plate are divided into about 4000 small surface elements, which are found to be enough for reasonable accuracy in electric field calculation. It has also been confirmed that the electric field strength at the CNT apex in the real VACNT system is well represented by the electric field strength at the apex of the central CNT of the 9x9 CNT computing model.

Computer simulation of electric field analysis for vertically aligned carbon nanotubes: II. Electric field on the nanotube apex

Vertically-aligned carbon nanotubes (VA-CNT) are extremely attractive for use as field emission sources. The field emission characteristics of VA-CNTs are determined by the electric field strength on the CNT apexes, and therefore depend strongly on the geometrical parameters such as radius of curvature of the CNT apex, an average density of CNTs and non-uniformity of CNT lengths. This paper describes a computer simulation of electric field analysis for VA-CNTs by means of an improved 3D boundary charge method, where the VA-CNTs are modeled by 9X9 CNTs standing vertically on the cathode substrate. We have calculated the electric field strength on the CNT apex for various geometrical parameters of VA-CNTs. It has been found that the electric field on the CNT apex is inversely proportional to the radius of curvature of the CNT apex, and significantly decrease when the CNT density exceeds 100/cm2.

Improved 3D boundary charge method

In calculating potential field for a system consisting of several conductors by means of the boundary (or surface) charge method (BCM or SCM), every conductor surface is divided into n small surface elements, and the surface (or boundary) charge density on each surface element is obtained by solving a set of n-dimensional simultaneous linear equations, where the coefficient matrix element is expressed as a double integral. In the 3D BCM, the coefficient matrix element is usually obtained by direct double numerical integration, which is a serious obstacle to a practical use of the method because of extremely long computation time. We have been developing an improved 3D BCM, where any given conductor geometry can faithfully be modeled by a suitable combination of parts and/or all of several basic surfaces such as plane surface, cylindrical surface, conical surface, discoidal surface, spherical surface and torus surface. We have found that the first integration in the double integral of the coefficient matrix element can be done analytically for the above-mentioned basic surfaces, thereby greatly improving the computation time without any loss of accuracy.

Characterization of curved cathode guns by the generalized trajectory method: upgrade of G-optk programme for applications to non-planar objects.

A mathematical scheme has been proposed to extend the applicability of the generalized trajectory method to deal with curved cathodes such as cold field emitters and thermionic point cathodes. A connecting space is introduced between the cathode surface and the first reference plane, and the actual ray condition on the cathode is transformed into the trajectory condition at the reference plane: the generalized trajectory calculation is commenced from the reference plane. The electron acceleration due to the cathode surface field, which results in the increase of the transverse momentum p(x) at the reference plane, has been found to significantly influence the estimate of the spherical aberration coefficient. The new mathematical formulation has been incorporated into the upgraded G-optk programme and enabled it to carry out precise characterization of curved cathode guns.

Optimization of the operating condition of the accelerating tube for the high voltage electron microscope equipped with the field emission gun

Abstract Numerical calculations have been conducted on the electron optical characteristics of the accelerating tube (AT) for the high voltage electron microscope (HVEM) equipped with the field emission gun (FEG). The emitted electrons are firstly accelerated to V0 by the FEG and finally to Va by the AT which consists of 34 stages of accelerating electrodes with an inner diameter of 33 mm and has an overall length of 1423 mm. The AT is treated as a thick electrostatic accelerating lens. Several electron optical problems arising from a combination of the AT with the FEG are studied. In order to reduce an unfavorable aberration effect of the AT-lens, the beam crossover must be brought to a position near the entrance plane of the AT. This can be done by a transfer lens which is placed between the FEG and the AT. The introduction of a partial retarding field in the AT is also very effective for a flexible operation of the FEG system without serious aberration effects of the AT-lens.

Computer simulation of electron optical characteristics of accelerating tube for high-voltage electron microscope

Numerical calculations were conducted on the electron optical characteristics of the accelerating tube (AT) for the high voltage electron microscope. The emitted electrons are firstly accelerated to V0 by the TE gun or the FE gun and finally to Va by the AT which consists of 34 electrodes with the inner diameter of 33 mm and has the overall length of 1423 mm. The AT is treated as a thick electrostatic accelerating lens. Several electron optical problems arising from a combination of the AT with a thermionic emission (TE) gun or a field emission (FE) gun are studied. For the TE gun the aberration effect of the AT lens is found to be safely neglected for any combination of Va and V0. In the case of the FE gun, on the other hand, the aberration effect of the AT lens can not be neglected and deteriorates the brightness of the beam. This situation can be overcome by placing an electron lens between the FE gun and the AT.