Numerical Calculation of the Potential Distribution in Ion Slit Lens Systems III

1960 ◽  
Vol 15 (3) ◽  
pp. 253-259 ◽  
Author(s):  
A. J. H. Boerboom
Keyword(s):  
Numerical Calculation ◽  
Field Strength ◽  
Arbitrary Number ◽  
Potential Distribution ◽  
Computing Methods ◽  
Mutual Distance ◽  
Christoffel Transformation

In previous papers 1, 2 the potential distribution was calculated in ion slit lens systems, consisting of three slits in three parallel electrodes and satisfying certain conditions concerning their shape.In the present paper the computing methods are generalized to slit systems of an arbitrary number of electrodes, with as the only restriction, that slits broader than the distances to neighbouring slits are separated by slits, narrower than the respective distance, and that a pair of electrodes with a mutual distance smaller than their slit widths are separated from the neighbouring slits by distances greater than the respective slit widths.For slit systems, satisfying this condition the parameters are computed, necessary to perform the SCHWARZ-CHRISTOFFEL transformation. Formulae are given to compute the potential distribution and field strength. In a typical example the potential distribution and field strength are computed in the region around two parallel electrodes with broad slits compared with the distance between the electrodes.

Numerical Calculation of the Potential Distribution in Ion Slit Lens Systems I

1959 ◽  
Vol 14 (9) ◽  
pp. 809-816 ◽  
Author(s):  
A. J. H. Boerboom
Keyword(s):  
Numerical Calculation ◽  
Iteration Method ◽  
Arbitrary Number ◽  
Conformal Transformation ◽  
Potential Distribution ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Lens System ◽  
Slit System ◽  
Christoffel Transformation

The potential distribution is calculated in an ion lens, consisting of three parallel collinear slits in three parallel electrodes. The slit system is supposed to be infinite in the direction of the slits, so the problem becomes two dimensional in a plane perpendicular on the direction of the slits. In this plane the potential distribution is calculated by the method of conformal transformation.The SCHWARZ—CHRISTOFFEL transformation is used to map conformally the region between the projections of the electrodes of the slit system. It proves to be very simple to perform this transformation. Formulae are given for the case of an ion lens consisting of slits in three parallel plates. A series expansion and an iteration method are developed to find the necessary parameters. Both methods prove to be satisfactory if the slit widths are smaller than the distance to the neighbouring electrodes. Symmetrical lenses, not satisfying this condition will be treated in a second paper. In a third paper slit system will be treated with an arbitrary number of electrodes.In the transformed region LAPLACE'S equation is solved, having as boundary conditions the potentials on the electrodes. In this way the exact potential distribution in the lens system is found. In a typical example the potential distributions are calculated along the axis for several potentials on the electrodes, together with the corresponding fields.

Numerical Calculation of the Potential Distribution in Ion Slit Lens Systems II

1960 ◽  
Vol 15 (3) ◽  
pp. 244-252 ◽  
Author(s):  
A. J. H. Boerboom
Keyword(s):  
Numerical Calculation ◽  
Potential Distribution ◽  
Central Electrode ◽  
Iteration Methods ◽  
Christoffel Transformation

The potential distribution is computed in certain ion slit lens systems, consisting of three parallel slits in three parallel electrodes. In a previous paper 1 the case was treated where the slit widths were smaller than the distances to the neighbouring electrodes. In the present paper this requirement has been dropped; for the sake of simplicity, however, the computations are confined to the case, where the central electrode represents a plane of symmetry.Various approximation and iteration methods are given to find the necessary parameters to perform the SCHWARZ-CHRISTOFFEL transformation. Several typical examples are given.

Analysis of Influence on Seawater Electric Field Measurement by Sphericity Sensor

2014 ◽  
Vol 716-717 ◽  
pp. 876-879
Author(s):  
Xiao Bei Wang ◽  
Li Xia ◽  
Xiang Jun Wang ◽  
Dou Ji
Keyword(s):  
Boundary Condition ◽  
Numerical Calculation ◽  
Electric Field ◽  
Calculation Method ◽  
Field Measurement ◽  
Potential Distribution ◽  
Field Model ◽  
Electric Field Measurement ◽  
Numerical Calculation Method

The underwater electric field model of spherical sensor is established. According to the condition that boundary condition is some certain eigenvalue, affects on underwater electric field by spherical sensor is derived. At last, the underwater potential distribution around spherical sensor is calculated through numerical calculation method.

scholarly journals Effects of a Crossarm Brace Application on a 275 kV Fiberglass-Reinforced Polymer Crossarm Subjected to a Lightning Impulse

Energies ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 6248
Author(s):  
Muhammad Syahmi Abd Rahman ◽  
Mohd Zainal Abidin Ab Kadir ◽  
Muhamad Safwan Ab-Rahman ◽  
Miszaina Osman ◽  
Shamsul Fahmi Mohd Nor ◽  
...  
Keyword(s):  
Field Strength ◽  
Simulation Study ◽  
Transmission Lines ◽  
Potential Distribution ◽  
Mechanical Performance ◽  
Swing Angle ◽  
Frp Composite ◽  
Reinforced Polymer ◽  
Transmission Towers ◽  
Lightning Impulse

The crossarm is an important component of transmission towers, providing insulation for transmission lines at different voltage ratings. Recently, composite crossarms were widely used as a composite tower component and were found to be the most favorable choice for replacing old wooden crossarms. Owing to the satisfactory pilot operation and multiple sets of testing, fiberglass-reinforced polymer (FRP) composite crossarms have been used in Malaysia in both 132 and 275 kV transmission lines since the late 1990′s. Since then, some modifications have been proposed to improve the mechanical performance of the crossarm, in order to ensure the reliability of its performance. In this investigation, the effect of a proposed improvement, achieved by installing a brace for the crossarm, was investigated numerically. A simulation study was conducted, with a consideration of the lightning impulse voltage (LIV) and swing angle exhibited by the crossarm. The potential and electric field (E-Field) distribution were analyzed and are presented in this paper. It was found that the potential distribution and E-Field strength for the crossarm and the surrounding air were greatly affected by the installation of the brace.

The Potential Distribution in a Toroidal Condenser

1960 ◽  
Vol 15 (4) ◽  
pp. 347-350 ◽  
Author(s):  
A. J. H. Boerboom
Keyword(s):  
Series Expansion ◽  
Electrostatic Potential ◽  
Potential Distribution ◽  
Median Plane ◽  
Mutual Distance

The electrostatic potential is calculated in a toroidal condenser consisting of two rotational symmetric electrodes having the median plane as a plane of symmetry. The result is expressed as a series expansion in the coordinates around the main circle and in the mutual distance of the electrodes in the median plane.

Potential flow of segmental jet deflectors

1971 ◽  
Vol 46 (3) ◽  
pp. 465-475 ◽  
Author(s):  
H. Y. Chang ◽  
J. F. Conly
Keyword(s):  
Potential Flow ◽  
Arbitrary Number ◽  
Special Cases ◽  
Christoffel Transformation

A solution is developed for the deflexion of an inviscid, incompressible, twodimensional jet by a series of segments of arbitrary number, lengths, and angles. The Schwarz–Christoffel transformation and free-streamline theory are used. Results are calculated for a number of configurations, using an IBM 360 computer. Excellent comparison is found with several previous calculations for special cases.

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