Two simple models for analytical calculation of eddy currents in thin conducting plates

1997 ◽  
Vol 33 (3) ◽  
pp. 2245-2257 ◽  
Author(s):  
N.J. Siakavellas
Keyword(s):  
Eddy Currents ◽  
Analytical Calculation ◽  
Thin Conducting ◽  
Simple Models

DIFFUSION OF PULSED EDDY CURRENTS IN THIN CONDUCTING PLATES

2008 ◽  
Author(s):  
T. W. Krause ◽  
C. Mandache ◽  
J. H. V. Lefebvre ◽  
Donald O. Thompson ◽  
Dale E. Chimenti
Keyword(s):  
Eddy Currents ◽  
Thin Conducting ◽  
Pulsed Eddy Currents

Use of variational methods to the eddy currents calculation in thin conducting plates

1978 ◽  
Vol 14 (5) ◽  
pp. 383-385 ◽  
Author(s):  
R. Sikora ◽  
J. Purczynski ◽  
W. Lipinski ◽  
M. Gramz
Keyword(s):  
Variational Methods ◽  
Eddy Currents ◽  
Thin Conducting

Fast analytical calculation method for eddy current induced by gradient fields in an MRI system

2017 ◽  
Vol 36 (6) ◽  
pp. 1690-1705
Author(s):  
Zheng Xu ◽  
Jiamin Wu ◽  
Lu Li ◽  
Yucheng He ◽  
Wei He ◽  
...  
Keyword(s):  
Eddy Current ◽  
Analytical Method ◽  
Eddy Currents ◽  
Analytical Calculation ◽  
Harmonic Component ◽  
Gradient Coil ◽  
Gradient Coils ◽  
Content Type ◽  
Gradient Fields ◽  
Simulation Results

Purpose Eddy currents are inevitable in magnetic resonance imaging (MRI) systems. These currents are mainly induced by gradient fields. This study aims to propose a fast analytical method to calculate eddy currents induced by frequently switching gradient fields in a traditional C-shape MRI system. Design/methodology/approach Fourier decomposition and magnetic vector potentials were used to calculate the eddy currents. Calculations with the proposed analytical method revealed the spatial distribution and temporal evolution of eddy currents. Findings Calculation and Maxwell simulation results were consistent. The agreement between calculation and simulation results indicates that increasingly sophisticated structures could be developed. The calculated results could guide the design of improved gradient coils. Originality/value Eddy currents induced by gradient current are decomposed into currents induced by each time-harmonic component, and then adding them together to obtain complete contribution of the eddy current. The analytical method was used to characterize the properties of symmetric and asymmetric eddy currents induced by gradient coils in MRI systems. The analytical method can be used to improve the gradient shield during the design of the gradient coil in the MRI system.

scholarly journals Induction Heating of the Filling Conveyor Molds

2001 ◽  
Vol 14 (5) ◽  
pp. 583-589
Author(s):  
Viktor N. Timofeev ◽  
Keyword(s):  
Boundary Conditions ◽  
Induction Heating ◽  
Thermal Energy ◽  
High Performance ◽  
Eddy Currents ◽  
Liquid Aluminum ◽  
Analytical Calculation ◽  
Complex Form ◽  
Approximate Boundary Condition ◽  
Approximate Boundary Conditions

In the smelting and foundry production of aluminum ingots, filling conveyors are widely used. Aluminum ingots of a certain shape and weight are obtained by crystallizing liquid aluminum (melt) in the molds of the filling conveyor. As the mills move along the conveyor, the melt gradually hardens in them. In high-performance conveyors, the mills move through the water to increase the cooling rate of the melt. Therefore, after the mill is freed from the hardened ingot, water enters it. In order to avoid temperature shock and possible release of liquid metal, the molds must be dried and heated before pouring. At present, gas burners are used in aluminum plants for this purpose [1]. The purpose of this work is to study the possibility of induction heating of the filling conveyor molds. The calculation is carried out using Fourier series in complex form and approximate boundary conditions on the surface of ferromagnetic molds. The approximate boundary conditions avoid the need to calculate the electromagnetic field in a nonlinear ferromagnetic medium. In the heated object, the energy of the induced alternating electric field is irreversibly converted into thermal energy. This dissipation of thermal energy, which leads to the heating of the object, is determined by the presence of conduction currents (eddy currents). Induction heating is widely used in metallurgy for melting, heating and mixing of electrically conductive bodies. The method is based on the absorption of electromagnetic energy by bodies of an alternating magnetic field created by an inductor. The heated product is located in the immediate vicinity of the inductor. There are many publications on analytical and numerical, analysis of physical processes in the inductor-heated billet system. In this paper, an analytical calculation of electromagnetic processes in the system of inductor – ferromagnetic molds of the filling conveyor is carried out. The analytical solution is obtained by using the approximate boundary condition of L. R. Neumann on the surface of nonlinear ferromagnetic molds

scholarly journals Calculation model for the induced voltage in rectangular coils above conductive plates

2017 ◽  
Vol 30 (1) ◽  
pp. 27-38
Author(s):  
Siquan Zhang ◽  
Nathan Ida
Keyword(s):  
Eddy Currents ◽  
Plate Thickness ◽  
Analytical Calculation ◽  
Calculation Model ◽  
Induced Voltage ◽  
Voltage Variation ◽  
Conducting Materials ◽  
Exciting Frequency ◽  
Excitation Coil ◽  
Calculation Results

Electromagnetic NDT methods and in particular eddy currents play an important role in nondestructive testing of conducting materials. In testing conductive structures, rectangular coils are often more useful than circular coils. A particular configuration consists of two rectangular coils located above the conductive plates, one placed parallel to the plates serving as an excitation coil and the other perpendicular to the plates serving as a sensing coil. In this work we derive analytical expressions for the induced voltage variations in the pick-up coil. Then the influences of the plate thickness, the exciting frequency and the moving speed of the conductor on the induced voltage variation are analyzed. The analytical calculation results are verified using the finite element method.

Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 422-423
Author(s):  
John C. Russ
Keyword(s):  
Monte Carlo ◽  
Energy Loss ◽  
Secondary Electron ◽  
Secondary Electron Emission ◽  
Analytical Calculation ◽  
Mean Free Path ◽  
Single Scattering ◽  
High Energy ◽  
Secondary Electron Yield ◽  
Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

Big data and simple models used to track the spread of COVID-19 in cities

Nature ◽  
2020 ◽  
Vol 589 (7840) ◽  
pp. 26-28
Author(s):  
Kevin C. Ma ◽  
Marc Lipsitch
Keyword(s):  
Big Data ◽  
Simple Models
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