The optimization of geometric boundaries and placement of conductors to achieve specific design goals is the principle activity in computational electromagnetics. However the…
Abstract
The optimization of geometric boundaries and placement of conductors to achieve specific design goals is the principle activity in computational electromagnetics. However the heuristic determination of design variables soon leads to total confusion as the user attempts to wrestle with multiple choices. Even if there are just two states for n parameters there will be, 2n trials. The range of problems posed is vast. One such is the determination of magnet geometries needed to produce an unpolluted uniform field in Magnet Resonance Imaging (MRI) systems, and another application concerns the design of pole shapes in particle accelerators where the higher harmonic distortions must be minimized in dipoles and multipole magnets.
Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…
Abstract
Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.
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C.W. Trowbridge, C.R.I. Emson and H.R.McK. Hyder
The purpose of this paper is to investigate the use of the finite element (FE) method in calculating accurate field gradients to achieve good estimates of aberration coefficients…
Abstract
Purpose
The purpose of this paper is to investigate the use of the finite element (FE) method in calculating accurate field gradients to achieve good estimates of aberration coefficients in accelerator tubes.
Design/methodology/approach
Gradient fields up to third order are calculated using FE calculations with higher order basis functions. A commercial code with the ability to use high order basis functions was embedded within the MathCad system which provides a convenient interface for evaluating the aberration coefficients. Analytic and realistic models are used to test the methodology.
Findings
It is shown that the ability to use higher order FEs achieves sufficient accuracy and smoothness to allow the third order aberration coefficients to be determined with confidence.
Originality/value
The results demonstrate the importance of using higher order basis FEs in determining optical properties of accelerator tubes and other particle optical devices.
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P. Alotto and I. Perugia
An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation…
Abstract
An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation minimises the residual of the constitutive equation, and exactly imposes Maxwell’s equations with Lagrange multipliers. Finite elements satisfying the physical continuity properties for both the magnetic and the magnetic induction fields are used in the numerical approximation. The possibility of decoupling the formulation in two separate sets of equations is discussed. A preconditioned iterative method to solve the final algebraic linear system is presented. Finally, a very natural refinement indicator is defined to guide an adaptive mesh refinement procedure.
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J. Oakley, C.P. Riley, S. Taylor and C.W. Trowbridge
One of the difficulties in electromagnetic modelling has been the lack of standard CAD data to enable direct import of data into analysis software. Many solid modelling standards…
Abstract
One of the difficulties in electromagnetic modelling has been the lack of standard CAD data to enable direct import of data into analysis software. Many solid modelling standards have been proposed over the years, but due to the many separate interests involved and differing geometrical requirements, a definitive standard has been elusive. Recently the ACIS based SAT format has gained favour and can be produced by many proprietary CAD drawing packages. This paper exemplifies a modern electromagnetic analysis tool that is able to directly import SAT format data.
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C.F. Bryant, C.R.I. Emson, P. Fernandes and C.W. Trowbridge
Vector potential formulations of Maxwell’s equations need to be gauged, otherwise nodally based finite element approximations lead to an ill conditioned linear system. In this…
Abstract
Vector potential formulations of Maxwell’s equations need to be gauged, otherwise nodally based finite element approximations lead to an ill conditioned linear system. In this paper alternative Lorentz gauge formulations will be analysed. Particular attention will be paid to the conditions to be applied at material interfaces, bearing in mind ease of implementation in a finite element code and efficiency of solution. The methods discussed are designed to cope with the most challenging physical situations, namely, multiply connected abutting conductors made of different materials.
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Benchmark problem 5 of the TEAM workshops consists of four aluminium blocks placed in the space between the jaws of an electromagnet. Three dimensional eddy currents are induced…
Abstract
Benchmark problem 5 of the TEAM workshops consists of four aluminium blocks placed in the space between the jaws of an electromagnet. Three dimensional eddy currents are induced by 50 Hz time‐varying flux. Eleven sets of results from nine groups of contributors are compared with experimental measurements. The results from most of the computer codes tend to converge to common limits. These limits are in some places slightly different from some of the measured results. The reason for this discrepancy is thought to be due to the idealised boundary conditions, ignoring any losses in laminated iron, which are assumed in all the computer models.
Although edge elements satisfactorily solve the eddy current problem, formulations allowing the use of standard, node‐based elements, are still looked for. But “well‐posed”…
Abstract
Although edge elements satisfactorily solve the eddy current problem, formulations allowing the use of standard, node‐based elements, are still looked for. But “well‐posed” formulations have been elusive up to now. We propose one, based on a particular gauge, div(σ α)=−σ 2μ v, close to the “Lorenz gauge” of several recent publications, but not identical if one does not assume a piecewise uniform conductivity.
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TO many of us it is a matter for regret that we are not able to keep ourselves so closely in touch with library affairs in other parts of the world as we would wish. With American…
Abstract
TO many of us it is a matter for regret that we are not able to keep ourselves so closely in touch with library affairs in other parts of the world as we would wish. With American happenings we are, of course, fairly well acquainted, but Colonial effort has not received the attention which is its due. In many places in the Empire methods are, in certain ways, in advance of ours—in more than one country the legislation has been more enlightened than it was in England until quite recently—and everywhere the experience of keen progressive librarians facing their own particular problems must prove of interest and value to those in the home country. Therefore we believe that by devoting this issue to a discussion of some phases of Colonial librarianship we are but answering the large demand for such information.
C.W. Trowbridge and H.R.McK. Hyder
To investigate the effectiveness of a simple analytic model for the calculation of electrostatic fields and optical properties of particle beams in accelerator tubes.
Abstract
Purpose
To investigate the effectiveness of a simple analytic model for the calculation of electrostatic fields and optical properties of particle beams in accelerator tubes.
Design/methodology/approach
The analytic model is derived by superimposing the solution obtained from two co‐axial circular apertures. Potentials and fields derived from the model are compared to solutions based on finite element analysis together with first, third, and fifth order optical parameters and aberration. More realistic models are also compared.
Findings
It is shown that the model is capable of capturing many of the ion optical effects produced in small electrostatic accelerator tubes. Even for more realistic tube models the basic optical parameters, first and third order, are sufficiently accurate to allow a preliminary design to be achieved.
Originality/value
The work demonstrates that the first stages of the optical design of accelerator tubes can be rapidly achieved by analytic means which then provide good starting parameters for a fuller optimisation carried out by advanced numerical methods. The results also serve as a benchmark for numerical methods.