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An improvement in the calculation of the magnetic field for an arbitrary geometry coil with rectangular cross section. (English) Zbl 1076.78508

Summary: Hong Lei, Lian-Ze Wang and Zi-Niu Wu presented new simple and convenient solutions of the magnetic field for an arbitrary geometry coil with rectangular cross section. They treated two types of basic forms: the trapezoidal prism segment and curved prism segment. The curved prism segment has been divided into a series of small trapezoidal prism segments with the same cross section and its magnetic field is a vector sum of the individual fields created by each small trapezoidal prism conductor. For one trapezoidal prism conductor the magnetic field is obtained by 1-D integrals using Romberg numerical integration. In this paper, we give a completely analytical solution of these 1-D integrals that considerably saves the computational time especially in the computation of the magnetic field nearby the conductor surface, at the conductor surface and inside the conductor. From obtained analytical expressions the treatment of singularities can be easily done. Also, we tested four types of numerical integration (Gaussian, Romberg, Simpson and Lobatto) to find the most convenient singularity treatment of 1-D integrals. These obtained results are compared with those obtained analytically so that one can understand the advantage of the proposed approach. The paper points out on the accuracy and the computational cost.

MSC:

78A55 Technical applications of optics and electromagnetic theory
78M25 Numerical methods in optics (MSC2010)
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[1] Computational Magnetics. Chapman & Hall: New York, 1995.
[2] Finite Method Analysis of Electrical Machines. Kluwer Academic Publishers: Boston, 1995.
[3] , . Methode Numerique en Electromagnetisme: Geometrie Differentielle. Elements finis, Modeles d’hysteresis. Eyrolles: Paris, 1991.
[4] Conway, IEEE Transactionss on Magnetics 37 pp 2977– (2001)
[5] Lei, IEEE Transactions on Magnetics 38 pp 3589– (2002)
[6] . Table of Integrals, Series and Products. Academic Press Inc.: New York and London, 1965.
[7] . Handbook of Mathematical Functions, Series 55. National Bureau of Standards Applied Mathematics: Washington DC, December 1972; 595.
[8] Numerically evaluates an integral using a Gauss quadrature. Matlab Central, 1999.
[9] . Adaptive quadrature revisited. Matlab 6.0, 1998.
[10] , . Numerical Analysis (2nd edn). PWS Publishers: Boston, Massachusetts, 1978.
[11] Urankar, IEEE Transactions on Magnetics 56 pp 1171– (1990)
[12] Babic, IEEE Transactions on Magnetics 24 pp 423– (1998)
[13] Babic, IEEE Transactions on Magnetics 24 pp 3162– (1988)
[14] Babic, Journal of Applied Physics 67 pp 5827– (1990) · Zbl 0825.73383
[15] Babic, IEEE Transactions on Magnetics 33 pp 4134– (1997)
[16] Babic, IEEE Transactions on Magnetics 35 pp 491– (2002)
[17] Azzerboni, IEEE Transactions on Magnetics 27 pp 750– (1991)
[18] Azerboni, IEEE Transactions on Magnetics 34 pp 2601– (1998)
[19] Integration methods for the calculation of the magnetostatic field due to coils. CHALMERS, NO 2001-7 ISSN 1404-4382, Goteborg, Sweden, April 2001.
[20] Diserens, IEEE Transactions on Magnetics 19 pp 2304– (1983)
[21] Kajikawa, Cryogenic Engineering 30 pp 324– (1995)
[22] Ciric, Journal of Applied Physics 61 pp 2709– (1987)
[23] Ciric, IEEE Transactions on Magnetics 27 pp 669– (1991)
[24] Forbes, IEEE Transactions on Magnetics 33 pp 4405– (1997)
[25] Snape-Jenkinson, IEEE Transactions on Magnetics 33 pp 4159– (1999)
[26] Crozier, Journal of Magnetic Resonance 127 pp 223– (1997)
[27] Suh, Journal of Engineering Mathematics 37 pp 375– (2000)
[28] Urankar, IEEE Transactions on Magnetics 16 pp 1283– (1980)
[29] Urankar, IEEE Transactions on Magnetics 18 pp 911– (1982)
[30] Urankar, IEEE Transactions on Magnetics 18 pp 1860– (1982)
[31] Urankar, IEEE Transactions on Magnetics 20 pp 2145– (1984)
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