An improvement in the calculation of the magnetic field for an arbitrary geometry coil with rectangular cross section

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Volumn 18, Issue 6, 2005, Pages 493-504

  Babic, Slobodan I ^a,c   Akyel, Cevdet ^a,b  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^b IEEE   (Canada)

^c International Compumag Society   (Canada)

Author keywords

Arbitrary geometry coils; Biot Savart law; Computational electromagnetics; Gaussian's, Romberg's, Simpson's and Lobatto's numerical integrations; Rectangular cross section; Singularity treatment; Trapezoidal prism conductors

Indexed keywords

ARBITRARY GEOMETRY COILS; BIOT-SAVART LAW; COMPUTATIONAL ELECTROMAGNETICS; GEOMETRY COIL; RECTANGULAR CROSS SECTIONS; SINGULARITY TREATMENT; TRAPEZOIDAL PRISM CONDUCTORS;

INTEGRAL EQUATIONS; PRISMS; VECTORS;

MAGNETIC FIELD EFFECTS;

EID: 27744571099     PISSN: 08943370     EISSN: None     Source Type: Journal    
DOI: 10.1002/jnm.594     Document Type: Article

References (31)

1. Sykulski JK. Computational Magnetics. Chapman & Hall: New York, 1995.
2. Salon S. Finite Method Analysis of Electrical Machines. Kluwer Academic Publishers: Boston, 1995.
3. Bossavit A, Emson C, Mayergoyz ID. Methode Numerique en Electromagnetisme: Geometrie Differentielle. Elements finis, Modeles d'hysteresis. Eyrolles: Paris, 1991.
4. Conway JT. Exact solutions for the magnetic fields of axisymmetric solenoids and current distributions. IEEE Transactions on Magnetics 2001; 37(4):2977-2988.
5. Lei H, Wang L-Z, Wu Z-N. Integral analysis of a magnetic field for an arbitrary geometry coil with rectangular cross section. IEEE Transactions on Magnetics 2002; 38(6):3589-3593.
6. Gradshteyn IS, Ryzhik IM. Table of Integrals, Series and Products. Academic Press Inc.: New York and London, 1965.
7. Abramowitz M, Stegun IA. Handbook of Mathematical Functions, Series 55. National Bureau of Standards Applied Mathematics: Washington DC, December 1972; 595.
8. Brodtkorb A. Numerically evaluates an integral using a Gauss quadrature. Matlab Central, 1999.
9. Gander W, Gautschi W. Adaptive quadrature revisited. Matlab 6.0, 1998.
10. Burden RL, Faires JD, Reynolds AC. Numerical Analysis (2nd edn). PWS Publishers: Boston, Massachusetts, 1978.
11. Urankar L. Vector potential and magnetic field of current-carrying finite arc segment in analytical form-Part V: Polygon cross section. IEEE Transactions on Magnetics 1990; 56:1171-1180.
12. Babic S. Krstajic B, Milojkovic S. Andjelic Z. An efficient approach for the calculation of 3D magnetostatic of current-carrying regions of typical form. IEEE Transactions on Magnetics 1998: 24(1):423-426.
13. Babic S, Andjelic Z, Krstajic B, Salon S. Analytical calculation of the 3D magnetostatic field of a toroidal conductor with rectangular cross section. IEEE Transactions on Magnetics 1988; 24(6):3162-3164.
14. Babic S, Andjelic Z, Krstajic B. Salon S. Analytical magnetostatic field calculation for a conductor with uniform current in the longitudinal direction. Journal of Applied Physics 1990; 67(9):5827-5829.
15. Babic S, Gavrilovic MM. New expression for calculating magnetic fields due to current-carrying solid conductors. IEEE Transactions on Magnetics 1997; 33(5):4134-4136.
16. Babic S. Akyel C, Salon SJ, Kincic S. Exact expressions for calculating the magnetic field created by current-carrying in radial direction-massive disks. IEEE Transactions on Magnetics 2002; 35(2):491-495.
17. Azzerboni B, Cardelli E, Raugi M, Tellini A, Tina G. Analytical expressions for magnetic field from finite curved conductors. IEEE Transactions on Magnetics 1991; 27:750-757.
18. Azerboni B, Saraceno GA. Three-dimensional calculating of the magnetic field created by current-carrying massive disks. IEEE Transactions on Magnetics 1998; 34(5):2601-2604.
19. Fontana M. 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 NJ. A search for faster magnetic field routines for curved conductors. IEEE Transactions on Magnetics 1983; 19:2304-2306.
21. Kajikawa K, Kaiho K. Usable ranges of some expressions for calculation of the self-inductance of a circular coil of rectangular cross section. Cryogenic Engineering 1995; 30(7):324-332 (in Japanese).
22. Ciric IR. New models for current distributions and scalar potential formulations of magnetic field problems. Journal of Applied Physics 1987; 61:2709-2719.
23. Ciric IR. Simple analytical expressions for the magnetic field of current coils. IEEE Transactions on Magnetics 1991; 27:669-673.
24. Forbes LK, Crozier S. Doddrel D. Rapid computation of static fields produced by thick circular coil. IEEE Transactions on Magnetics 1997; 33(5):4405-4410.
25. Snape-Jenkinson CJ. Forbes LK, Crozier S. Direct algorithm for rapid calculation of magnetic field spherical harmonics. IEEE Transactions on Magnetics 1999; 33(5):4159-4469.
26. Crozier S. Doddrell DM. Compact MRI magnet design by stochastic optimization. Journal of Magnetic Resonance 1997; 127:223-237.
27. Suh JC. The evaluation of the Biol-Savart integral. Journal of Engineering Mathematics 2000; 37:375-395.
28. Urankar L. Vector potential and magnetic field of current-carrying finite arc segment in analytical form - Part I: filament approximation. IEEE Transactions on Magnetics 1980; 16:1283-1288.
29. Urankar L. Vector potential and magnetic field of current-carrying finite arc segment in analytical form - Part II: thin sheet approximation. IEEE Transactions on Magnetics 1982; 18:911-917.
30. Urankar L. Vector potential and magnetic field of current-carrying finite arc segment in analytical form - Part III: exact computation for rectangular cross section. IEEE Transactions on Magnetics 1982; 18:1860-1867.
31. Urankar L. Vector potential and magnetic field of current-carrying finite arc segment in analytical form - Part IV: general three-dimensional current density. IEEE Transactions on Magnetics 1984; 20:2145-2150.