Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

doi:10.1088/1674-1056/19/12/120302

Abstract The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows: 1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2) the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3) the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180o, there are two additional reverse concentrative areas on both sides of x axis.

Keywords: transient pulsed eddy current analytical solution elliptical electromagnetic concentrative coil functional magnetic stimulation

Received: 19 March 2010
Revised: 09 July 2010
Accepted manuscript online:

PACS:	0350D
	8760D
	8170C
	0200

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 50807001).

Cite this article:

Xiao Chun-Yan(肖春燕) and Zhang Jun(张军) Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils 2010 Chin. Phys. B 19 120302

[1]	Iramina K, Maeno T, Nonaka Y and Ueno S 2003 J. Appl. Phys. 93 6718
[2]	Ueno S, Tashiro T and Harada K 1988 J. Appl. Phys. 64 5862
[3]	Zhang J Y and Lei Y Z 2007 Nondestructive Testing 29 57
[4]	Ren C, Tarjan P P and Popovic D B 1995 IEEE Trans. Biomed. Eng. 42 918
[5]	Hsu K H and Durand D M 2001 IEEE Trans. Biomed. Eng. 48 1162
[6]	Salinas F S, Lancaster J L and Fox P T 2009 Phys. Med. Biol. 54 3631
[7]	Lin V W, Hsiao I N and Dhaka V 2000 IEEE Trans. Biomed. Eng. 47 600
[8]	Ruohonen J and Ilmoniemi R J 1998 Med. Biol. Eng. Comput. 36 297
[9]	Pu L N , Yin T, An H, Li S and Liu Z P 2008 Journal of Biomedical Engineering Research 27 74
[10]	Ho S L, Xu G Z, Fu W N, Yang Q X, Hou H J and Yan W L 2009 IEEE Trans. Magn. 45 4849
[11]	Tsaknakis H J and Kriezis E E 1982 IEEE Trans. Geosci. Remote Sensing 20 122
[12]	Tsaknakis H J and Kriezis E E 1985 IEEE Trans. Geosci. Remote Sensing 23 834
[13]	Xie L and Lei Y Z 2007 Chin. Phys. 16 2523
[14]	Thomson W T 1960 Laplace Transformation (Englewood Cliffs: Prentice-Hall INC.) p. 245
[15]	Campbell G A and Foster R M 1948 Fourier Integrals for Practical Application (New York: Van Nostrand Co.) pp. 56, 57
[16]	Li Y L and Huang J Y 2005 Chin. Phys. 14 646
[17]	Liu S S and Liu S D 2002 Special Functions (2nd edn.) (Beijing: China Meteorological Press) p. 434

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Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

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