Application of spheroidal functions in magnetostatics

IEEE Transactions on Magnetics

Volumn 40, Issue 2 II, 2004, Pages 846-849

  Kildishev, Alexander V ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Magnetic multipole image; Magnetostatics; Spheroidal harmonics

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; EXTRAPOLATION; FUNCTIONS; HARMONIC ANALYSIS; MAGNETIC FIELDS;

MAGNETIC MULTIPOLE IMAGE; MAGNETOSTATICS PROBLEM; SPHEROIDAL HARMONICS;

MAGNETOSTATICS;

EID: 2342559327     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMAG.2004.825429     Document Type: Article

References (28)

1. A. V. Kildishev, J. A. Nyenhuis, and A. V. Hetman, "Zonal magnetic signatures in spherical and prolate spheroidal analysis," in MARELEC'99, Brest, France, 1999, pp. 231-242.
2. A. V. Kildishev and S. A. Volokhov, "Sense coils and selective functions for tesseral multipole determination by integral transforms of magnetic signatures," Space Sci. Technol., vol. 2, no. 5-6, pp. 26-30, 1996.
3. F. E. Baker and S. H. Brown, "Magnetic induction of ferromagnetic prolate spheroidal bodies and infinitesimally thin current bands," J. Appl. Phys., vol. 53, pp. 3991-3996, June 1982.
4. P. Moon and D. E. Spencer, Field Theory Handbook; Including Coordinate Systems, Differential Equations and Their Solutions. New York: Springer-Verlag, 1961, pp. 28-29 and 31-33.
5. J. R. Herndon, "Algorithm 62 - a set of associated Legendre polynomials of the second kind," Commun. ACM, vol. 4, pp. 320-321, July 1961.
6. _, "Remark on algorithm 62," Commun. ACM, vol. 4, p. 544, Dec. 1961.
7. W. Gautschi, "Algorithm 259 - Legendre functions for arguments larger than one," Commun. ACM, vol. 8, no. 8, p. 488, 1965.
8. A. Gil and J. Segura, "Evaluation of Legendre functions of argument greater than one," Comput. Phys. Commun., no. 105, pp. 273-283, 1997.
9. _, "A code to evaluate prolate and oblate spheroidal harmonics," Comput. Phys. Commun., vol. 108, pp. 267-278, 1998.
10. J. Segura and A. Gil, "Evaluation of associated Legendre functions off the cut and parabolic cylinder functions," Electron. Trans. Numer. Anal., vol. 9, pp. 137-146, 1999.
11. E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonics. New York: Chelsea, 1955, p. 286, Eq. 158.
12. _, The Theory of Spherical and Ellipsoidal Harmonics. New York: Chelsea, 1955, p. 286, Eq. 158.
13. _, The Theory of Spherical and Ellipsoidal Harmonics. New York: Chelsea, 1955, p. 73, Example. 10.
14. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, A. Jeffrey, Ed. New York: Academic, 1980, Formula 8.731. Translated from Russian.
15. _, Table of Integrals, Series, and Products, A. Jeffrey, Ed. New York: Academic, 1980, Formulas 8.755.2 and 8.752.1. Translated from Russian.
16. Tables of Associated Legendre Functions. New York: NBS; Columbia Univ. Press, 1945, p. 303.
17. L. Frumkis and B.-Z. Kaplan, "Spherical and spheroidal shells as models in magnetic detection," IEEE Trans. Magn, vol. 35, pp. 4151-4158, Sept. 1999.
18. J. J. Holmes, "Theoretical development of laboratory techniques for magnetic measurement of large objects," IEEE Trans. Magn., vol. 37, pp. 3790-3797, Sept. 2001.
19. A. V. Kildishev and J. A. Nyenhuis, "Fast magnetic multipole imaging of elementary sources on the disk," J. Appl. Phys., vol. 91, no. 10, pp. 8721-8723, 2002.
20. K. Mori, "Modeling of magnetic field source by distributing dipoles on a disk," J. Appl. Phys., vol. 62, pp. 366-368, 1987.
21. A. V. Kildishev and J. A. Nyenhuis, "Multipole imaging of an elongated magnetic source," IEEE Trans. Magn., vol. 36, pp. 3108-3111, Sept. 2000.
22. _, "Fast spheroidal multipole imaging of elementary magnetic sources on the axis," J. Appl. Phys., vol. 89, no. 11, pp. 6716-6718, 2001.
23. S. Babic, C. Akyel, and S. Salon, "The mutual inductance of two thin coaxial coils in air," presented at the 14th Conf. Computation of Electromagnetic Fields (COMPUMAG), Saratoga Springs, NY, July 13-17, 2003, Paper P21106.
24. A. V. Kildishev and J. T. Conway, "Extrapolation of the scalar magnetic potential beyond a finite cylindrical boundary," unpublished.
25. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, A. Jeffrey, Ed. New York: Academic, 1980, Formula 8.821.3. Translated from Russian.
26. T. Miloh, "The ultimate image singularities for external ellipsoidal harmonics," SIAM J. Appl. Math., vol. 26, no. 2, pp. 334-344, 1974.
27. D. A. Nixon and F. E. Baker, "Using prolate spheroidal magnetization distributions for magnetic modeling," J. Appl. Phys., vol. 52, no. 2, pp. 539-541, 1981.
28. E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonics. New York: Chelsea, 1955, pp. 424-430.