PIERS Online Vol. 4 No. 6 2008 pp: 605-610

A Toroidal Harmonic Representation of the Yukawa-potential Kernel for a Circular Cylindrical Source

Jerry P. Selvaggi, Sheppard J. Salon, and M. V. K. Chari

doi:10.2529/PIERS071206060403

Abstract:

References:

1. Liu, B. and J. Goree, "Phonons in a one-dimensional Yukawa chain: Dusty plasma experiment and model," Phys. Rev., Vol. 71, 046410-12, 2005.

2. Henning, C., H. Baumgartner, A. Piel, P. Ludwig, V. Golubnichiy, M. Bonitz, and D. Block, "Ground state of a confined Yukawa plasma," Phys. Rev., Vol. 74, 056403-6, 2006.

3. Khrapak, S. A., A. V. Ivlev, G. E. Morfill, S. K. Zhdanov, and H. M. Thomas, "Scattering in the attractive Yukawa potential: Application to the ion-drag force in complex plasmas," IEEE Trans. on Plasma Sci., Vol. 32, April, 2004.
doi:10.1109/TPS.2004.826073

4. Harreis, H. M., C. N. Likos, and H. Lowen, "Azimuthal frustration and bundling in columnar DNA aggregates," Biophys. Jour., Vol. 84, 1378-3607, June, 2003.

5. Rowan, D. G., J. P. Hansen, and E. Trizac, "Screened electrostatic interactions between clay platelets," Mol. Phys., Vol. 98, No. 18, 1369-1378, 2000.
doi:10.1080/002689700417493

6. Wagner, K., E. Keyes, T. Kephart, and G. Edwards, "Analytical Debye-huckel model for electrostatic potentials around dissolved DNA," Biophys. Jour., Vol. 73, July 21-30, 1997.

7. Gillespie, A., R. Paul, and S. J. Paddison, "Electrical potential distribution in nanopores," Nanotech, Vol. 3, 497-499, 2003.

8. Bordag, M., B. Geyer, G. L. Klimchitskaya, and V. M. Mostepanenko, "New constraints for non-Newtonian gravity in the nanometer range from the improved precision measurement of the Casimir force," Phys. Rev. D, Vol. 62, 011701(R)-5, June, 2000.

9. Smullin, S. J., A. A. Geraci, D. M. Weld, and A. Kapitulnik, "Testing gravity at short distances," SLAC Summer Institute on Particle Physics (SSI04), Aug. 2-13, 2004.

10. Quinn, T. J., C. C. Speake, S. J. Richman, R. S. Davis, and A. Picard, "A new determination of G using two methods," Phys. Rev. Let., Vol. 87, No. 11, 111101-1-111101-4, Sept., 2001.

11. Shapiro, I. L., "Asymptotic behavior of effective Yukawa coupling constants in quantum R2 gravity with matter," Class. Quantum Grav., Vol. 6, 1197-1201, 1989.
doi:10.1088/0264-9381/6/8/019

12. Stacey, F. D., G. J. Tuck, and G. I. Moore, "Quantum gravity: Observational constraints on a pair of Yukawa terms," Phys. Rev. D (Particles and Fields), Vol. 36, No. 8, 2374-238015, Oct., 1987.
doi:10.1103/PhysRevD.36.2374

13. Cohl, H. S. and J. E. Tohline, "A compact cylindrical Green's function expansion for the solution of potential problems," Astrophys. Jour., Vol. 527, 86-101, Dec., 1999.
doi:10.1086/308062

14. MacRobert, T. M., Spherical Harmonics, 209-211, Pergamon Press, Oxford, 1967.

15. Lebedev, N. N., Special Functions and Their Applications, 184-199, Prentice-Hall, New Jersey, 1965.

16. Snow, C., "Hypergeometric and legendre functions with applications to integral equations of potential theory," Natl. Bur. Stand. App. Math. Ser., Vol. 19, 56-82, Washington D. C., 1952.

17. Snow, C., "Hypergeometric and legendre functions with applications to integral equations of potential theory," Natl. Bur. Stand. App. Math. Ser., Vol. 19, 228-238, Washington D. C., 1952.

18. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions, 336-337, Dover Publications Inc., New York, 1972.

19. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, Parts I and II, 744, McGraw Hill, New York, 1953.

20. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, Parts I and II, 1301-1304, McGraw Hill, New York, 1953.

21. Cohl, H. S., "Portent of Heine's reciprocal square root identity," 3D Stellar Evolution, ASP Conference Proceedings, Vol. 293, University of California Davis, Livermore, California, USA, July 22-26, 2002.

22. Cohl, H. S., J. E. Tohline, and A. R. P. Rau, "Developments in determining the gravitational potential using toroidal functions," Astron. Nachr., Vol. 321, 363-372, 2000.
doi:10.1002/1521-3994(200012)321:5/6<363::AID-ASNA363>3.0.CO;2-X

23. Cohl, H. S., A. R. P. Rau, J. E. Tohline, D. A. Browne, J. E. Cazes, and E. I. Barnes, "Useful alternative to the multipole expansion of 1/r potentials," Phys. Rev. A, Vol. 64, 052509-1-052509-5, Oct., 2001.

24. Selvaggi, J., S. Salon, O. Kwon, and M. V. K. Chari, "Calculating the External magnetic field from permanent magnets in permanent-magnet motors-an alternative method," IEEE Trans. Mag., Vol. 40, No. 5, 3278-3285, Sept., 2004.
doi:10.1109/TMAG.2004.831653

25. Selvaggi, J., S. Salon, and M. V. K. Chari, "An application of toroidal functions in electrostatics," Am. J. Phys., Vol. 75, No. 8, 724-727, Aug., 2007.
doi:10.1119/1.2737473

26. Selvaggi, J., S. Salon, O. Kwon, and M. V. K. Chari, "Computation of the external magnetic field, near-field or far-field, from a circular cylindrical magnetic source," IEEE Trans. Mag., Vol. 43, No. 4, 1153-1156, April, 2007.
doi:10.1109/TMAG.2007.892275

27. Selvaggi, J., S. Salon, O. Kwon, and M. V. K. Chari, "Computation of the three-dimensional magnetic field from solid permanent-magnet bipolar cylinders by employing toroidal harmonics," IEEE Trans. Mag., Vol. 43, No. 10, 3833-3839, Oct., 2007.
doi:10.1109/TMAG.2007.902995

28. Jackson, J. D., Classical Electrodynamics, 125-127, John Wiley & Sons, New York, 1999.

29. Smythe, W. R., Static and Dynamic Electricity, 187-189, McGraw-Hill, New York, 1968.

30. Smythe, W. R., Static and Dynamic Electricity, 204, McGraw-Hill, New York, 1968.

31. Maple, Maple, Waterloo Maple Inc., Waterloo, Ontario, Canada, 2004.

32. Gil, A., J. Segura, and N. M. Temme, "Computing toroidal functions for wide ranges of the parameters," National Research Institute for Mathematics and Computer Science, Amsterdam, Netherland, May 31, 2000.

33. Grobner, W. and N. Hofreiter, Integraltafel Zweiter Teil Bestimmte Integrale, 199, Springer-Verlag, Wein, 1966.

34. Wang, Z. X. and D. R. Guo, Special Functions, 254-255, World Scientific, Singapore, 1989.