TE, TM Fields in Toroidal Electromagnetism

ABSTRACT

We analyze the behaviour of TE, TM electromagnetic fields in a toroidal space through Maxwell and wave equations. Their solutions are discussed in a space endowed with a refractive index making separable the wave equations.

Cite this paper

P. Hillion, "TE, TM Fields in Toroidal Electromagnetism,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 25-28. doi: 10.4236/am.2013.41006.

P. Hillion, "TE, TM Fields in Toroidal Electromagnetism,"

References

[1] V. H. Weston, “Solutions of the Toroidal Wave Equation and Their Applications,” Ph.D. Thesis, University of Toronto, Toronto, 1954.

[2] P. Laurin, “Scattering by a Torus, Ph.D. Thesis, University of Michigan, Ann Arbor, 1967.

[3] W. N.-C. Sy, “Magnetic Field Due to Helical Currents on a Torus,” Journal of Physics A: Mathematical and General, Vol. 14, No. 8, 1981, pp. 2095-2112. doi:10.1088/0305-4470/14/8/031

[4] G. Venkov, “Low Frequency Electromagnetic Scattering by a Perfect Conducting Torus, the Rayleigh Approximation,” International Journal of Applied Electromagnetism and Mechanics, Vol. 24, 2007, pp. 96-103.

[5] J. A. Hernandez and A. K. T. Assis, “Electric Potential for a Resistive Toroidal Conductor Carrying a Steady Azimuthal Current,” Physical Review E, Vol. 68, No. 4, 2003, 10 p.

[6] J. A. Hernandez and A. K. T. Assis, “Surface Charges and External Electric Field in a Toroid Carrying a Steady Current,” Brazilian Journal of Physics, Vol. 34, No. 4b, 2004, pp. 1738-1744.

[7] U. Lehonardt and T. Tyc, “Broadband Invisibility by Non-Euclidean Cloaking,” Science, Vol. 313, No. 5910, 2009, pp. 110-112. http://www.sciencemag.org/cgi/data/116632/DC1/1

[8] P. M. Morse and H. Feshbach, “Methods of Theoretical Physics,” Mac-Graw Hill, New York, 1953.

[9] H. Margenau and E. M. Murphy, “The Mathematics of Physics and Chemistry,” Van Nostrand, New York, 1955.

[10] H. Bateman, “Partial Differential Equations of Mathematical Physics,” University Press, Cambridge, 1959.

[11] P. Hillion, “Rayleigh Acoustic Scattering from a Torus,” Journal of Applied Mathematics, Vol. 1, No. 1, 2011, pp. 1-11.

[12] F. W. J. Olver, “Asymptotic and Special Functions,” Academic Press, New York, 1974.

[13] P. C. Fereira, I. Kagan and B. Tekir, “Toroidal Compactification in String Theory from Chern-Simons Theory,” Nuclear Physics B, Vol. 689, No. 1-2, 2000, pp. 167-195. doi:10.1016/S0550-3213(00)00407-7

[14] M. Bianchi, G. Pradisi and A. Sagnotti, “Toroidal Compactification and Symmetry Breaking in Open String Theories,” Nuclear Physics B, Vol. 376, No. 2, 1992, pp. 369-386. doi:10.1016/0550-3213(92)90129-Y

[15] A. Guth, “The Inflationary Universe. The Quest for a New Theory of Cosmic Origin,” Perseus Books, New York, 1997.

[16] A. A. Starobinski, “A New Type of Isotropic Cosmological Models without Singularities,” Physics Letters B, Vol. 91, No. 1, 1980, pp. 99-102. doi:10.1016/0370-2693(80)90670-X

[17] M. Mc. Guigan, “Constraints for Toroidal Cosmology,” Physical Review E, Vol. 41, No. 10, 1990, pp. 3090-3100. doi:10.1103/PhysRevD.41.3090

[18] M. Bastero-Gill, P. H. Frampton and L. Mersini, “Modified Dispersion Relations from Closed Strings in Toroidal Cosmology,” Physical Review D, Vol. 65, No. 10, 2002, 12 p. doi:10.1103/PhysRevD.65.106002

[19] J. Smulevici, “On the Area of the Symmetric Orbits of Cosmological Space-Time with Toroidal or Hyperbolic Symmetry,” 2009.

[1] V. H. Weston, “Solutions of the Toroidal Wave Equation and Their Applications,” Ph.D. Thesis, University of Toronto, Toronto, 1954.

[2] P. Laurin, “Scattering by a Torus, Ph.D. Thesis, University of Michigan, Ann Arbor, 1967.

[3] W. N.-C. Sy, “Magnetic Field Due to Helical Currents on a Torus,” Journal of Physics A: Mathematical and General, Vol. 14, No. 8, 1981, pp. 2095-2112. doi:10.1088/0305-4470/14/8/031

[4] G. Venkov, “Low Frequency Electromagnetic Scattering by a Perfect Conducting Torus, the Rayleigh Approximation,” International Journal of Applied Electromagnetism and Mechanics, Vol. 24, 2007, pp. 96-103.

[5] J. A. Hernandez and A. K. T. Assis, “Electric Potential for a Resistive Toroidal Conductor Carrying a Steady Azimuthal Current,” Physical Review E, Vol. 68, No. 4, 2003, 10 p.

[6] J. A. Hernandez and A. K. T. Assis, “Surface Charges and External Electric Field in a Toroid Carrying a Steady Current,” Brazilian Journal of Physics, Vol. 34, No. 4b, 2004, pp. 1738-1744.

[7] U. Lehonardt and T. Tyc, “Broadband Invisibility by Non-Euclidean Cloaking,” Science, Vol. 313, No. 5910, 2009, pp. 110-112. http://www.sciencemag.org/cgi/data/116632/DC1/1

[8] P. M. Morse and H. Feshbach, “Methods of Theoretical Physics,” Mac-Graw Hill, New York, 1953.

[9] H. Margenau and E. M. Murphy, “The Mathematics of Physics and Chemistry,” Van Nostrand, New York, 1955.

[10] H. Bateman, “Partial Differential Equations of Mathematical Physics,” University Press, Cambridge, 1959.

[11] P. Hillion, “Rayleigh Acoustic Scattering from a Torus,” Journal of Applied Mathematics, Vol. 1, No. 1, 2011, pp. 1-11.

[12] F. W. J. Olver, “Asymptotic and Special Functions,” Academic Press, New York, 1974.

[13] P. C. Fereira, I. Kagan and B. Tekir, “Toroidal Compactification in String Theory from Chern-Simons Theory,” Nuclear Physics B, Vol. 689, No. 1-2, 2000, pp. 167-195. doi:10.1016/S0550-3213(00)00407-7

[14] M. Bianchi, G. Pradisi and A. Sagnotti, “Toroidal Compactification and Symmetry Breaking in Open String Theories,” Nuclear Physics B, Vol. 376, No. 2, 1992, pp. 369-386. doi:10.1016/0550-3213(92)90129-Y

[15] A. Guth, “The Inflationary Universe. The Quest for a New Theory of Cosmic Origin,” Perseus Books, New York, 1997.

[16] A. A. Starobinski, “A New Type of Isotropic Cosmological Models without Singularities,” Physics Letters B, Vol. 91, No. 1, 1980, pp. 99-102. doi:10.1016/0370-2693(80)90670-X

[17] M. Mc. Guigan, “Constraints for Toroidal Cosmology,” Physical Review E, Vol. 41, No. 10, 1990, pp. 3090-3100. doi:10.1103/PhysRevD.41.3090

[18] M. Bastero-Gill, P. H. Frampton and L. Mersini, “Modified Dispersion Relations from Closed Strings in Toroidal Cosmology,” Physical Review D, Vol. 65, No. 10, 2002, 12 p. doi:10.1103/PhysRevD.65.106002

[19] J. Smulevici, “On the Area of the Symmetric Orbits of Cosmological Space-Time with Toroidal or Hyperbolic Symmetry,” 2009.