, function () { return new ActiveXObject('Msxml2.XMLHTTP'); }, function () { return new ActiveXObject('MSXML.XMLHttp'); }, function () { return new ActiveXObject('Microsoft.XMLHTTP'); } ) || null; }, post: function (sUrl, sArgs, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { //alert(errmsg); } } }; xhr2.open('POST', encodeURI(sUrl), bAsync); xhr2.setRequestHeader('Content-Length', sArgs.length); xhr2.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded'); xhr2.send(sArgs); }, get: function (sUrl, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { alert(errmsg); } } }; xhr2.open('GET', encodeURI(sUrl), bAsync); xhr2.send('Null'); } } function SetSearchLink(item) { var url = "../journal/recordsearchinformation.aspx"; var skid = $(":hidden[id$=HiddenField_SKID]").val(); var args = "skid=" + skid; url = url + "?" + args + "&urllink=" + item; window.setTimeout("showSearchUrl('" + url + "')", 300); } function showSearchUrl(url) { var callback2 = function (xhr2) { } ajax2.get(url, true, callback2, "try"); }
AM> Vol.4 No.1, January 2013
Share This Article:
Cite This Paper >>

TE, TM Fields in Toroidal Electromagnetism

Abstract Full-Text HTML XML Download Download as PDF (Size:136KB) PP. 25-28
DOI: 10.4236/am.2013.41006    4,828 Downloads   6,585 Views  
Author(s)    Leave a comment
Pierre Hillion


Institut Henri Poincaré, Paris, France.


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.


TE, TM Fields; Toroidal Space; Wave Equation; Laplace Equation

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.

Conflicts of Interest

The authors declare no conflicts of interest.


[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.

comments powered by Disqus
AM Subscription
E-Mail Alert
AM Most popular papers
Publication Ethics & OA Statement
AM News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.