Vol. 103
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2010-04-29
Evolution of Transient Electromagnetic Fields in Radially Inhomogeneous Nonstationary Medium
By
Progress In Electromagnetics Research, Vol. 103, 403-418, 2010
Abstract
To solve radiation problems in time domain directly the modal representation of transient electromagnetic fields is considered. Using evolutionary approach the initial nonstationary three-dimensional electrodynamic problem is transformed into the problem for one-dimensional evolutionary equations by the construction of the modal basis for electromagnetic fields with arbitrary time dependence in spherical coordinate system. Elimination of the radial components of electrical and magnetic field from Maxwell equation system permits to form the four-dimensional differential operators. It is proved that the operators are self- adjoint ones. The eigen-functions of the operators form the basis. The completeness of the basis is proved by means of Weyl Theorem about orthogonal detachments of Hilbert space. The expansion coefficients of arbitrary electromagnetic field are found from the set of evolutionary equations. The transient electromagnetic field can be found directly without Fourier transform application by means of one-dimensional FDTD method for the medium with dependence on longitudinal coordinate and time or using Laplace transform and wave splitting for the case of homogeneous stationary medium. The above mentioned methods are compared with the three-dimensional FDTD method for the case of the problem of small loop excitation by transient current.
Citation
Oleksandr M. Dumin O. O. Dumina Victor A. Katrich , "Evolution of Transient Electromagnetic Fields in Radially Inhomogeneous Nonstationary Medium," Progress In Electromagnetics Research, Vol. 103, 403-418, 2010.
doi:10.2528/PIER10011909
http://www.jpier.org/PIER/pier.php?paper=10011909
References

1. Taflove, A. and S. C. Hagness, Computational Electromagnetics: The Finite-difference Time-domain Method, 2nd Ed., Artech House, Boston, London, Norwood, MA, USA, 2000.

2. Sirenko, Y. K., S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures, New Methods and Techniques, Springer, New York, 2007.

3. Shreim, A. M. and M. F. Hadi, "Integral PML absorbing boundary conditions for the high-order M24 FDTD algorithm," Progress In Electromagnetics Research, Vol. 76, 141-152, 2007.
doi:10.2528/PIER07070303

4. Zheng, K., W. Y. Tam, D. B. Ge, and J. D. Xu, "Unaxial PML absorbing boundary condition for truncating the boundary of DNG metamaterials," Progress In Electromagnetics Research Letters, Vol. 8, 125-134, 2009.
doi:10.2528/PIERL09030901

5. Liang, F. and G. Wang, "Fourth-order locally one-dimensional FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 14-15, 2035-2043, 2008.
doi:10.1163/156939308787538017

6. LaComb, J. A., "Spoke top antenna for transient radiation," Progress In Electromagnetics Research Letters, Vol. 11, 1-9, 2009.
doi:10.2528/PIERL09080602

7. Tretyakov, O. A., "Modal basis method," Radiotekhika i electronika, Vol. 31, No. 6, 1071-1082, 1986 (in Russian).

8. Tretyakov, O. A. and F. Erden, "Temporal cavity oscillations caused by a wide-band waveform," Progress In Electromagnetics Research B, Vol. 6, 183-204, 2008.
doi:10.2528/PIERB08031222

9. Antyufeyeva, M. S., A. Y. Butrym, and O. A. Tretyakov, "Transient electromagnetic fields in a cavity with dispersive double negative medium," Progress In Electromagnetics Research M, Vol. 8, 51-65, 2009.
doi:10.2528/PIERM09062307

10. Antyufeyeva, M. S. and O. A. Tretyakov, "Electromagnetic fields in a cavity filled with some nonstationary medium," Progress In Electromagnetics Research B, Vol. 19, 177-203, 2010.
doi:10.2528/PIERB09112402

11. Tretyakov, O. A., "Evolutionary waveguide equations," Radiotekhika i electronika, Vol. 34, No. 5, 917-926, 1989 (in Russian).

12. Tretyakov, O. A., "Essentials of nonstationary and nonlinear electromagnetic field theory," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Vol. 572, Science House Co., Ltd, Tokyo, 1993.

13. Weyl, H., "The method of orthogonal projection in potential theory ," Duke Math. J., Vol. 7, 411-444, 1940.
doi:10.1215/S0012-7094-40-00725-6

14. Velychko, L. G. and Y. K. Sirenko, "Controlled changes in spectra of open quasi-optical resonators," Progress In Electromagnetics Research B, Vol. 16, 85-105, 2009.
doi:10.2528/PIERB09060202

15. Motavali, H. and A. Rostami, "Exactly modal analysis of inhomogeneous slab waveguide using Nikiforov-Uvarov method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5-6, 681-692, 2008.
doi:10.1163/156939308784159507

16. Butrym, A. Y. and B. A. Kochetov, "Time domain mode basis method for a waveguide with transverse inhomogeneous multi-connected cross-section. 1. The general theory of method," Radio Physics and Radio Astronomy, Vol. 14, No. 2, 162-173, 2009 (in Russian).

17. Tretyakov, O. A. and A. N. Dumin, "Radiation of transient electromagnetic fields from plane radiator," Electromagnetic Waves & Electron. Systems, Vol. 3, No. 1, 12-22, 1998 (in Russian).

18. Dumin, A. N., "Radiation of transient localized waves from an open-ended coaxial waveguide with infinite flange," Telecommunications and Radio Engineering, Vol. 53, No. 6, 30-34, 1999.

19. Dumin, A. N., A. Y. Butrym, O. A. Tretyakov, V. A. Katrich, and O. A. Dumina, Transient electromagnetic fields in unbounded space with inhomogeneous medium, Proceedings of the 2nd International Workshop on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS'04), 104-106, Sevastopol, Ukraine, 2004.

20. Butrym, A. Y. and B. A. Kochetov, "Mode expansion in time domain for conical lines with angular medium inhomogeneity," Progress In Electromagnetics Research B, Vol. 19, 151-176, 2010.
doi:10.2528/PIERB09102606

21. Butrym, A. Yu., B. A. Kochetov, and M. N. Legenkiy, Numerical analysis of simply TEM conical-like antennas using mode matching in time domain , Proceedings of the 3rd European Conference on Antennas and Propagation (EuCAP 2009), 3471-3475, Berlin, Germany, 2009.

22. Zhou, S.-G., J. Ma, J.-Y. Deng, and Q.-Z. Liu, "A low-profile and broadband conical antenna," Progress In Electromagnetics Research Letters, Vol. 7, 97-103, 2009.
doi:10.2528/PIERL09021602

23. Ghosh, D., T. K. Sarkar, and E. L. Mokole, "Design of a wide-angle biconical antenna for wideband communications," Progress In Electromagnetics Research B, Vol. 16, 229-245, 2009.
doi:10.2528/PIERB09061508

24. Shlivinski, A. and E. Heyman, "Time-domain near-field analysis of short-pulse antennas --- Part I: Spherical wave (multipole) expansion ," IEEE Trans. Antennas and Propagation, Vol. 47, No. 2, 271-279, 1999.
doi:10.1109/8.761066

25. Tretyakov, O., A. Dumin, O. Dumina, and V. Katrich, Modal basis method in radiation problems, Proc. Int. Conf. on Math. Methods in Electromagnetic Theory (MMET-2004), 312-314, Dnepropetrovsk, Ukraine, 2004.

26. Dumin, O. M., O. O. Dumina, and V. O. Katrich, Propagation of spherical transient electromagnetic wave through radially inhomogeneous medium, Proc. Int. Conf. on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS-2006), 276-278, Sevastopol, Ukraine, 2006.

27. Dumin, O., O. Dumina, and V. Katrich, Evolution of transient electromagnetic fields in spherical coordinate system, Proc. XI-th Int. Conf. on Math. Methods in Electromagnetic Theory (MMET-2006), 363-365, Kharkiv, Ukraine, 2006.

28. Dumin, O. M., O. O. Dumina, and V. O. Katrich, Comparative analysis of the analytical and numerical solutions of transient wave propagation problem , Proc. XI-th Int. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic wave Theory (DIPED-06) , 43-46, Tbilisi, Georgia, 2006.

29. Butrym, A. Y. and B. A. Kochetov, Mode basis method for spherical TEM-transmission lines and antennas, Proc. Int. Conf. on Antenna Theory and Techniques (ICATT-2007), 243-245, Sevastopol, Ukraine, 2007.

30. Kamke, E., "Handbook of Ordinary DiĀ®erential Equations," Nauka, Moscow, 1965 (in Russian).

31. Zheng, Y., B. A. Kochetov, and A. Y. Butrym, "Finite difference scheme in time domain and analytical solution for Klein-Gordon Equation," Bulletin of Karazin Kharkiv National University, No. 712, ''Radiophysics and electronics", No. 10, 91-94, 2006 (in Russian).

32. Sorour, T. E. and A. B. El-Rouby, "An isotropic algorithm for solving Maxwell's Equations in 2D," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5-6, 829-838, 2008.
doi:10.1163/156939308784159615