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PIER PIER B PIER C PIER M PIER Letters
2010-04-29
Evolution of Transient Electromagnetic Fields in Radially Inhomogeneous Nonstationary Medium
By
Oleksandr M. Dumin,

    Dr. Oleksandr M. Dumin

    Department of Applied Electrodynamics

    V. N. Karazin Kharkiv National University

    Ukraine

    Homepage

O. O. Dumina,

    Dr. O. O. Dumina

    Department of Higher Mathematics

    Ukrainian State Academy of Railway Transport

    Ukraine

    Homepage

Victor A. Katrich

    Dr. Victor A. Katrich

    Department of Radiophysics

    V. N. Karazin Kharkov National University

    Ukraine

    Homepage

Progress In Electromagnetics Research, Vol. 103, 403-418, 2010
doi:10.2528/PIER10011909
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, and 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
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 Di®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

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