2019-02-21
Electromagnetic Field Solutions in an Isotropic Medium with Weakly-Random Fluctuations in Time and Some Applications in the Electrodynamics of the Ionosphere
By
Progress In Electromagnetics Research B, Vol. 83, 77-92, 2019
Abstract
Stochastic wave equations are derived to describe electromagnetic wave propagation in an isotropic medium in which the electric permittivity and the magnetic permeability are weakly-random functions of time. Approximate analytical solutions are obtained using separation of variables and the WKB method for some configurations that can be used to model the electromagnetic field in the ionosphere. The form of the initial and boundary conditions determines whether the solution takes a form representing a direct current electric field or continuous pulsation electromagnetic waves. The temporal variation of the calculated induced electromotive force (EMF) is in agreement with observations.
Citation
Victor Nijimbere, and Lucy J. Campbell, "Electromagnetic Field Solutions in an Isotropic Medium with Weakly-Random Fluctuations in Time and Some Applications in the Electrodynamics of the Ionosphere," Progress In Electromagnetics Research B, Vol. 83, 77-92, 2019.
doi:10.2528/PIERB18102003
References

1. Elsborg, R., L. Remvig, H. Beck-Nielsen, and C. Juh, "Detecting hypoglycemia by using brain as a biosensor," Biosensors for Health, Environment and Biosecurity, P. Andrea (ed.), InTechOpen, 2011.        Google Scholar

2. Basset, C. A., "Beneficial effects of electromagnetic fields," J. Cell. Biochem., Vol. 51, No. 4, 387-393, 1993.
doi:10.1002/jcb.2400510402        Google Scholar

2. Bal, G. and O. Pinaud, "Imaging using transport model for wave-wave correlations," Math. Models Appl. Sc., Vol. 21, No. 5, 1071-1093, 2011.
doi:10.1142/S0218202511005258        Google Scholar

4. Bender, M. and A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, Inc., 1978.

5. Bladel, J. V., Electromagnetic Fields, Springer-Verlag, 1985.

6. Cheng, D. K., Field and Wave Electromagnetics, Addison-Wesley, 1992.

7. Figueiredo, C. A. O. B., C. M. Wrasse, H. Takahashi, Y. Otsuka, K. Shiokawa, and D. Barros, "Largescale traveling ionospheric disturbances observed by GPS dTEC maps over North and South America on Saint Patrick’s Day storm in 2015," JGR Space Phys., Vol. 122, No. 4, 4755-4763, 2017.        Google Scholar

8. Hunsucker, R. D. and J. K. Hargreaves, The High-latitude Ionosphere and Its Effects on Radio Propagation, Cambridge University Press, 2003.

9. IEEE Standard, , Definition of terms for radio wave propagation, No. 211, 1969.

10. Kelley, M. C., The Earth’s Ionosphere. Plasma Physics and Electrodynamics, Academic Press, 2006.

11. Kelley, M. C., "LF and MF observations of the lightning electromagnetic pulse at ionospheric altitudes," Geophys. Res. Lett., Vol. 24, 1111-1114, 1997.
doi:10.1029/97GL00991        Google Scholar

12. Holzworth, R. H., M. C. Kelley, C. L. Siefring, L. C. Hale, and J. D. Mitchell, "Electrical measurements in the atmosphere and the ionosphere over an active thunderstorm, 2. Direct current electric fields and conductivity," J. Geophys. Res., Vol. 19, No. A10, 9824-9830, 1985.
doi:10.1029/JA090iA10p09824        Google Scholar

13. King, J. W., "Sun-weather relationships," Astronaut. Aeronaut., Vol. 13, 10-19, 1975.        Google Scholar

14. Kormiltsev, V. V. and A. N. Mesentsev, "Electric prospecting of polarising media,", Ural Division of Ac. Sc. of the USSR, Sverdlovsk, 1989.        Google Scholar

15. Lastovicka, J., "Effects of geomagnetic storms-different morphology in the upper middle atmosphere and troposphere," Stud. Geophys. Geod., Vol. 41, No. 1, 73-81, 1997.
doi:10.1023/A:1023340824496        Google Scholar

16. Makeig, S., T.-P. Jung, D. Ghahremani, and T. J. Sejnowski, "Independent component analysis of simulated ERP data," Integrated Human Brain Science: Theory, Method, Applications, T. Nakada (ed.), Elsevier, 2000.        Google Scholar

17. Nguyen, D. C., K. A. Dao, V. P. Tran, and D. Diep Dao, "Numerical estimation of the complex refractive indexes by the altitude depending on wave frequency in the ionized region of the Earth atmosphere for microwaves information and power transmissions," Progress In Electromagnetics Research M, Vol. 52, 21-31, 2016.
doi:10.2528/PIERM16042707        Google Scholar

18. Nijimbere, V., Ionospheric gravity wave interactions and their representation in terms of stochastic partial differential equations, Ph.D. Thesis, Carleton University, 2014.

19. Parks, G. K., Physics of Space Plasma, 2nd Ed., Westview Press, 2005.

20. Papanicolau, G., L. Ryzhik, and K. Sølna, "Statistical stability in time reversal," SIAM J. Appl. Math., Vol. 64, No. 4, 1133-1135, 2004.
doi:10.1137/S0036139902411107        Google Scholar

21. Pedrosa, I. A., A. Y. Petrov, and A. Rosas, "On the electrodynamics in time-dependent media," Eur. Phys. J. D, Vol. 66, No. 11, 309-313, 2012.
doi:10.1140/epjd/e2012-30308-9        Google Scholar

22. Ratcliffe, J. A., An Introduction to the Ionosphere and Magnetosphere, Cambridge University Press, 1972.

23. Singh, D., V. Gopalakrishnan, R. P. Singh, A. K. Kamra, S. Singh, V. Pant, and A. K. Singh, "The atmospheric global electric circuit: An overview," Atmos. Res., Vol. 84, 91-110, 2007.
doi:10.1016/j.atmosres.2006.05.005        Google Scholar

24. Wang, M., F. Ding, W. Wan, B. Ning, and B. Zhao, "Monitoring global traveling ionospheric disturbances using the worldwide GPS network during the October 2003 storms," Earth Planets Space, Vol. 59, 407-419, 2007.
doi:10.1186/BF03352702        Google Scholar

25. Yeh, K. C. and C. H. Liu, Theory of Ionospheric Waves, Vol. 17, International Geophysics Series, 1972.

26. Zastawniak, T. and Z. Brzezniak, Basic Stochastic Processes, Springer-Verlag, 2003.