volume | PIER Journals

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.

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.

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

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

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.

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

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

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

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

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

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.

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

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

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

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

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

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.

Dr. Victor Nijimbere

Dr. Lucy J. Campbell