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Spatio-temporal development of the filaments due to the thermal self-focusing instability near the critical surface in ionospheric plasmas

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Abstract

We study fully nonlinear spatio-temporal development of the thermal self-focusing instability of high-power radio waves near the critical surface of the ionosphere. These simulations improve on our earlier work by including an evolution equation for the density instead of using the assumption of constant pressure to determine the perturbed density connected with the known temperature perturbation. Using our two-dimensional nonlinear code we analyze the time scale and associated velocity for the development of the field-aligned irregularities as they spread from the critical surface both in the underdense as well as the overdense regions. The scaling of this velocity as a function of the radiated power of the heater electromagnetic wave (ERP) is determined. We also study the characteristic size of the self-focused filament as a function of ERP. Finally, the spectrum of the density and temperature fluctuations as well as modifications in the equilibrium values of these parameters for different values of ERP are presented.

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References

  1. A. G. Litvak,Izv. Vyssh. Uchebn. Zaved., Radiofiz.,11, 814 (1970).

    ADS  Google Scholar 

  2. H. C. Carlson and L. M. Duncan,Radio Sci.,12, 1001 (1977).

    ADS  Google Scholar 

  3. H. C. Carlson, Y. V. Wickwar, and J. P. Mantas,J. Atmos. Terr. Phys.,44, 1089 (1982).

    Article  ADS  Google Scholar 

  4. P. Stubbe et al.,J. Atmos. Terr. Phys.,55, 1025 (1982).

    Article  ADS  Google Scholar 

  5. J. A. Fejer et al.,J. Atmos. Terr. Phys.,47, 1165 (1985).

    Article  ADS  Google Scholar 

  6. L. M. Erukhimov et al.Radiophys. Quant. Electron.,30, 156 (1987).

    Article  ADS  Google Scholar 

  7. A. Y. Wong et al.,Phys. Rev. Lett.,63, 271 (1989).

    Article  ADS  Google Scholar 

  8. M. T. Rietveld, H. Kohl, H. Kopka, and P. Stubbe,J. Atmos. Terr. Phys.,44, 577 (1993).

    Article  ADS  Google Scholar 

  9. F. W. Perkins and E. J. Valeo,Phys. Rev. Lett.,32, 1234 (1974).

    Article  ADS  Google Scholar 

  10. B. L. Cragin, J. A. Fejer, and E. Leer,Radio Sci.,12, 273 (1977).

    ADS  Google Scholar 

  11. A. V. Gurevich,Nonlinear Phenomena in the Ionosphere, Springer-Verlag, New York (1978).

    Google Scholar 

  12. F. W. Perkins and M. V. Goldman,J. Geophys. Res.,86, 600 (1981).

    ADS  Google Scholar 

  13. P. A. Bernhardt and L. M. Duncan,J. Atmos. Terr. Phys.,44, 1061 (1982).

    Article  ADS  Google Scholar 

  14. P. A. Bernhardt and L. M. Duncan,J. Atmos. Terr. Phys.,49, 1107 (1987).

    Article  ADS  Google Scholar 

  15. W. F. Utlaut,J. Geophys. Res.,75, 6402 (1970).

    ADS  Google Scholar 

  16. G. D. Thome and F. W. Perkins,Phys. Rev. lett.,32, 1238 (1974).

    Article  ADS  Google Scholar 

  17. S. Basu, S. Basu, S. Ganguli, and W. E. Gordon,J. Geophys. Res.,88, 9217 (1983).

    ADS  Google Scholar 

  18. S. Basu, S. Basu, P. Stubbe, H. Kopka, and J. Waaramaa,J. Geophys. Res.,92, No. 11, 149 (1987).

    Google Scholar 

  19. S. Basu, E. Costa, R. C. Livingston, K. M. Groves, H. C. Carlson, P. K. Chaturvedi, and P. Stubbe,J. Geophys. Res.,102, (1997).

  20. L. M. Duncan and R. A. Behnke,Phys. Rev. Lett.,41, 998 (1978).

    Article  ADS  Google Scholar 

  21. A. Frey, P. Stubbe, and H. Kopka,Geophys. Res. Lett.,11, 523 (1984).

    ADS  Google Scholar 

  22. D. T. Farley, C. LaHoz, and B. G. Fejer,J. Geophys. Res.,88, 2093 (1983).

    ADS  Google Scholar 

  23. P. A. Bernhardt, L. M. Duncan, and C. A. Tepley,Science,242, 1022 (1988).

    Article  ADS  Google Scholar 

  24. J. W. Wright, H. Kopka, and P. Stubbe,Geophys. Res. Lett.,15, 1531 (1988).

    ADS  Google Scholar 

  25. M. C. Kelley et al.,J. Geophys. Res.,100, 17367 (1995).

    Article  ADS  Google Scholar 

  26. D. F. DuBois, A. Rose Harvey, and D. Russel,J. Geophys. Res.,95, No. 21, 221 (1990).

    Google Scholar 

  27. J. A. FejerRev. Geophys.,17, 8693 (1979).

    Google Scholar 

  28. P. Stubbe, H. Kopka, B. Thidé, and H. Derblom,J. Geophys. Res.,89, 7523 (1984).

    ADS  Google Scholar 

  29. A. C. Das and J. A. Fejer,J. Geophys. Res.,84, 6701 (1979).

    Article  ADS  Google Scholar 

  30. A. V. Gurevich, A. V. Lukyanov, and K. P. Zybin,Phys. Lett. A,211, 363 (1996).

    Article  ADS  Google Scholar 

  31. P. N. Guzdar, P. K. Chaturvedi, K. Papadopolous, and S. L. Ossakow,J. Geophys. Res.,103, 2231 (1998).

    Article  ADS  Google Scholar 

  32. G. M. Milikh, M. J. Freeman, and L. M. Duncan,Radio Sci.,29, 1355 (1994).

    Article  ADS  Google Scholar 

  33. V. L. Ginzburg,The Propagation of Electromagnetic Waves in Plasmas, 2nd ed., Pergamon, New York (1970).

    Google Scholar 

  34. P. N. Guzdar, P. K. Chaturvedi, K. Papadopolous, M. Keskenin, and S. L. Ossakow,J. Geophys. Res.,101, 2453 (1996).

    Article  ADS  Google Scholar 

  35. N. V. Bakhmet'eva, V. N. Bubukina, Yu. A. Ignat'et, et al.,J. Atm. Solar Terr. Phys.,59, 2257 (1997).

    Article  ADS  Google Scholar 

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 7, pp. 670–681, July 1999.

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Gondarenko, N.A., Guzdar, P.N., Milikh, G.M. et al. Spatio-temporal development of the filaments due to the thermal self-focusing instability near the critical surface in ionospheric plasmas. Radiophys Quantum Electron 42, 589–600 (1999). https://doi.org/10.1007/BF02677564

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  • DOI: https://doi.org/10.1007/BF02677564

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