Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T00:34:30.446Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-focusing of electromagnetic beams in the ionosphere considering Earth's magnetic field

Published online by Cambridge University Press:  01 August 2008

MAHENDRA SINGH SODHA  and
ASHUTOSH SHARMA
MAHENDRA SINGH SODHA
Affiliation:
Disha Academy of Research and Education, Disha Crown, Katchna Road, Shankar Nagar, Raipur 492007, India ([email protected])
ASHUTOSH SHARMA
Affiliation:
Ramanna Fellowship Programme, Department of Education Building, Lucknow University, Lucknow 226 007, India
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper the focusing/defocusing of (i) a single Gaussian electromagnetic beam and (ii) a number of coaxial Gaussian electromagnetic beams, propagating in the extraordinary mode along the Earth's magnetic field in the ionosphere has been investigated in the paraxial approximation. The growth of a sinusoidal instability on account of self-focusing has also been studied. The nonlinearity in the dielectric function, responsible for the focusing/defocusing arises from the redistribution of the electron density, caused by the non-uniform distribution of the electron temperature. The electron temperature is determined by the energy balance for electrons/ions taking into account the Ohmic heating, the collisions and the radiation from the sun. The wave frequency has been assumed to be greater than the plasma frequency. The electron cyclotron frequency due to the Earth's magnetic field in the ionosphere is much larger than the electron collision frequency. This is specifically true for a height of 150 km. Numerical results have been presented for a range of parameters and a discussion of the same has been presented.

Type
Papers
Information
Journal of Plasma Physics , Volume 74 , Issue 4 , August 2008 , pp. 473 - 491
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akhmanov, S. A., Sukhorukov, A. P. and Khokhlov, R. V. 1968 Self-focusing and diffraction of light in a nonlinear medium. Sov. Phys. Usp. 10, 609.CrossRefGoogle Scholar
Bailey, V. A. and Martin, D. F. 1934 The influence of electric waves on the ionosphere. Philos. Mag. 18, 369.CrossRefGoogle Scholar
Belikovich, V. V., Benediktov, E. A., Ziuzin, V. A., Komrakov, G. P. and Krasil'Nikov, M. I. 1990 Phase perturbation of high-intensity radio waves reflected from the F-region of the ionosphere. Radiofizika 33, 143.Google Scholar
Blagoveshchenskaya, N. F., Andre, A. D. and Kornienko, V. A. 1995 Ionospheric wave processes during HF heating experiments. Adv. Space Res. 15 (12), 45.CrossRefGoogle Scholar
Corozzi, T. D. 2000 Radio waves in the ionosphere: propagation, generation and detection. IRF Science Report 272, Swedish Institute of Space Physics, Uppsala, Sweden.Google Scholar
Djuth, F. T., Pedersen, T. R., Gerken, E. A., Bernhardt, P. A., Selcher, C. A., Bristow, W. A. and Kosch, M. J. 2004 Ionospheric modification at twice the electron cyclotron frequency. Phys. Rev. Lett. 94, 125001.CrossRefGoogle Scholar
Esarey, E., Sprangle, P., Krall, J. and Ting, A. 1997 Self focusing and guiding of short laser pulses in ionizing gases and plasmas. IEEE J. Quantum Electron. 33, 1879.CrossRefGoogle Scholar
Fejer, J. A. 1955 Interaction of pulsed radio waves in the ionosphere. J. Atmos. Terr. Phys. 7, 322.CrossRefGoogle Scholar
Getmantsev, G. G., Zuikov, N. A., Kotik, D. S., Mironenko, L. F., Mityakov, N. A., Rapoport, V. O., Sazonov, Y. A., Trachtengerts, V. Y. and Eidman, V. Y. 1974 Combination frequencies in the interaction between high-power short-wave radiation and ionospheric plasma. Sov. Phys. JETP Lett. 20, 101.Google Scholar
Ghanshyam, and Tripathi, V. K. 1993 Self focusing and filamentation of laser beams in collisional plasmas with finite thermal conduction. J. Plasma Phys. 49, 243.CrossRefGoogle Scholar
Ginzburg, V. L. and Gurevich, A. V. 1960 Nonlinear phenomena in a plasma located in an alternating electric field. Sov. Phys. Usp. 3, 115.CrossRefGoogle Scholar
Golov, P. I. and Kochubei, A. N. 1988 Self-focusing and nonlinear refraction in the high-latitude ionosphere in the case of energy transmission by a microwave beam. Radiotekh. Elektron. 33, 1793.Google Scholar
Gondarenko, N. A., Ossakow, S. L. and Milikh, G. M. 2005 Generation and evolution of density irregularities due to self-focusing in ionospheric modifications. J. Geophys. Res. 110, A09304.CrossRefGoogle Scholar
Gurevich, A. V. 1978 Nonlinear Phenomena in the Ionosphere. New York: Springer.CrossRefGoogle Scholar
Gurevich, A. V., Milikh, G. M. and Shlyuger, I. S. 1976 Non-linear thermal focusing of radio waves in the lower ionosphere. Geomagn. Aeron. 16, 366.Google Scholar
Guzdar, P. N., Chaturvedi, P. K., Papadopoulos, K. and Ossakow, S. L. 1998 The thermal self-focusing instability near the critical surface, in the high-latitude ionosphere. J. Geophys. Res. 103, 2231.CrossRefGoogle Scholar
Guzdar, P. N., Gondarenko, N. A., Milikh, G. M., Sharma, A. S., Papadopoulos, K. and Ossakow, S. L. 1999 Generation of large scale ionospheric irregularities due to HF-heating. Radiophys. Quantum Electron. 42, 670.Google Scholar
Hauser, T., Scheid, W. and Hora, H. 1988 Analytical calculation of relativistic self-focusing. J. Opt. Soc. Am. B 5, 2029.CrossRefGoogle Scholar
Honary, F., Stocker, A. J., Robinson, T. R., Jones, T. B. and Stubbe, P. 1995 Ionospheric plasma response to HF radio waves operating at frequencies close to electron gyro harmonics. J. Geophys. Res. 100, 21, 489.CrossRefGoogle Scholar
Hora, H. 1969 Self-focusing of laser beams in a plasma by ponderomotive forces. Z. Phys. 226, 156.CrossRefGoogle Scholar
Hora, H. 1991 Plasmas at Higher Temperature and Density. New York: Springer.Google Scholar
Hora, H., Kane, E. L. and Hughes, J. L. 1978 Generation of MeV and GeV ions by relativistic self-focusing from laser irradiated targets. J. Appl. Phys. 49, 923.CrossRefGoogle Scholar
Keskinen, M. J. and Basu, S. 2003 Thermal self-focusing instability in the high-latitude ionosphere. Radio Sci. 38 (6), 1095.CrossRefGoogle Scholar
Kuo, S. P. and Huang, J. 1994 Nonlinear wave phenomena in ionospheric modification by powerful radio waves. Phys. Fluids 1, 357.Google Scholar
Kuo, S. P. and Lee, S. H. 2004 Generation of extremely low frequency radiation by ionospheric electrojet modulation using powerful high-frequency heating waves. Radio Sci. 39, RS1S32.CrossRefGoogle Scholar
Kuo, S. P., Lee, S. H., Bivolaru, D., Kossey, P., Lee, M. C., Riddolls, R. J. and Sentman, D. 2003 Experimental and numerical studies on ELF/VLF wave generation by amplitude modulated HF heating waves. Phys. Scr. 67, 448.CrossRefGoogle Scholar
Laxmi, V. N. and Tripathi, V. K. 1992 Effect of radio frequency waves on ionospheric irregularities. Reviews in Contemporary Physics: Plasma Physics (ed. Kamal, R., Maheshwari, K. P. and Sawhney, R. L.). Hoboken, NJ: Wiley, p. 1.Google Scholar
Litvak, A. G. 1968 Possibility of self-focusing of electromagnetic wave in the ionosphere. Izv. Vyssh. Ucheb. Zaved Radiofiz. 11, 1433.Google Scholar
Maslin, N. M. 1975 Theory of the modifications imposed on the ionospheric plasma by a powerful radio wave reflected in the D or E region. Proc. R. Soc. London, A 343, 109.Google Scholar
Morales, G. J. 1987 RF heating the ionosphere (AIP Conf. Proc., 159), p. 450.Google Scholar
Palmer, A. J. 1971 Stimulated scattering and self-focusing in laser-produced plasmas. Phys. Fluids 14, 2714.CrossRefGoogle Scholar
Papadopoulos, K., Wallace, T., McCarrick, M., Milikh, G. M. and Yang, X. 2003 On the efficiency of ELF/VLF generation using HF heating of the Auroral electrojet. Plasma Phys. Rep. 29, 561.CrossRefGoogle Scholar
Perkins, F. W. and Goldman, M. V. 1981 Self focusing of radio waves in an underdense ionosphere. J. Geophys. Res. 86, 600.CrossRefGoogle Scholar
Prakash, G., Sharma, A., Verma, M. P. and Sodha, M. S. 2007 Nonlinear electromagnetic propagation parameters of the ionosphere. Ind. J. Phys. 81.Google Scholar
Richardson, M. C. and Alcock, A. J. 1971 Interferometric observation of plasma filaments in laser-produced spark. Appl. Phys. Lett. 18, 357.CrossRefGoogle Scholar
Robinson, T. R. 1989 The heating of the high latitude ionosphere by high power radio waves. Phys. Rep. 179, 79.CrossRefGoogle Scholar
Selvam, A. M. 1987 The dynamics of non-linear ionospheric RF wave processes (AIP Conf. Proc., 159), p. 460.Google Scholar
Sharma, A., Prakash, G., Verma, M. P. and Sodha, M. S. 2003 Three regimes of intense laser beam propagation in plasma. Phys. Plasmas 10, 4079.CrossRefGoogle Scholar
Sharma, A., Verma, M. P. and Sodha, M. S. 2004 Self focusing of electromagnetic beams in collisional plasmas with nonlinear absorption. Phys. Plasmas 11, 4275.CrossRefGoogle Scholar
Shearer, J. W. and Eddleman, J. L. 1973 Laser light forces and self-focusing in fully ionized plasmas. Phys. Fluids 16, 1753.CrossRefGoogle Scholar
Shukla, P. K. and Stenflo, L. 1984 Nonlinear propagation of electromagnetic waves in magnetized plasmas. Phys. Rev. A 30, 2110.CrossRefGoogle Scholar
Sodha, M. S., Ghatak, A. K. and Tripathi, V. K. 1974a Self Focusing of Laser Beams in Dielectrics, Semiconductors and Plasmas. Delhi: Tata McGraw Hill.Google Scholar
Sodha, M. S., Ghatak, A. K. and Tripathi, V. K. 1976a Self Focusing of Laser Beams in Plasmas and Semiconductors (Progr. Opt., 13) (ed. Wolf, E.). New York: Elsevier, p. 169.Google Scholar
Sodha, M. S., Govind, and Sharma, R. P. 1979a Cross-focusing of two coaxial Gaussian EM beams in a magnetoplasma and plasma wave generation. Plasma Physics 21, 13.Google Scholar
Sodha, M. S. and Kaw, P. K. 1969 Theory of the generation of harmonics and combination frequencies in a plasma. Adv. Electron. Electron Phys. 27, 187.CrossRefGoogle Scholar
Sodha, M. S., Khanna, R. K. and Tripathi, V. K. 1974b The self-focusing of EM beams in a strongly ionized magnetoplasma. J. Phys. D: Appl. Phys. 7, 2188.CrossRefGoogle Scholar
Sodha, M. S., Mittal, R. S., Kumar, S. and Tripathi, V. K. 1974c Self-focusing of electromagnetic waves in a magnetoplasma. Opto Electronics 6, 167.CrossRefGoogle Scholar
Sodha, M. S. and Patel, L. A. 1980 Self-focusing of a laser beam in a magnetoplasma. Opt. Acta 27, 783.CrossRefGoogle Scholar
Sodha, M. S. and Sharma, A. 2006 Stationary self-focusing of Gaussian electromagnetic beams in the ionosphere. Rad. Sc. 41, RS4008.Google Scholar
Sodha, M. S. and Sharma, A. 2007 Comparison of two approaches to the study of filamentation in plasmas. Phys. Plasmas 14, 044501.CrossRefGoogle Scholar
Sodha, M. S., Sharma, A. and Agarwal, S. K. 2007a Focusing of electromagnetic beams in ionosphere with thermal conduction. J. Geophys. Res. 112, A03302.CrossRefGoogle Scholar
Sodha, M. S., Sharma, R. P., Kaushik, S. C. and Maheshwari, K. P. 1978 Filamentation of extraordinary and ordinary modes in a magnetoplasma. J. Plasma Physics 20, 585.CrossRefGoogle Scholar
Sodha, M. S., Sharma, R. P., Kumar, S. and Tripathi, V. K. 1976b Cross-focusing of extraordinary and ordinary modes in a magnetoplasma. Opt. Acta 23, 305.CrossRefGoogle Scholar
Sodha, M. S., Sharma, J. K., Kumar, S. and Tripathi, V. K. 1979 b Anomalous penetration of laser radiation in an overdense magnetoplasma. J. Appl. Phys. 50, 2638.CrossRefGoogle Scholar
Sodha, M. S., Sharma, A., Verma, M. P. and Faisal, M. 2007 b Self focusing instability in ionospheric plasma with thermal conduction. Phys. Plasmas 14, 052901.CrossRefGoogle Scholar
Sodha, M. S., Sinha, S. K. and Sharma, R. P. 1979 c The self-focusing of laser beams in magnetoplasma: the moment theory approach. J. Phys. D: Appl. Phys. 12, 1079.CrossRefGoogle Scholar
Sodha, M. S. and Tripathi, V. K. 1977 Steady state self-focusing and filamentation of whistlers in a plasma. J. Appl. Phys. 48, 1078.CrossRefGoogle Scholar
Sodha, M. S., Verma, M. P. and Sharma, A. 2005 Phase matching for third harmonic generation in collisional magnetoplasma. Phys. Plasmas 12, 112302.CrossRefGoogle Scholar
Umstadter, D. 2001 Review of physics and applications of relativistic plasmas driven by ultra-intense lasers. Phys. Plasmas 8, 1774.CrossRefGoogle Scholar