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Relativistic Gaussian laser beam self-focusing in collisional quantum plasmas

Published online by Cambridge University Press:  04 May 2015

S. Zare
Department of Physics, Sharif University of Technology, Tehran, Iran
S. Rezaee
Department of Physics, Sharif University of Technology, Tehran, Iran
E. Yazdani
Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran
A. Anvari
Department of Physics, Sharif University of Technology, Tehran, Iran
R. Sadighi-Bonabi*
Department of Physics, Sharif University of Technology, Tehran, Iran
Address correspondence and reprint requests to: R. Sadighi-Bonabi, Department of Physics, Sharif University of Technology, P.O. Box 11365-9567, Tehran, Iran. E-mail:


Propagation of Gaussian X-ray laser beam is presented in collisional quantum plasma and the beam width oscillation is studied along the propagation direction. It is noticed that due to energy absorption in collisional plasma, the laser energy drops to an amount less than the critical value of the self-focusing effect and consequently, the laser beam defocuses. It is found that the oscillation amplitude of the laser spot size enhances while passing through collisional plasma. For the greater values of collision frequency, the beam width oscillates with higher amplitude and defocuses in a shallower plasma depth. Also, it is realized that in a dense plasma environment, the laser self-focusing occurs earlier with the higher oscillation amplitude, smaller laser spot size and more oscillations.

Research Article
Copyright © Cambridge University Press 2015 

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Akhmanov, S.A., Sukhorukov, A.P. & Khokhlov, R.V. (1968). Self-focusing and diffraction of light in a nonlinear medium. Phys. – Usp. 10, 609636.CrossRefGoogle Scholar
Ali, S. & Shukla, P.K. (2006). Potential distributions around a moving test charge in quantum plasmas. Phys. Plasmas 13, 102112.CrossRefGoogle Scholar
Andreev, A.V. (2000). Self-consistent equations for the interaction of an atom with an electromagnetic field of arbitrary intensity. JETP Lett. 72, 238240.CrossRefGoogle Scholar
Ang, L.K., Koh, W.S., Lau, Y.Y. & Kwan, T.J.T. (2006). Space-charge-limited flows in the quantum regime. Phys. Plasmas 13, 056701.CrossRefGoogle Scholar
Ang, L.K. & Zhang, P. (2007). Ultrashort-pulse Child–Langmuir law in the quantum and relativistic regimes. Phys. Rev. Lett. 98, 164802.CrossRefGoogle Scholar
Azechi, H. (2006). Present status of the FIREX programme for the demonstration of ignition and burn. Plasma Phys. Control. Fusion 48, B267.CrossRefGoogle Scholar
Badziak, J., Glowacz, S., Hora, H., Jablonski, S. & Wolowski, J. (2006). Studies on laser-driven generation of fast high-density plasma blocks for fast ignition. Laser Part. Beams 24, 249254.CrossRefGoogle Scholar
Barnes, W.L., Dereux, A. & Ebbesen, T.W. (2003). Surface plasmon sub-wavelength optics. Nature (London) 424, 824.CrossRefGoogle Scholar
Becker, K., Koutsospyros, K., Yin, S.M., Christodoulatos, C., Abramzon, N., Joaquin, J.C. & Brelles-Mariño, G. (2005). Environmental and biological applications of microplasmas. Plasma Phys. Control. Fusion 47, B513.CrossRefGoogle Scholar
Becker, K.H., H., Schoenbach, K. & Eden, J.G. (2006). Microplasmas and applications. J. Phys. D. Appl. Phys. 39, R55.CrossRefGoogle Scholar
Boyd, R.W., Lukishova, S.G. & Shen, Y.R. (2008). Self-focusing: Past and Present: Fundamentals and Prospects. Vol. 114, New York: Springer.Google Scholar
Bulanov, S.V., Esirkepov, T.Z., Habs, D., Pegoraro, F. & Tajima, T. (2009). Relativistic laser-matter interaction and relativistic laboratory astrophysics. Eur. Phys. J. D 55, 483507.CrossRefGoogle Scholar
Chabrier, G., Douchin, F. & Potekhin, A.Y. (2002). Dense astrophysical plasmas J. Phys. Condens. Matter 14, 9133.CrossRefGoogle Scholar
Chandra, S. & Ghosh, B. (2012). Modulational instability of electron plasma waves in finite temperature quantum plasma. World Acad. Sci. Eng. Tech. 71, 792.Google Scholar
Chandra, S., Paul, S.N. & Ghosh, B. (2012). Linear and non-linear propagation of electron plasma waves in quantum plasma. Indian J. Pure Appl. Phys. 50, 314.Google Scholar
Eliasson, B. & Shukla, P.K. (2008). Nonlinear quantum fluid equations for a finite temperature. Fermi Plasma. Phys. Scr. 78, 025503.CrossRefGoogle Scholar
Etehadi Abari, M. & Shokri, B. (2012). Study of nonlinear ohmic heating and ponderomotive force effects on the self focusing and defocusing of Gaussian laser beams in collisional under dense plasmas. Phys. Plasma 19, 113107.CrossRefGoogle Scholar
Faure, J., Malka, V., Marquès, J.-R., David, P.-G., Amiranoff, F., Ta Phuoc, K. & Rousse, A. (2002). Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas. Phys. Plasmas 9, 756759.CrossRefGoogle Scholar
Ghosh, B., Chandra, S. & Paul, S.N. (2012). Relativistic effects on the modulational instability of electron plasma waves in quantum plasma. Pramana J. Phys. 78, 779790.CrossRefGoogle Scholar
Glenzer, S.H. & Redmer, R. (2009). X-ray Thomson scattering in high energy density plasmas. Rev. Mod. Phys. 81, 16251663.CrossRefGoogle Scholar
Gupta, N., Islam, M.R., Jang, D.G., Suk, H. & Jaroszynski, D.A. (2013). Self-focusing of a high-intensity laser in a collisional plasma under weak relativistic-ponderomotive nonlinearity. Phys. Plasmas 20, 123103.CrossRefGoogle Scholar
Habibi, M. & Ghamari, F. (2014). Relativistic self-focusing of ultra-high intensity X-ray laser beams in warm quantum plasma with upward density profile. Phys. Plasmas 21, 052705.CrossRefGoogle Scholar
Hillery, M., O'Connell, R.F., Scully, M.O. & Wigner, E.P. (1984). Distribution functions in physics: Fundamentals. Phys. Rep. 106, 121167.CrossRefGoogle Scholar
Hora, H. (1975). Theory of relativistic self-focusing of laser radiation in plasmas. J. Opt. Soc. Am. 65, 882886.CrossRefGoogle Scholar
Hora, H. (1985). The transient electrodynamic forces at laser–plasma interaction. Phys. Fluids 28, 37053706.CrossRefGoogle Scholar
Hu, S.X. & Keitel, C.H. (1999). Spin signatures in intense laser–ion interaction. Phys. Rev. Lett. 83, 47094712.CrossRefGoogle Scholar
Hussain, S. & Mahmood, S. (2011). Magnetoacoustic solitons in quantum plasma. Phys. Plasmas 18, 082109.CrossRefGoogle Scholar
Jafari Milani, M.R., Niknam, A.R. & Farahbod, A.H. (2014). Ponderomotive self-focusing of Gaussian laser beam in warm collisional plasma. Phys. Plasmas 21, 063107.CrossRefGoogle Scholar
Kaur, S. & Sharma, A.K. (2009). Self focusing of a laser pulse in plasma with periodic density ripple. Laser Part. Beams 27, 193199.CrossRefGoogle Scholar
Killian, T.C. (2006). Experiments in Botany. Nature (London) 441, 298.Google Scholar
Koyama, K., Adachi, M., Miura, E., Kato, S., Masuda, S., Watanabe, T., Tanimoto, M. (2006). Monoenergetic electron beam generation from a laser-plasma accelerator. Laser Part. Beams 24, 95100.CrossRefGoogle Scholar
Kozlov, V.V. & Smolyanov, O.G. (2007). Wigner function and diffusion in a collision-free medium of quantum particles. Theory Probab. Appl. 51, 168181.CrossRefGoogle Scholar
Kremp, D., Bornath, T., Bonitz, M. & Schlanges, M. (1999). Quantum kinetic theory of plasmas in strong laser fields. Phys. Rev. E 60, 47254732.CrossRefGoogle ScholarPubMed
Kremp, D., Schlanges, M. & Kraft, W.D. (2005). Quantum Statistics of Nonideal Plasmas. Berlin: Springer.Google Scholar
Landau, L.D. & Lifshitz, E.M. (1980). Statistical Physics. Oxford: Butterworth-Heinemann, pp. 19081968.Google Scholar
Latyshev, A.V. & Yushkanov, A.A. (2014). Longitudinal electric conductivity in a quantum plasma with a variable collision frequency in the framework of the Mermin approach. Theor. Math. Phys. 178, 130141.CrossRefGoogle Scholar
Manfredi, G. (2005). How to model quantum plasmas. Fields Inst. Commun. 46, 263287.Google Scholar
Marklund, M. (2005). Classical and quantum kinetics of the Zakharov system. Phys. Plasmas 12, 082110.CrossRefGoogle Scholar
Marklund, M. & Brodin, G. (2007). Dynamics of spin-1/2 quantum plasmas. Phys. Rev. Lett. 98, 025001.CrossRefGoogle ScholarPubMed
Marklund, M. & Shukla, P.K. (2006). Nonlinear collective effects in photon-photon and photon-plasma interactions. Rev. Mod. Phys. 78, 591640.CrossRefGoogle Scholar
Markowich, P.A., Ringhofer, C.A. & Schmeiser, C. (1990). Semiconductor Equations. New York: Springer-Verlag.CrossRefGoogle Scholar
Mermin, N.D. (1970). Lindhard dielectric function in the relaxation-time approximation. Phys. Rev. B 1, 23622363.CrossRefGoogle Scholar
Na, S.C. & Jung, Y.-D. (2009). Temperature effects on the nonstationary Karpman–Washimi ponderomotive magnetization in quantum plasmas. Phys. Plasmas 16, 074504.CrossRefGoogle Scholar
Opher, M., Silva, L.O., Dauger, D.E., Decyk, V.K. & Dawson, J.M. (2001). Nuclear reaction rates and energy in stellar plasmas: The effect of highly damped modes. Phys. Plasmas 8, 24542460.CrossRefGoogle Scholar
Patil, S.D. & Takale, M.V. (2013). Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma. Phys. Plasmas 20, 072703.CrossRefGoogle Scholar
Patil, S.D., Takale, M.V., Navare, S.T., Dongare, M.B. & Fulari, V.J. (2013). Self-focusing of Gaussian laser beam in relativistic cold quantum plasma. Optik – Int. J. Light Electron Opt. 124, 180183.CrossRefGoogle Scholar
Prakash, G. (2005). Focusing of an intense Gaussian laser beam in a radially inhomogeneous medium. J. Opt. Soc. Am. B 22, 12681275.CrossRefGoogle Scholar
Pukhov, A. (2003). Strong field interaction of laser radiation. Rep. Progress Phys. 66, 47.CrossRefGoogle Scholar
Sadighi-Bonabi, R., Habibi, M. & Yazdani, E. (2009). Improving the relativistic self-focusing of intense laser beam in plasma using density transition. Phys. Plasmas 16, 083105.CrossRefGoogle Scholar
Sari, A.H., Osman, F., Doolan, K.R., Ghoranneviss, M., Hora, H., Höpfl, R., Hantehzadeh, M.H. (2005). Application of laser driven fast high density plasma blocks for ion implantation. Laser Part. Beams 23, 467473.CrossRefGoogle Scholar
Schlenvoigt, H.-P., Haupt, K., Debus, A., Budde, F., Jäckel, O., Pfotenhauer, S., Brunetti, E. (2007). A compact synchrotron radiation source driven by a laser-plasma wakefield accelerator. Nat. Phys. 4, 130133.CrossRefGoogle Scholar
Sharma, A. & Kourakis, A. (2010). Relativistic laser pulse compression in plasmas with a linear axial density gradient. Plasma Phys. Control. Fusion 52, 065002.CrossRefGoogle Scholar
Sharma, A., Prakash, G., Verma, M. & Sodha, M. (2003). Three regimes of intense laser beam propagation in plasmas. Phys. Plasmas 10, 40794084.CrossRefGoogle Scholar
Shukla, P.K. (2009). Plasma physics: A new spin on quantum plasmas. Nat. Phys. 5, 9293.CrossRefGoogle Scholar
Shukla, P.K., Ali, S., Stenflo, L. & Marklund, M. (2006). Nonlinear wave interactions in quantum magnetoplasmas. Phys. Plasmas 13, 112111.CrossRefGoogle Scholar
Shukla, P.K. & Eliasson, B. (2010). Nonlinear aspects of quantum plasma physics. Phys. – Usp. 53, 51.CrossRefGoogle Scholar
Shukla, P.K. & Stenflo, L. (2006). Stimulated scattering instabilities of electromagnetic waves in an ultracold quantum plasma. Phys. Plasmas 13, 044505.CrossRefGoogle Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1974). Self Focusing of Laser Beams in Dielectrics, Semiconductors and Plasmas. Tata McGraw-Hill, New Delhi.Google Scholar
Sodha, M.S. & Sharma, A. (2006). Mutual focusing/defocusing of Gaussian electromagnetic beams in collisional plasmas. Phys. Plasmas 13, 053105.CrossRefGoogle Scholar
Upadhyay, A., Tripathi, V.K., Sharma, K. & Pant, H.C. (2002). Asymmetric self-focusing of a laser pulse in plasma. J. Plasma Phys. 68, 7580.CrossRefGoogle Scholar
Varshney, M., Qureshi, K.A. & Varshney, D. (2006). Relativistic self-focusing of a laser beam in an inhomogeneous plasma. J. Plasma Phys. 72, 195203.Google Scholar
Wang, Y., Yuan, C., Zhou, Z., Li, L. & Du, Y. (2011). Propagation of Gaussian laser beam in cold plasma of Drude model. Phys. Plasmas 18, 113105.CrossRefGoogle Scholar
Wigner, E. (1932). On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749759.CrossRefGoogle Scholar