Skip to main content

Effect of q Parameter and Critical Beam Radius on Propagation Dynamics of q Gaussian Beam in Cold Quantum Plasma

  • Conference paper
  • First Online:
Nonlinear Dynamics and Applications


The q Gaussian intensity distribution is very interesting as in the limit \( q \rightarrow \infty \), it reduces to the Gaussian intensity profile. Naturally, the freedom of exploring the q exponent enables us to study a wide range of propagation dynamics. The quantum plasma offers wide possibilities of its existence right from astrophysical situations to laboratory plasmas. Keeping in mind the wide applicability domain of cold quantum plasma, we have theoretically investigated the propagation behavior of q Gaussian laser beam in cold quantum plasma. The ordinary nonlinear differential equation is set up by following Akhmanov’s parabolic equation approach under WKB and paraxial approximations. The effect of the q parameter on the critical curve is explored graphically. The variation in the beam width parameter f over normalized distance \(\zeta \) due to variation in the q-parameter is graphically depicted and discussed at the end. It is observed that the supercritical region and self focusing length are affected by the q parameter significantly.

Supported by DST-SERB, New Delhi, the Special Assistance Program (SAP), Department of Physics, Shivaji University, Kolhapur.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  1. Deutsch, C., Furukawa, H., Mima, K., Murakami, M., Nishihara, K.: Interaction physics of the fast ignitor concept. Phys. Rev. Lett. 77, 2483 (1996).

  2. Tabak, M., Hammer, J., Glinsky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D., Mason, R.J.: Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626 (1994).

  3. Regan, S.P., Bradley, D.K., Chirokikh, A.V., Craxton, R.S., Meyerhofer, D.D., Seka, W., Short, R.W., Simon, A., Town, R.P.J., Yaakobi, B.: Laser-plasma interactions in long-scale-length plasmas under direct-drive National Ignition Facility conditions. Phys. Plasmas 6, 2072 (1999).

    Article  ADS  Google Scholar 

  4. Malka, V.: Laser plasma accelerators. Phys. Plasmas 19, 055501 (2012).

  5. Wiggins, S.M., Issac, R.C., Welsh, G.H., Brunetti, E., Shanks, R.P., Anania, M.P., Cipiccia, S., Manahan, G.G., Aniculaesei, C., Ersfeld, B., Islam, M.R., Burgess, R.T.L., Vieux, G., Gillespie, W.A., MacLeod, A.M., van der Geer, S.B., de Loos, M.J., Jaroszynski, D.A.: High quality electron beams from a laser wakefield accelerator. Plasma Phys. Control. Fus. 52, 124032 (2010).

  6. Fiuza, F., Stockem, A., Boella, E., Fonseca, R.A., Silva, L.O., Haberberger, D., Tochitsky, S., Gong, C., Mori, W.B., Joshi, C.: Laser-driven shock acceleration of monoenergetic ion beams. Phys. Rev. Lett. 109, 215001 (2012).

    Article  ADS  Google Scholar 

  7. Hooker, S.M.: Developments in laser-driven plasma accelerators. Nat. Photonics 7, 775 (2013).

    Article  ADS  Google Scholar 

  8. Sprangle, P., Esarey, E., Ting, A.: Nonlinear theory of intense laser-plasma interactions. Phys. Rev. Lett. 64, 2011 (1990).

    Article  ADS  Google Scholar 

  9. Ferrari, H.E., Lifschitz, A.F., Maynard, G., Cros B.: Electron acceleration by laser wakefield and X-ray emission at moderate intensity and density in long plasmas. Phys. Plasmas 18, 083108 (2011).

  10. Liu, Y., Dong, Q., Peng, X., Jin, Z., Zhang, J.: Soft X-ray emission, angular distribution of hot electrons, and absorption studies of argon clusters in intense laser pulses. Phys. Plasmas 16, 043301 (2009).

    Article  ADS  Google Scholar 

  11. Bagchi, S., Kiran, P.P., Yang, K., Rao, A.M., Bhuyan, M.K., Krishnamurthy, M., Kumar, G.R.: Bright, low debris, ultrashort hard x-ray table top source using carbon nanotubes. Phys. Plasmas 18, 014502 (2011).

    Article  ADS  Google Scholar 

  12. Patil, S.D., Takale, M.V., Navare, S.T., Dongare, M.B., Fulari, V.J.: Self-focusing of Gaussian laser beam in relativistic cold quantum plasma. Optik 124, 180–183(2013).

  13. Habibi, M., Ghamari, F.: Stationary self-focusing of intense laser beam in cold quantum plasma using ramp density profile. Phys. Plasmas 19, 103110 (2012).

  14. Walia, K., Tripathi, D.: Self-focusing of elliptical laser beam in cold quantum plasma. Optik 186, 46–51(2019).

  15. Thakur, V., Kant, N.: Combined effect of chirp and exponential density ramp on relativistic self-focusing of Hermite-Cosine-Gaussian laser in collisionless cold quantum plasma. Braz. J. Phys. 49, 113–118 (2019).

  16. Habibi, M., Ghamari, F.: Improved focusing of a Cosh-Gaussian laser beam in quantum plasma: higher order paraxial theory. IEEE Trans. Plasma Sci. 43, 2160–2165 (2015).

  17. Patel, P.K., Key, M.H., MacKinnon, A.J., Berry, R., Borghesi, M., Chambers, D.M., Chen, H., Clarke, R., Damian, C., Eagleton, R., Freeman, R., Glenzer, S., Gregori, G., Heathcote, R., Hey, D., Izumi, N., Kar, S., King, J., Nikroo, A., Niles, A., Park, H.S., Pasley, J., Patel, N., Shepherd, R., Snavely, R.A., Steinman, D., Stoeckl, C., Storm, M., Theobald, W., Town, R., Van Maren, R., Wilks, S.C., Zhang, B.: Integrated laser-target interaction experiments on the RAL petawatt laser. Plasma Phys. Control Fus. 47, B833–B840 (2005).

  18. Nakatsutsumi, M., Davies, J.R., Kodama, R.: Space and time resolved measurements of the heating of solids to ten million kelvin by a petawatt laser. New J. Phys. 10, 043046 (2008).

  19. Sharma, A., Kourakis, I.: Spatial evolution of a q-Gaussian laser beam in relativistic plasma. Laser Part. Beams 28, 479–489 (2010).

  20. Kaur, R., Gill, T.S.: Relativistic effects on evolution of a q-Gaussian laser beam in magnetoplasma: application of higher order corrections. Phys. Plasmas 24, 053105 (2017).

  21. Wang, L., Hong, X.-R., Sun, J.-A., Tang, R.-A., Yang, Y., Zhou, W.-J., Tian, J.-M., Duan, W.-S.: Effects of relativistic and channel focusing on q-Gaussian laser beam propagating in a preformed parabolic plasma channel. Phys. Lett. A, 381, 2065–2071 (2017).

  22. Valkunde, A.T., Vhanmore, B.D., Urunkar, T.U., Gavade, K.M., Patil, S.D., Takale, M.V.: Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma. AIP Conf. Proc. 1953, 140088 (2018).

  23. Vhanmore, B.D., Patil, S.D., Valkunde, A.T., Urunkar, T.U., Gavade, K.M., Takale, M.V., Gupta, D.N.: Effect of q-parameter on relativistic self focusing of q Gaussian laser beam in plasma. Optik 158, 574–579 (2018).

  24. Kashyp, R., Aggrawal, M., Gill, T.S., Arora, N.S., Kumar, H., Moudhagill, D.: Self-focusing of q-Gaussian laser beam in relativistic plasma under the effect of light absorption. Optik Int. J. Light Electron. Opt. 182, 1030–1038 (2019).

  25. Gupta, N., Kumar, S.: Generation of second harmonics of relativistically self-focused q-Gaussian laser beams in underdense plasma with axial density ramp. Opt. Quant. Electron. 53, 193 (2021).

    Article  Google Scholar 

  26. Gupta, N.: Second harmonic generation of q-Gaussian laser beam in plasma channel created by ignitor heater technique. Laser Part. Beams 37, 184–196 (2019).

  27. Akhmanov, S.A., Sukhorukov, A.P., Khokhlov, R.V.: Self-focusing and diffraction of light in a nonlinear medium. Sov. Phys. Uspekhi 10(5), 609–636 (1968).

    Article  ADS  Google Scholar 

  28. Sodha, M.S., Ghatak, A.K., Tripathi, V.K.: Self focusing of laser beams in plasmas and semiconductors. Prog. Opt. 13, 169–265 (1976).

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to P. T. Takale .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Takale, P.T. et al. (2022). Effect of q Parameter and Critical Beam Radius on Propagation Dynamics of q Gaussian Beam in Cold Quantum Plasma. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham.

Download citation

Publish with us

Policies and ethics