Skip to main content
SpringerLink
Log in

Effect of an external magnetic field on the self-focusing of a cosh-Gaussian laser beam in plasma under the relativistic-ponderomotive effect

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

This work presents an analytical and numerical study of the relativistic-ponderomotive effect on self-focusing of an intense cosh-Gaussian laser beam in a collisionless magnetized plasma by considering an external magnetic field in the direction of propagation of the laser beam. The nonlinear differential equation for the beam width parameter/intensity of a cosh-Gaussian laser beam in a magnetized plasma is obtained by Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations. The self-focusing of the cosh-Gaussian beam at different values of the magnetic field parameter is investigated. The results have also been compared to relativistic nonlinearity. The results show that the self-focusing effect of cosh-Gaussian beam in magnetized plasma becomes stronger, when relativistic and ponderomotive nonlinearities acts together. In addition, the self-trapping of cosh-Gaussian beam in magnetized plasma has also been studied. Numerical results are presented for the well-established laser and plasma parameters.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Availability of data and materials

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

  • Abedi-Varaki, M.: The effect of the wiggler magnetic field strength on the self-focusing of an intense laser pulse propagating through a magnetized non-Maxwellian plasma. Phys. Plasmas 24, 122308 (2017)

    Google Scholar 

  • Abedi-Varaki, M.: Effect of obliquely external magnetic field on the intense laser pulse propagating in plasma medium. Int. J. Mod. Phys. B 34, 2050044 (2020)

    ADS  MathSciNet  Google Scholar 

  • Abedi-Varaki, M., Jafari, S.: Self-focusing and de-focusing of intense left- and right-hand polarized laser pulse in hot magnetized plasma in the presence of an external non-uniform magnetized field. Braz. J. Phys. 47, 473–480 (2017)

    ADS  Google Scholar 

  • Aggarwal, M., Vij, S., Kant, N.: Propagation of cosh Gaussian laser beam in plasma with density ripple in relativistic-ponderomotive regime. Optik 125, 5081–5084 (2014)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  • Banerjee, S., Valenzuela, A.R., Shah, R.C., Maksimchuk, A., Umstadter, D.: High harmonic generation in relativistic laser–plasma interaction. Phys. Plasmas 9, 2393–2398 (2002)

    ADS  Google Scholar 

  • Betti, R., Hurricane, O.: Inertial-confinement fusion with lasers. Nat. Phys. 12, 435–448 (2016)

    Google Scholar 

  • Borghesi, M., Mackinnon, A.J., Gaillard, R., Willi, O., Pukhov, A., Meyer-ter-Vehn, J.: Large quasistatic magnetic fields generated by a relativistically intense laser pulse propagating in a preionized plasma. Phys. Rev. Lett. 80, 5137–5140 (1998)

    ADS  Google Scholar 

  • Brandi, H.S., Manus, C., Mainfray, G., Lehner, T., Bonnaud, G.: Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma I. Paraxial approximation. Phys. Fluids B 5, 3539–3550 (1994)

    ADS  Google Scholar 

  • Corde, S., Ta Phuoc, K., Lambert, G., Fitour, R., Malka, V., Rousse, A., Beck, A., Lefebvre, E.: Femtosecond X-rays from laser-plasma accelerators. Rev. Mod. Phys. 85, 1–48 (2013)

    ADS  Google Scholar 

  • Devi, L., Malik, H.K.: Role of magnetic field on self-focusing of super-Gaussian laser beam under relativistic effect. Optik 207, 164439 (2020)

    ADS  Google Scholar 

  • Esarey, E., Schroeder, C.B., Leemans, W.P.: Physics of laser-driven plasma-based electron accelerators. Rev. Mod. Phys. 81, 1229–1286 (2009)

    ADS  Google Scholar 

  • Feit, M.D., Komashko, A.M., Rubenchik, A.M.: Relativistic self-focusing in underdense plasma. Physica D 152–153, 705–713 (2001)

    ADS  MATH  Google Scholar 

  • Fuchs, J., Malka, G., Adam, J.C., Amiranoff, F., Baton, S.D., Blanchot, N., Héron, A., Laval, G., Miquel, J.L., Mora, P., Pépin, H., Rousseaux, C.: Dynamics of subpicosecond relativistic laser pulse self-channeling in an underdense preformed plasma. Phys. Rev. Lett. 80, 1658–1661 (1998)

    ADS  Google Scholar 

  • Gill, T.S., Mahajan, R., Kaur, R.: Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic and ponderomotive regime. Phys. Plasmas 18, 033110 (2011)

    ADS  Google Scholar 

  • Gill, T.S., Kaur, R., Mahajan, R.: Self-focusing of super-Gaussian laser beam in magnetized plasma under relativistic and ponderomotive regime. Optik 126, 1683–1690 (2015)

    ADS  Google Scholar 

  • Gupta, N., Bhardwaj, S.B.: Nonlinear interaction of Bessel–Gauss laser beams with plasmas with axial temperature ramp. J. Opt. 51, 950–959 (2022)

    Google Scholar 

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

    Google Scholar 

  • Gupta, N., Kumar, S.: Nonlinear interaction of elliptical q-Gaussian laser beams with plasmas with axial density ramp: effect of ponderomotive force. Opt. Quantum Electron. 53, 253 (2021b)

    Google Scholar 

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

    ADS  Google Scholar 

  • Hora, H.: Theory of relativistic self-focusing of laser radiation in plasmas. J. Opt. Soc. Am. 65, 882–886 (1975)

    ADS  Google Scholar 

  • Jafari Milani, M.R., Niknam, A.R., Farahbod, A.H.: Ponderomotive self-focusing of Gaussian laser beam in warm collisional plasma. Phys. Plasmas 21, 063107 (2014)

    ADS  Google Scholar 

  • Jaroszynski, D.A., Bingham, R., Brunetti, E., Ersfeld, B., Gallacher, J., van der Geer, B., Issac, R., Jamison, S.P., Jones, D., de Loos, M., Lyachev, A., Pavlov, V., Reitsma, A., Saveliev, Y., Vieux, G., Wiggins, S.M.: Radiation sources based on laser–plasma interactions. Philos. Trans. r. Soc. A 364, 689–710 (2006)

    ADS  Google Scholar 

  • Jha, P., Mishra, R.K., Upadhyaya, A.K., Raj, G.: Self-focusing of intense laser beam in magnetized plasma. Phy. Plasmas 13, 103102 (2006)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  • Konar, S., Mishra, M., Jana, S.: Nonlinear evolution of cosh-Gaussian laser beams and generation of flat top spatial solitons in cubic quintic nonlinear media. Phys. Lett. A 362, 505–510 (2007)

    ADS  Google Scholar 

  • Kruer, W.L.: The Physics of Laser Plasma Interaction. Addison-Wesley, New York (1988)

    Google Scholar 

  • Lei, A.L., Tanaka, K.A., Kodama, R., Adumi, K., Habara, H., Kitagawa, Y., Kondo, K., Matsuoka, T., Tanimoto, T., Yabuuchi, T., Mima, K., Nagai, K., Nagatomo, H., Norimatsu, T., Sawai, K., Suzuki, K., Yu, W., Xu, H., Yang, X.O., Cao, L.H., Cai, H.B., Sentoku, Y., Pukhov, A., Kumar, R., Snavely, R., Freeman, R., Yu, M., Zheng, J.: Study of ultra-intense laser propagation in overdense plasmas for fast ignition. Phys. Plasmas 16, 056307 (2009)

    ADS  Google Scholar 

  • Liao, G.-Q., Tong, Y.: Review of intense terahertz radiation from relativistic laser produced plasmas. IEEE Trans. Plasma Sci. 47, 3002–3008 (2019)

    ADS  Google Scholar 

  • Malekshahi, M., Dorranian, D., Askari, H.R.: Self-focusing of the high intensity ultra-short laser pulse propagating through relativistic magnetized plasma. Opt. Commun. 332, 227–232 (2014)

    ADS  Google Scholar 

  • Mori, W.B., Joshi, C., Dawson, J.M., Forslund, D.W., Kindel, J.M.: Evolution of self-focusing of intense electromagnetic waves in plasma. Phys. Rev. Lett. 60, 1298–1301 (1988)

    ADS  Google Scholar 

  • Nanda, V., Kant, N.: Strong self-focusing of a cosh-Gaussian laser beam in collisionless magneto-plasma under plasma density ramp. Phys. Plasmas 21, 072111 (2014)

    ADS  Google Scholar 

  • Patil, S.D., Takale, M.V., Navare, S.T., Fulari, V.J., Dongare, M.B.: Relativistic self-focusing of cosh-Gaussian laser beams in a plasma. Opt. Laser Tech. 44, 314–317 (2012)

    ADS  Google Scholar 

  • Patil, S.D., Takale, M.V., Fulari, V.J., Gupta, D.N., Suk, H.: Combined effect of ponderomotive and relativistic self-focusing on laser beam propagation in a plasma. Appl. Phys. B 111, 1–6 (2013)

    ADS  Google Scholar 

  • Purohit, G., Gaur, B.: Self-focusing of cosh-Gaussian laser beam and its effect on the excitation of ion-acoustic wave and stimulated Brillouin backscattering in collisionless plasma. Opt. Quantum Electron. 51, 398 (2019)

    Google Scholar 

  • Purohit, G., Sharma, R.K., Kothiyal, P.: Relativistic-ponderomotive effect on the self-focusing of a high-intensity cosh-Gaussian laser beam in plasma: higher-order paraxial regime. J. Opt. (2022). https://doi.org/10.1007/s12596-022-00931-y

    Article  Google Scholar 

  • Rawat, P., Purohit, G.: Self-focusing of a cosh-Gaussian laser beam in magnetized plasma under relativistic-ponderomotive regime. Contrib. Plasma Phys. 59, 226–235 (2018)

    ADS  Google Scholar 

  • Rawat, P., Rawat, V., Gaur, B., Purohit, G.: Generation of terahertz radiation by intense hollow Gaussian laser beam in magnetized plasma under relativistic-ponderomotive regime. Phys. Plasmas 24, 073113 (2017)

    ADS  Google Scholar 

  • Sharma, A., Tripathi, V.K.: Relativistic and ponderomotive self-focusing of a laser pulse in magnetized plasma. Laser Part. Beams 30, 659–664 (2012)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  • Startsev, E.A., Mc Kinstrie, C.J.: Multiple scale derivation of the relativistic ponderomotive force. Phys. Rev. E 55, 7527–7535 (1997)

    ADS  Google Scholar 

  • Sun, G.Z., Ott, E., Lee, Y.C., Guzdar, P.: Self-focusing of short intense pulses in plasmas. Phys. Fluids 30, 526–532 (1987)

    ADS  Google Scholar 

  • Vhanmore, B.D., Valkunde, A.T., Urunkar, T.U., Gavade, K.M., Patil, S.D., Takale, M.V.: Self-focusing of higher-order asymmetric elegant hermite-cosh-Gaussian laser beams in collisionless magnetized plasma. Eur. Phys. J. D 73, 45 (2019)

    ADS  Google Scholar 

  • Wang, Y., Zhou, Z.: Propagation characters of Gaussian laser beams in collisionless plasma: Effect of plasma temperature. Phys. Plasmas 18, 043101 (2011)

    ADS  Google Scholar 

  • Wilson, T.C., Li, F.Y., Weikum, M., Sheng, Z.M.: Influence of strong magnetic fields on laser pulse propagation in underdense plasma. Plasma Phys. Control. Fusion 59, 065002 (2017)

    ADS  Google Scholar 

  • Zare, S., Yazdani, E., Rezaee, S., Anvari, A., Sadighi-Bonabi, R.: Relativistic self-focusing of intense laser beam in thermal collisionless quantum plasma with ramped density profile. Phys. Rev. ST Accel. Beams 18, 041301 (2015)

    ADS  Google Scholar 

Download references

Funding

No funding was received for conducting this study.

Author information

Authors and Affiliations

  1. Laser Plasma Computational Laboratory, Department of Physics, DAV Post Graduate College, Dehradun, Uttarakhand, 248001, India

    Gunjan Purohit

Authors
  1. Gunjan Purohit
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Not applicable.

Corresponding author

Correspondence to Gunjan Purohit.

Ethics declarations

Conflict of interest

The author declares no conflict of interest.

Ethical approval

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Purohit, G. Effect of an external magnetic field on the self-focusing of a cosh-Gaussian laser beam in plasma under the relativistic-ponderomotive effect. Opt Quant Electron 55, 429 (2023). https://doi.org/10.1007/s11082-023-04717-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-04717-9

Keywords

Search

Navigation