Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-25T07:19:37.235Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear evolution of the filamentation instability and chaos in laser–plasma interaction

Published online by Cambridge University Press:  28 November 2016

S. Sharma ,
N. Kumar ,
S. Hussain  and
R.P. Sharma
S. Sharma
Affiliation:
Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, India
N. Kumar*
Affiliation:
Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, India Sri Venkateswara College, University of Delhi, New Delhi-110021, India
S. Hussain
Affiliation:
Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, India
R.P. Sharma
Affiliation:
Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, India
*
Address correspondence and reprint requests to: N. Kumar, Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, India and Sri Venkateswara College, University of Delhi, New Delhi-110021, India. E-mail: narenderk@svc.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

Filamentation is one of the most common nonlinear phenomena taking place in the laser–plasma interaction that splits the laser beam into high-intensity spikes. The present study deals with the nonlinear evolution of filamentation instability in laser–plasma interaction and the development of chaos in contrast to linear growth as reported by Kaw et al. in 1973. We have considered a non-uniform perturbation superimposed on plane-wave pump such that due to non-uniformity of the perturbation a finite intensity gradient arises and gives rise to ponderomotive force. This causes filamentation of wave, which has been studied presently using numerical methods as well as analytical tools. The results reveal that the intensity of perturbation gets localized and delocalized with the distance of propagation. The numerical simulation results also reveal that the intensity of perturbation route from ordered to chaotic behavior depending upon the pump laser and perturbation parameters. To study the chaotic behavior, Lyapunov exponents has also been calculated. The semi-analytical method is also developed to have an insight into some of the features of simulation like the formation of localized structures.

Keywords

Filamentation instabilityLyapunov exponentsPonderomotive nonlinearity
Type
Research Article
Information
Laser and Particle Beams , Volume 35 , Issue 1 , March 2017 , pp. 10 - 18
Copyright
Copyright © Cambridge University Press 2016 

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

Abbi, S.C. & Mahr, H. (1971). Correlation of filaments in nitrobenzene with laser spikes. Phys. Rev. Lett. 26, 604.CrossRefGoogle Scholar
Akhmanov, S.A., Sukhorukov, A.P. & Khokhlov, R.V. (1968). Self-focusing and diffraction of light in a nonlinear medium. Sov. Phys. – Usp. 10, 609.CrossRefGoogle Scholar
Aközbek, N., Scalora, M., Bowden, C.M. & Chin, S.L. (2001). White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air. Opt. Commun. 191, 353.CrossRefGoogle Scholar
Berge, L. (1998). Wave collapse in physics: principles and applications in light and plasma waves. Phys. Rep. 303, 259.CrossRefGoogle Scholar
Bingham, R., Mendonca, J.T. & Shukla, P.K. (2004). Plasma based charged-particle accelerators. Plasma Phys. Control. Fusion 46, R1–R23.CrossRefGoogle Scholar
Clayton, C.E., Everett, M.J., Lal, A., Gordon, D., Marsh, K.A. & Joshi, C. (1994). Acceleration and scattering of injected electrons in plasma beat wave accelerator experiments. Phys. Plasmas 1, 1753.CrossRefGoogle Scholar
Corkum, P.B., Rolland, C. & Rao, T. (1986). Supercontinuum generation in gases. Phys. Rev. Lett. 57, 2268.CrossRefGoogle ScholarPubMed
Deutsch, C., Furukawa, H., Mima, K., Murakami, M. & Nishihara, K. (1996). Interaction physics of the fast ignitor concept. Phys. Rev. Lett. 77, 2483.CrossRefGoogle ScholarPubMed
Eastabrook, K. (1976). Critical surface bubbles and corrugations and their implications to laser fusion. Phys Fluids 19, 1733.CrossRefGoogle Scholar
Faure, J., Malka, V., Marques, J.R. & Amiranoff, F. (2000). Interaction of an ultra-intense laser pulse with a nonuniform preformed plasma. Phys. Plasmas 7, 3009.CrossRefGoogle Scholar
Hamster, H., Sullivan, A., Gordon, S., White, W. & Falcone, R.W. (1993). Subpicosecond, electromagnetic pulses from intense laser–plasma interaction. Phys. Rev. Lett. 71, 2725.CrossRefGoogle ScholarPubMed
Infeld, E. (1981). Quantitive theory of the Fermi-Pasta-Ulam recurrence in the nonlinear Schrödinger equation. Phys. Rev. Lett. 47, 717.CrossRefGoogle Scholar
Karpowicz, N. & Zhang, X.C. (2009). Coherent terahertz echo of tunnel ionization in gases. Phys. Rev. Lett. 102, 093001.CrossRefGoogle ScholarPubMed
Kaw, P.K., Schmidt, G. & Wilcox, T. (1973). Filamentation and trapping of electromagnetic radiation in plasma. Phys. Fluids 16, 1522.CrossRefGoogle Scholar
Kelley, P.L. (1965). Self-focusing of optical beams. Phys. Rev. Lett. 15, 1005.CrossRefGoogle Scholar
Kodama, R., Takahashi, K., Tanaka, A., Tsukamoto, M., Hashimoto, H., Kato, Y. & Mima, K. (1996). Study of laser-hole boring into overdense plasmas. Phys. Rev. Lett. 77, 4906.CrossRefGoogle ScholarPubMed
Kostin, V.A. & Vvedenskii, N.V. (2010). Ionization-induced conversion of ultrashort Bessel beam to terahertz pulse. Opt. Lett. 35, 247.CrossRefGoogle ScholarPubMed
Kothari, N.C. & Abbi, S.C. (1990). Instability growth and filamentation of very intense laser beams in self-focusing media. Progr. Theor. Phys. 83, 414.CrossRefGoogle Scholar
Kruer, W.L. (1974). The Physics of Laser Plasma Interaction. New York: Addison-Wesley.Google Scholar
Langdon, B.A. & Lasinski, B.F. (1975). Filamentation and subsequent decay of laser light in plasmas. Phys. Rev. Lett. 34, 934.CrossRefGoogle Scholar
Lemoff, B.E., Yin, G.Y., Gordon, C.L. III, Barty, C.P.J. & Harris, S.E. (1995). Demonstration of a 10-Hz femtosecond-pulse-driven XUV laser at 41.8 nm in Xe IX. Phys. Rev. Lett. 74, 1574.CrossRefGoogle Scholar
Loy, M.M.T. & Shen, Y.R. (1969). Small-scale filaments in liquids and tracks of moving foci. Phys. Rev. Lett. 22, 994.CrossRefGoogle Scholar
Martin, O. (1985). Lyapunov exponents of stochastic dynamical systems. J. Stat. Phys. 41, 249.CrossRefGoogle Scholar
Moon, H.T. (1990). Homoclinic crossings and pattern selection. Phys. Rev. Lett. 64, 412.CrossRefGoogle ScholarPubMed
Ozaki, T., Elouga, L.B.B., Ganeev, R., Kieffer, J.C., Suzuki, M. & Kuroda, H. (2007). Intense harmonic generation from Silver ablation. Laser Part. Beams 25, 321.CrossRefGoogle Scholar
Rae, S.C., Burnett, K. & Cooper, J. (1994). Generation and propagation of high-order harmonics in a rapidly ionizing medium. Phys. Rev. A 50, 3438.CrossRefGoogle Scholar
Randall, C.J. (1980). Laser Program Annual Report. Lawrence Livermore National Laboratory, Livermore, Calif., UCRL-50021-79.Google Scholar
Rousse, A., Phuoc, K.T., Shah, R., Pukhov, R., Lefebvre, E., Malka, V., Kiselev, S., Burgy, F., Rousseau, J.P., Umstadter, D. & Hulin, D. (2004). Production of a keV x-ray beam from synchrotron radiation in relativistic laser–plasma interaction. Phys. Rev Lett. 93, 135005.CrossRefGoogle ScholarPubMed
Schmitt, A.J. (1988). The effects of optical smoothing techniques on filamentation in laser plasmas. Phys. Fluids 31, 3079.CrossRefGoogle Scholar
Shen, M.M. & Nicholson, D.R. (1987). Stochasticity in numerical solutions of the nonlinear Schrödinger equation. Phys. Fluids 30, 3150.CrossRefGoogle Scholar
Sheng, Z.M., Wu, H.C., Wang, W.M., Chem, M., Dong, X.G., Zheng, J. & Zhang, J. (2008). Simulation of high power THz emission from laser interaction with tenuous plasma and gas targets. Commun. Comput. Phys. 4, 1258.Google Scholar
Shibata, H. (1999). Lyapunov exponent of partial differential equation. Physica A 264(1–2), 226.CrossRefGoogle Scholar
Silberbarg, Y. (1990). Collapse of optical pulses. Opt. Lett. 15, 1282.CrossRefGoogle Scholar
Snyder, A.W., Chen, Y., Poladian, L. & Mitchell, D.J. (1990). Fundamental modes of highly nonlinear fibers. Electron. Lett. 26, 643.CrossRefGoogle Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1974). Self Focusing of Laser Beams in Dielectrics, Plasma and Semiconductors. Delhi: Tata-McGraw-Hill.Google Scholar
Sparangle, P. & Esarey, E. (1991). Stimulated backscattered harmonic generation from intense laser interactions with beams and plasmas. Phys. Rev. Lett. 67, 2021.CrossRefGoogle Scholar
Tabak, M., Hammer, J., Glinisky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. (1994). Ignition and high gain with ultra powerful lasers. Phys. Plasmas 1, 1626.CrossRefGoogle Scholar
Ting, A., Moore, C.I., Krushelnick, K., Manka, C., Esarey, E., Sprangle, P., Hubbard, R., Burris, H.R. & Baine, M. (1997 b). Plasma wakefield generation and electron acceleration in a self-modulated laser wakefield accelerator experiment. Phys. Plasmas 4, 1889.CrossRefGoogle Scholar
Ting, A., Krushelnick, K., Burris, H.R., Fisher, A., Manka, C. & Moore, C.I. (1996 a). Backscattered supercontinuum emission from high-intensity laser–plasma interactions. Opt. Lett. 21, 1096.CrossRefGoogle ScholarPubMed
Valeo, E. (1974). Stability of filamentary structures. Phys Fluids 17, 1391.CrossRefGoogle Scholar
Wilks, S.C., Kruer, W.L., Tabak, M. & Langdon, A.B. (1992). Absorption of ultra-intense laser pulses. Phys. Rev. Lett. 69, 1383.CrossRefGoogle ScholarPubMed
Young, P.E., Foord, M.E., Hammer, J.H., Kruer, W.L., Tabal, M. & Wilks, S.C. (1995 a). Time-dependent channel formation in a laser-produced plasma. Phys. Rev. Lett. 75, 1082.CrossRefGoogle Scholar
Young, P.E., Hammer, J.H., Wilks, S.C. & Kruer, W.L. (1995 b). Laser beam propagation and channel formation in underdense plasmas. Phys. Plasmas 2, 2825.CrossRefGoogle Scholar
Yuen, H.C. & Lake, B.M. (1982). Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech. 22, 67.CrossRefGoogle Scholar
Yuen, H.C. & Fergunson, W.E. (1978). Relationship between Benjamin–Feir instability and recurrence in the nonlinear Schrödinger equation. Phys. Fluids 21, 1275.CrossRefGoogle Scholar
Zeng, Z., Cheng, Y., Song, X., Li, R. & Xu, Z. (2007). Generation of an extreme ultraviolet Supercontinuum in a two-color laser field. Phys. Rev. Lett. 98, 203901.CrossRefGoogle Scholar
Zhou, J., Peatross, J., Murnane, M.M., Kapteyn, H.C. & Christov, P. (1996). Enhanced high-Harmonic generation using 25 fs laser pulses. Phys. Rev. Lett. 76, 752.CrossRefGoogle ScholarPubMed