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Order statistics and extreme properties of spatially smoothed laser beams in laser-plasma interaction

Published online by Cambridge University Press:  07 September 2010

S. Hüller  and
A. Porzio
S. Hüller*
Affiliation:
Centre de Physique Théorique, CNRS, Ecole Polytechnique, Palaiseau Cedex, France
A. Porzio
Affiliation:
Centre de Physique Théorique, CNRS, Ecole Polytechnique, Palaiseau Cedex, France LAGA, Institut Galilée, Université Paris13, CNRS, Villetaneuse, France
*
Address correspondence and reprint requests to: S. Hüller, Centre de Physique Théorique, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France. E-mail: [email protected]
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Abstract

The order statistics of intense speckles or “laser hot spots” are studied in the context of the so-called “optically smoothed” light beams of laser-matter interaction. We investigate theoretically and by means of numerical simulations the distribution function for the k-th most intense speckle maxima in the upper tail speckle distribution. From these distributions for each order k, a distribution function for the intense speckles as a function of their peak intensity can be established, which allows to compute their impact on nonlinear processes, like parametric instabilities. This is done for the example of stimulated Brillouin scattering, using the so-called independent hot spot model, for which the backscatter reactivity level is computed, which proves to be in very good agreements with numerical simulations. This result is of great interest for nonlinear processes, like instabilities, where extreme speckles play an important role.

Keywords

Extreme theoryLaser-plasma interactionOrder statisticsSpecklesStatistical optics
Type
Research Article
Information
Laser and Particle Beams , Volume 28 , Issue 3 , September 2010 , pp. 463 - 477
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Biancalana, V. & Chessa, P. (1994). Handling of quasi-Gaussian beams by phase plates: Far-field simulation. Appl. Opt. 33, 3465–3477.CrossRefGoogle ScholarPubMed
Embrechts, P., Kluppelberg, C. & Mikosch, T. (1997). Modelling extremal events. New York: Springer.CrossRefGoogle Scholar
Garnier, J. (1999). Statistical properties of the hot spots of smoothed beams produced by random phase plates revisited. Phys. Plasmas 6, 1601.CrossRefGoogle Scholar
Goodman, J. (1985). Statistical Optics. New York: John Wiley & Sons.Google Scholar
Goodman, J. (1984). Statistical properties of laser speckle patterns. Laser Speckle and Related Phenomena. Vol. 9, 9–74, New York: Springer.Google Scholar
Hüller, S., Mounaix, Ph. & Tikhonchuk, V.T. (1998). SBS reflectivity from spatially smoothed laser beam: Random phase plates versus polarization smoothing. Phys. Plasmas 5, 2706.CrossRefGoogle Scholar
Hüller, S. (2003). Interplay between parametric instabilities in fusion-relevant laser plasmas. Le Vide 307, 44–60.Google Scholar
Hüller, S., Masson-Laborde, P.E., Pesme, D., Casanova, M., Detering, F. & Maximov, A. (2006). Harmonic decomposition to describe the nonlinear evolution of Stimulated Brillouin Scattering. Phys. Plasmas 13, 22703.CrossRefGoogle Scholar
Kato, Y., Mima, K., Miyanaga, N., Arinaga, S., Kitagawa, Y., Nakatsuka, M. & Yamanaka, C. (1984). Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression. Phys. Rev. Lett. 53, 1057.CrossRefGoogle Scholar
Kline, J.L. & Montgomery, D.S. (2005). Kinetic and fluid Langmuir wave nonlinearities driven by stimulated Raman scattering in a diffraction limited single-hot-spot. Laser and Particle Beams 23, 27–31.CrossRefGoogle Scholar
Leadbetter, M.R., Lindgren, G. & Rootzen, H. (1982). Extreme and Related Properties of Random Sequences and Processes. New York: Springer.Google Scholar
Leadbetter, M.R. (1983). Extreme and local dependence in stationary sequences. Z. Wahrscheinlichkeitstheorie verw. Gebiete 65, 291–306.CrossRefGoogle Scholar
Malka, V., Renard, N., Hüller, S., Pesme, D., Amiranoff, F., Baton, S.D., Modena, A., Mounaix, P., Rousseaux, C. & Salvati, M. (2000). Strong self-focusing and localization of SBS in quasi-stationary plasma. Phys. Plasmas 7, 4259–4265.CrossRefGoogle Scholar
Masson-Laborde, P.E., Hüller, S., Pesme, D., Casanova, M. & Loiseau, P. (2006). Modeling parametric scattering instabilities in large-scale expanding plasmas. J. Phys. IV France 133, 247.CrossRefGoogle Scholar
Middleton, D. (1960). An introduction to Statistical communications theory, New York: John Wiley & Sons.Google Scholar
Montgomery, D.S., Johnson, R.P., Cobble, J.A., Fernandez, J.C., Lindman, E.L., Rose, H.A. & Estabrook, K.G. (1999). Characterization of plasma and laser conditions for single hot spot experiments. Laser and Part. Beams 7, 349–359.CrossRefGoogle Scholar
Mounaix, Ph., Divol, L., Hüller, S. & Tikhonchuk, V.T. (2000). Effects of Spatial and Temporal Smoothing on Stimulated Brillouin Scattering in the Independent-Hot-Spot Model Limit. Phys. Rev. Lett. 85, 4526.CrossRefGoogle ScholarPubMed
Myatt, J., Pesme, D., Hüller, S., Maximov, A.M., Rozmus, W. & Capjack, C.E. (2001). Nonlinear propagation of a randomized laser beam through an expanding plasma. Phys. Rev. Lett. 87, 5003.CrossRefGoogle ScholarPubMed
Obenschain, S.P., Grun, J., Herbst, M.J., Kearney, K.J., Manka, C.K., McLean, E.A., Mostovych, A.N., Stamper, J.A., Whitlock, R.R., Bodner, S.E., Gardner, J.H. & Lehmberg, R.H. (1986). Laser-target interaction with induced spatial incoherence. Phys. Rev. Lett. 56, 2807–2810.CrossRefGoogle ScholarPubMed
Ohtsubo, J. & Asakura, A. (1977). Statistical properties of laser speckle produced in the diffraction field. Applied Opt. 16, 1742.CrossRefGoogle ScholarPubMed
Ohtsubo, J. & Asakura, A. (1977). Statistical properties of the sum of partially developed speckle patterns. Opt. Lett. 1, 98.CrossRefGoogle ScholarPubMed
Pesme, D., Hüller, S., Myatt, J., Riconda, C., Maximov, A., Tikhonchuk, V.T., Labaune, C., Fuchs, J., Depierreux, S. & Baldis, H.A. (2002). Laser-plasma interaction studies in the context of megajoule lasers for inertial fusion. Plasma Phys. Contr. Fusion 44, B53.CrossRefGoogle Scholar
Porzio, A. & Hüller, S. (2010). Extremal Properties of weakly correlated random variable arising in speckle patterns, J. Statist. Phys. 138, 1010–1044.CrossRefGoogle Scholar
Rose, H.A. & Dubois, D.F. (1993). Statistical properties of hot spots produced by a random phase plate. Phys. Fluids B 5, 590–596.CrossRefGoogle Scholar
Rose, H.A. & DuBois, D.F. (1993). Initial development of ponderomotive filaments in plasma from intense hot spots produced by a random phase plate. Phys. Fluids B 5, 3337–3356.CrossRefGoogle Scholar
Rose, H.A. & DuBois, D.F. (1994). Laser hot spots and the breakdown of linear instability theory with application to stimulated Brillouin scattering. Phys. Rev. Lett. 72, 2883.CrossRefGoogle ScholarPubMed
Rose, H.A. (1997). Saturation of stimulated Brillouin scatter by self-consistent flow profile modification in laser hot spots Phys. Plasmas 4, 437–442.CrossRefGoogle Scholar
Rosenbluth, M.N. (1973). Parametric Instabilities in inhomogeneous media. Phys. Rev. Lett. 29, 565–567.Google Scholar
Schmitt, A.J. & Afeyan, B.B. (1998). Time-dependent filamentation and stimulated Brillouin forward scattering in inertial confinement fusion plasmas. Phys. Plasmas 5, 503.CrossRefGoogle Scholar
Tikhonchuk, V.T., Labaune, C. & Baldis, H.A. (1996). Modeling of a stimulated Brillouin scattering experiment with statistical distribution of speckles. Phys. Plasmas 3, 3777.CrossRefGoogle Scholar
Tikhonchuk, V.T., Hüller, S., Mounaix, P. (1997). Effect of the speckle self-focusing on the stationary stimulated Brillouin scattering reflectivity from a randomized laser beam in an inhomogeneous plasma. Phys. Plasmas 4, 4369–4381.CrossRefGoogle Scholar
Tikhonchuk, V.T., Fuchs, J., Labaune, C., Depierreux, S., Hüller, S., Myatt, J. & Baldis, H.A. (2001). Stimulated Brillouin and Raman scattering from a randomized laser beam in large inhomogeneous plasmas. II: Model description and comparison with experiments. Phys. Plasmas 8, 1636.CrossRefGoogle Scholar
Weber, S., Riazuelo, G., Michel, P., Loubère, R., Walraet, F., Tikhonchuk, V.T., Malka, V., Ovadia, J. & Bonnaud, G. (2004). Modeling of laser-plasma interaction on hydrodynamic scales: Physics development and comparison with experiments. Laser Part. Beams 22, 189–195.Google Scholar