Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T07:11:42.803Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatial evolution of a q-Gaussian laser beam in relativistic plasma

Published online by Cambridge University Press:  07 September 2010

A. Sharma  and
I. Kourakis
A. Sharma*
Affiliation:
Centre for Plasma Physics, School of Mathematics & Physics, Queen's University Belfast, Belfast, United Kingdom
I. Kourakis
Affiliation:
Centre for Plasma Physics, School of Mathematics & Physics, Queen's University Belfast, Belfast, United Kingdom
*
Address correspondence and reprint requests to: A. Sharma, Centre for Plasma Physics, School of Mathematics & Physics, Queen's University Belfast, BT7 1NN Belfast, United Kingdom. E-mail: a_physics2001@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In a recent experimental study, the beam intensity profile of the Vulcan petawatt laser beam was measured; it was found that only 20% of the energy was contained within the full width at half maximum of 6.9 μm and 50% within 16 μm, suggesting a long-tailed non-Gaussian transverse beam profile. A q-Gaussian distribution function was suggested therein to reproduce this behavior. The spatial beam profile dynamics of a q-Gaussian laser beam propagating in relativistic plasma is investigated in this article. A non-paraxial theory is employed, taking into account nonlinearity via the relativistic decrease of the plasma frequency. We have studied analytically and numerically the dynamics of a relativistically guided beam and its dependence on the q-parameter. Numerical simulation results are shown to trace the dependence of the focusing length on the q-Gaussian profile.

Keywords

Beam Dynamicsq-GaussianRelativistic Plasma
Type
Research Article
Information
Laser and Particle Beams , Volume 28 , Issue 3 , September 2010 , pp. 479 - 489
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Annou, R., Tripathi, V.K. & Srivastava, M.P. (1996). Plasma channel formation by short pulse laser. Phys. Plasmas 3, 1356–1359.CrossRefGoogle Scholar
Askaryan, G.A. (1962). Interaction between laser radiation and oscillating surfaces. Sov. Phys. JETP 15, 1161–1162.Google Scholar
Board of Physics and Astronomy (2003). Frontiers in High Energy Density Physics: The X–Games of Contemporary Science. Washington, DC: National Academies Press.Google Scholar
Borisov, A.B., Borovskiy, A.V., Shiryaev, O.B., Korobkin, V.V., Prokhorov, A.M., Solem, J.C., Luk, T.S., Boyer, K. & Rhodes, C.K. (1992). Relativistic and charge–displacement self–channeling of intense ultrashort laser pulses in plasmas. Phys. Rev. A 45, 5830–5845.CrossRefGoogle ScholarPubMed
Campbell, E.M., Freeman, R.R. & Tanaka, A.K. (2006). Fast ignition inertial fusion: an introduction and preview. Fusion Sci. Technol. 49, 249–253.CrossRefGoogle Scholar
Chessa, P., Wispelaere, E. De, Dorchies, F., Malka, V., Marques, J.R., Hamoniaux, G., Mora, P. & Amiranoff, F. (1999). Temporal and angular resolution of the ionization–induced refraction of a short laser pulse in helium gas. Phys. Rev. Lett. 82, 552–555.CrossRefGoogle Scholar
Collier, M.R. (2004). Are magnetospheric suprathermal particle distributions inconsistent with maximum entropy considerations? Adv. Space Res. 33, 2108–2112.CrossRefGoogle Scholar
Derenzo, S.E., Mast, T.S., Zaklad, H. & Muller, R.A. (1974). Electron avalanche in liquid xenon. Phys. Rev. A 9, 2582–2591.CrossRefGoogle Scholar
Deutsch, C., Bret, A., Firpo, M.C., Gremillet, L., Lefebvre, E. & Lifschitz, A. (2008). Onset of coherent electromagnetic structures in the relativistic electron beam deuterium–tritium fuel interaction of fast ignition concern. Laser Part. Beams 26, 157–165.CrossRefGoogle Scholar
Faenov, A.Yu., Magunov, A.I., Pikuz, T.A., Skobelev, I.Yu., Gasilov, S.V., Stagira, S., Calegari, F., Nisoli, M., De Silvestri, S., Poletto, L., Villoresi, P. & Andreev, A.A. (2007). X–ray spectroscopy observation of fast ions generation in plasma produced by short low–contrast laser pulse irradiation of solid targets. Laser Part. Beams 25, 267–275.CrossRefGoogle Scholar
Faure, J., Glinec, Y., Pukhov, A., Kiselev, S., Gordienko, S., Lefebvre, E., Rousseau, J.P., Burgy, F. & Malka, V. (2004). A laser–plasma accelerator producing monoenergetic electron beams. Nature (London) 431, 541–544.CrossRefGoogle ScholarPubMed
Geddes, C.G., Toth, C.S., Van Tilborg, J., Esarey, E., Schroeder, C.B., Bruhwiler, D., Nieter, C., Cary, J. & Leemans, W.P. (2004). High quality electron beams from a laser wakefield accelerator using plasma–channel guiding. Nature (London) 431, 538–541.CrossRefGoogle ScholarPubMed
Gordon, D., Tzeng, K.C., Clayton, C.E., Dangor, A.E., Malka, V., Marsh, K.A., Modena, A., Mori, W.B., Muggli, P., Najmudin, Z., Neely, D., Danson, C. & Joshi, C. (1998). Observation of electron energies beyond the linear dephasing limit from a laser–excited relativistic plasma wave. Phys. Rev. Lett. 80, 2133–2136.CrossRefGoogle Scholar
Gurevich, A.V. (1978). Nonlinear Phenomena in the Ionosphere. Springer-Verlag: Berlin.CrossRefGoogle Scholar
Hellberg, M.A., Mace, R.L., Baluku, T.K., Kourakis, I. & Saini, N.S. (2009). Comment on Mathematical and physical aspects of Kappa velocity distribution. Phys. Plasmas 16, 094701–094705.CrossRefGoogle Scholar
Hora, H. (1975). Theory of relativistic self–focusing of laser radiation in plasmas. J. Opt. Soc. Am. 65, 882–886.CrossRefGoogle Scholar
Hora, H. (2007). New aspects for fusion energy using inertial confinement. Laser Part. Beams 25, 37–45.CrossRefGoogle Scholar
Joshi, C., Malka, V., Darrow, C.B., Danson, C., Neely, D. & Walsh, F.N. (2002). Electron acceleration from the breaking of relativistic plasma waves. Nature (London) 377, 606–608.Google Scholar
Kline, J.L., Montgomery, D.S., Rousseaux, C., Baton, S.D., Tassin, V., Hardin, R.A., Flippo, K.A., Johnson, R.P., Shimada, T., Yin, L., Albright, B.J., Rose, H.A. & Amiranoff, F. (2009). Investigation of stimulated Raman scattering using a short–pulse diffraction limited laser beam near the instability threshold. Laser Part. Beams 27, 185–190.CrossRefGoogle Scholar
Lifschitz, A.Z., Faure, J., Glinec, Y., Malka, V. & Mora, P. (2006). Proposed scheme for compact GeV laser plasma accelerator. Laser Part. Beams 24, 255–259.CrossRefGoogle Scholar
Litvak, A.G. (1969). Finite-amplitude wave beams in a magnetoactive plasma. Sov. Phys. JETP 30, 344.Google Scholar
Liu, C.S. & Tripathi, V.K. (2001). Self-focusing and frequency broadening of an intense short–pulse laser in plasmas. J. Opt. Soc. Am. A 18, 1714–1718.CrossRefGoogle ScholarPubMed
Livadiotis, G. & Mccomas, D.J. (2009). Beyond kappa distributions: Exploiting Tsallis statistical mechanics in space plasmas. J. Geophys. Res. 114, A11105–A11125.Google Scholar
Malka, V., Fritzler, S., Lefebvre, E., Aleonard, M.M., Burgy, F., Chambaret, J.P., Chemin, J.F., Krushelnick, K., Malka, G., Mangles, S.P.D., Najmudin, Z., Pittman, M., Rousseau, J.P., Scheurer, J.N., Walton, B. & Dangor, A.E. (2002). Electron acceleration by a wake field forced by an intense ultrashort laser pulse. Science 298, 1596–1600.CrossRefGoogle ScholarPubMed
Mangles, S.P.D., Murphy, C.D., Najmudin, Z., Thomas, A.G.R., Collier, J.L., Dangor, A.E., Divall, E.J., Foster, P.S., Gallacher, J.G., Hooker, C.J., Jaroszynski, D.A., Langley, A.J., Mori, W.B., Norreys, P.A., Tsung, F.S., Viskup, R., Walton, B.R. & Krushelnick, K. (2004). Monoenergetic beams of relativistic electrons from intense laser-plasma interactions. Nature (London) 431, 535–538.CrossRefGoogle ScholarPubMed
Max, C.E., Arons, J. & Langdon, A.B. (1974). Self-modulation and self-focusing of electromagnetic waves in plasmas. Phys. Rev. Lett. 33, 209–212.CrossRefGoogle Scholar
Misra, S. & Mishra, S.K. (2009). Focusing of dark hollow Gaussian electromagnetic beam in a plasma with relativistic–pondermotive regime. Progr. Electromagnetic Res. B 16, 291–309.CrossRefGoogle Scholar
Modena, A., Najmudin, Z., Dangor, A.E., Clayton, C.E., Marsh, K.A., Monot, P., Auguste, T., Gibbon, P., Jakober, F., Mainfray, G., Dulieu, A., Louis-Jacquet, M., Malka, G. & Miquel, J.L. (1995). Experimental demonstration of relativistic self–channeling of a multiterawatt laser pulse in an underdense plasma. Phys. Rev. Lett. 74, 2953–2956.Google Scholar
Nakajima, K., Fisher, D., Kawakubo, T., Nakanishi, H., Ogata, A., Kato, Y., Kitagawa, Y., Kodama, R., Mima, K., Shiraga, H., Suzuki, K., Yamakawa, K., Zhang, T., Sakawa, Y., Shoji, T., Nishida, Y., Yugami, N., Downer, M. & Tajima, T. (1995). Observation of ultrahigh gradient electron acceleration by a self–modulated intense short laser pulse. Phys. Rev. Lett. 74, 4428–4431.CrossRefGoogle ScholarPubMed
Nakatsutsumi, M., Davies, J.R., Kodama, R., Green, J.S., Lancaster, K.L., Akli, K.U., Beg, F.N., Chen, S.N., Clark, D., Freeman, R.R., Gregory, C.D., Habaral, H., Heathcote, R., Hey, D.S., Highbarger, K., Jaanimagi, P., Key, M.H., Krushelnick, K., Ma, T., Macphee, A., Mackinnon, A.J., Nakamura, H., Stephens, R.B., Storm, M., Tampo, M., Theobald, W., Van. Woerkom, L., Weber, R.L., Wei, M.S., Woolsey, N.C. & Norreys, P.A. (2008). Space and time resolved measurements of the heating of solids to ten million kelvin by a petawatt laser. New J. Phys. 10, 043046–043058.CrossRefGoogle Scholar
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. (2005). Integrated laser–target interaction experiments on the RAL petawatt laser. Plasma Phys. Cont. Fusion 47, B833–B840.CrossRefGoogle Scholar
Romagnani, L., Borghesi, M., Cecchetti, C.A., Kar, S., Antici, P., Audebert, P., Bandhoupadjay, S., Ceccherini, F., Cowan, T., Fuchs, J., Galimberti, M., Gizzi, L.A., Grismayer, T., Heathcote, R., Jung, R., Liseykina, T.V., Macchi, A., Mora, P., Neely, D., Notley, M., Osterholtz, J., Pipahl, C.A., Pretzler, G., Schiavi, A., Schurtz, G., Toncian, T., Wilson, P.A. & Will, O. (2008). Proton probing measurement of electric and magnetic fields generated by ns and ps laser-matter interactions. Laser Part. Beams 26, 241–248.CrossRefGoogle Scholar
Roth, M., Cowan, T.E., Key, M.H., Hatchett, S.P., Brown, C., Fountain, W., Johnson, J., Pennington, D.M., Snavely, R.A., Wilks, S.C., Yasuike, K., Ruhl, H., Pegoraro, F., Bulanov, S.V., Campbell, E.M., Perry, M.D. & Powell, H. (2001). Fast ignition by intense laser-accelerated proton beams. Phys. Rev. Lett. 86, 436–439.CrossRefGoogle ScholarPubMed
Seifter, A., Kyrala, G.A., Goldman, S.R., Hoffman, N.M., Kline, J.L. & Batha, S.H. (2009). Demonstration of symcaps to measure implosion symmetry in the foot of the NIF scale 0.7 hohlraums. Laser Part. Beams 27, 123–127.CrossRefGoogle Scholar
Sharma, A., Kourakis, I. & Sodha, M.S. (2008). Propagation regimes for an electromagnetic beam in magnetized plasma. Phys. Plasmas 15, 103103–103109.CrossRefGoogle Scholar
Sharma, A., Prakash, G., Verma, M.P. & Sodha, M.S. (2003). Three regimes of intense laser beam propagation in plasmas. Phys. Plasmas 10, 4079–4084.CrossRefGoogle Scholar
Sharma, A., Verma, M.P. & Sodha, M.S. (2004). Self-focusing of electromagnetic beams in collisional plasmas with nonlinear absorption. Phys. Plasmas 11, 4275–4279.CrossRefGoogle Scholar
Sharma, R.P. & Chauhan, P.K. (2008). Nonparaxial theory of cross-focusing of two laser beams and its effects on plasma wave excitation and particle acceleration: Relativistic case. Phys. Plasmas 5, 063103–063108.CrossRefGoogle Scholar
Singh, R., Sharma, A.K. & Tripathi, V.K. (2010). Relativistic self distortion of a laser pulse and ponderomotive acceleration of electrons in an axially inhomogeneous plasma. Laser Part. Beams doi:10.1017/S0263034610000200.CrossRefGoogle Scholar
Sodha, M.S. & Faisal, M. (2008). Propagation of high power electromagnetic beams in overdense plasmas: Higher order paraxial theory. Phys. Plasmas 15, 033102–033105.CrossRefGoogle Scholar
Sodha, M.S. & Kaw, P.K. (1969). Theory of generation of harmonics and combination frequencies in a plasma. Adv. Electron. Electron Phys. 27, 187–293.CrossRefGoogle Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1974). Self-Focusing of Laser Beams in Dielectric Plasmas and Semiconductors. Delhi: India: Tata–McGraw–Hill.Google Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1976). Self focusing of laser beams in plasmas and semiconductors. Prog. Opt. 13, 169–265.CrossRefGoogle Scholar
Sodha, M.S., Mishra, S.K. & Misra, S. (2009 a). Focusing of dark hollow Gaussian electromagnetic beams in a plasma. Laser Part. Beams 27, 57–68.CrossRefGoogle Scholar
Sodha, M.S., Mishra, S.K. & Misra, S. (2009 b). Focusing of dark hollow Gaussian electromagnetic beams in a magnetoplasma. J. Plasma Phys. 75, 731–748.CrossRefGoogle Scholar
Stuart, B.C., Feit, M.D., Herman, S., Rubenchik, A.M., Shore, B.W. & Perry, M.D. (1996). Optical ablation by high-power short-pulse lasers. J. Opt. Soc. Am. B 13, 459–468.CrossRefGoogle Scholar
Svanberg, S. & Wahlstrom, C.G. (1995). X-ray Lasers. Bristol, UK: Institute of Physics, Bristol.Google Scholar
Tabak, M., Hammer, J., Glinsky, 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 ultrapowerful lasers. Phys. Plasmas 1, 1626–1630.CrossRefGoogle Scholar
Tajima, T. & Dawson, J.M. (1979). Laser Electron Accelerator. Phys. Rev. Lett. 43, 267–270.CrossRefGoogle Scholar
Treumann, R.A. (2001). Statistical mechanics of stable states far from equilibrium: thermodynamics of turbulent plasmas. Astrophys. & Space Sci. 277, 81–95.CrossRefGoogle Scholar
Treumann, R.A., Jaroschek, C.H. & Scholer, M. (2004). Stationary plasma states far from equilibrium. Phys. Plasmas 11, 1317–1325.CrossRefGoogle Scholar
Tsallis, C. (1988). Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479–487.CrossRefGoogle Scholar
Vasyliunas, V.M. (1968). A survey of low energy electrons in the evening sector of the magnetosphere with OGO1 and OGO3. J. Geophys.Res. 73, 2839–2884.CrossRefGoogle Scholar