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Growth of a ring ripple on a Gaussian electromagnetic beam in a plasma with relativistic - ponderomotive nonlinearity

Published online by Cambridge University Press:  08 December 2009

M.S. Sodha ,
S. Misra  and
S.K. Mishra
M.S. Sodha*
Affiliation:
Disha Academy of Research and Education, Raipur, India
S. Misra
Affiliation:
Ramanna Fellowship Program, Department of Education Building, Lucknow University, Lucknow, India
S.K. Mishra
Affiliation:
Ramanna Fellowship Program, Department of Education Building, Lucknow University, Lucknow, India
*
Address correspondence and reprint requests to: M.S. Sodha, Disha Academy of Research and Education, Disha Crown, Katchna Road, Shankarnagar, Raipur - 492 007, India. E-mail: [email protected]
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Abstract

This paper presents a theoretical model for the propagation/growth of a ring ripple, on a Gaussian electromagnetic beam, propagating in plasma with dominant relativistic-ponderomotive nonlinearity. A paraxial like approach has been invoked to understand the nature of propagation of the ring ripple like instability; in this approach, all the relevant parameters correspond to a narrow range around the irradiance maximum of the ring ripple. The dielectric function is determined by the composite (Gaussian and ripple) electric field profile of the beam. Thus, a unique dielectric function for the beam propagation and a radial field sensitive diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple has been taken into account. The effect of different parameters on the critical curves has been highlighted and the variation of the beam width parameter with the distance of propagation has been obtained for the three typical cases viz of steady divergence, oscillatory divergence and self-focusing of the ripple.

Keywords

Paraxial like approachRelativistic-ponderomotive nonlinearityRing rippleSelf-focusing
Type
Research Article
Information
Laser and Particle Beams , Volume 27 , Issue 4 , December 2009 , pp. 689 - 698
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abbi, S.C. & Mahr, H. (1971). Correlation of filaments in nitrobenzene with laser spikes. Phys. Rev. Lett. 26, 604–606.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, 609–636.CrossRefGoogle Scholar
Askaryan, G.A. (1962). Effects of the gradient of a strong electromagnetic beam on electrons and atoms. Sov. Phys. JETP 15, 1088–1090.Google Scholar
Badziak, J., Glowacz, S., Jablonski, S., Parys, P., Wolowski, J. & Hora, H. (2005). Generation of picosecond high-density ion fluxes by skin-layer laser-plasma interaction. Laser Part. beams 23, 143–147.CrossRefGoogle Scholar
Berger, R.L., Lasinski, B.F., Kaiser, T.B., Williams, E.A., Langdon, A.B. & Cohen, B.I. (1993). Theory and three-dimensional simulation of light filamentation in laser-produced plasma. Phys. Fluids B 5, 2243–2258.CrossRefGoogle Scholar
Borisov, A.B., Borovisiky, 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, 5830–5844.CrossRefGoogle ScholarPubMed
Borisov, A.B., Shiryaev, O.B., McPherson, A., Boyer, K. & Rhodes, C.K. (1995). Stability analysis of relativistic and charge-displacement self-channelling of intense laser pulses in underdense plasmas. Plasma Phys. Contr. Fusion 37, 569–597.CrossRefGoogle Scholar
Bourdier, A., Patin, D. & Lefebvre, E. (2007). Stochastic heating in ultra high intensity laser: Plasma interaction. Laser Part. Beams 25, 169–180.CrossRefGoogle Scholar
Brandi, H.S., Manus, C., Mainfray, G., Lehner, T. & Bonnaud, G. (1993). Relativistic and ponderomotive self focusing of a laser beam in a radially inhomogeneous plasma-I. Paraxial approximation. Phys. Fluids 5, 3539–3550.CrossRefGoogle Scholar
Chen, H. & Wilks, S.C. (2005). Evidence of enhanced effective hot electron temperatures in ultraintense laser-solid interactions due to reflexing. Laser Part. Beams 23, 411–428.CrossRefGoogle Scholar
Cook, R.C., Kozioziemski, B.J., Nikroo, A., Wilkens, H.L., Bhandarkar, S., Forsman, A.C., Haan, S.W., Hoppe, M.L., Huang, H., Mapoles, E., Moody, J.D., Sater, J.D., Seugling, R.M., Stephens, R.B., Takagi, M. & Xu, H.W. (2008). National Ignition Facility target design and fabrication. Laser & Part. Beams 26, 479–487.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
Esarey, E., Sprangle, P., Krall, J. & Ting, A. (1996). Overview of plasma-based accelerator concepts. IEEE Trans. Plasma Sci. PS 24, 252–288.CrossRefGoogle Scholar
Esarey, E., Sprangle, P., Ting, A. & Krall, J. (1988). Relativistic focusing and Beat wave phase velocity control in the plasma Beat wave accelerator. Appl. Phys. Lett. 53, 1266–1268.CrossRefGoogle Scholar
Ghanshyam, , & Tripathi, V.K. (1993). Self-focusing and filamentation of laser beams in collisional plasmas with finite thermal conduction. J. Plasma Phys. 49, 243–253.CrossRefGoogle Scholar
Gill, T.S. & Saini, N.S. (2007). Nonlinear interaction of a rippled laser beam with an electrostatic upper hybrid wave in collisional plasmas. Laser Part. Beams 25, 1–11.CrossRefGoogle Scholar
Gondarenko, N.A., Ossakow, S.L. & Milikh, G.M. (2005). Generation and evolution of density irregularities due to self-focusing in ionospheric modifications. J. Geophys. Res. 110, A093041/13.CrossRefGoogle Scholar
Gupta, M.K., Sharma, R.P. & Gupta, V.L. (2005). Cross focusing of two laser beams and plasma wave excitation. Phys. Plasmas 12, 1231011/7.CrossRefGoogle Scholar
Gurevich, A.V. (1978). Nonlinear processes in Ionosphere. Berlin: Springer.CrossRefGoogle Scholar
Guzdar, P.N., Chaturvedi, P.K., Papadopoulos, K. & Ossakow, S.L. (1998). The thermal self-focusing instability near the critical surface in the high-latitude ionosphere. J. Geophys. Res. 103, 2231–2237.CrossRefGoogle Scholar
Hora, H. (1969). Self focusing of laser beams in a plasma by Ponderomotive forces. Z. Phys. 226, 156–159.CrossRefGoogle Scholar
Hora, H. (1975). Theory of relativistic self focusing of laser radiations in plasmas. J. Opt. Soc. Am. 65, 882–886.CrossRefGoogle Scholar
Hora, H. (2005). Difference between relativistic petawatt-picosecond laser-plasma interaction and subrelativistic plasma-block generation. Laser Part. Beams 23, 441–451.CrossRefGoogle Scholar
Hora, H., Badziak, J., Glowacz, S., Jablonski, S., Skladanowski, Z., Osman, F., Cang, Yu., Zhang, J., Miley, G.H., Peng, H., He, X., Zhang, W., Rohlena, K., Ullschmied, J. & Jungwirth, K. (2005). Fusion energy from plasma block ignition. Laser Part. Beams 23, 423–432.CrossRefGoogle Scholar
Joshi, C., Clayton, C.E., Yasuda, A. & Chen, F.F. (1982). Direct observation of laser beam filamentation in an underdense plasma. J. Appl. Phys. 53, 215–217.CrossRefGoogle Scholar
Kaw, P.K., Schmidt, G. & Wilcox, T. (1973). Filamentation and trapping of electromagnetic radiation in plasmas. Phys. Fluids 16, 1522–1525.CrossRefGoogle Scholar
Keskinen, M.J. & Basu, S. (2003). Thermal self-focusing instability in the high-latitude ionosphere. Radio Sci. 38, 109531/7.CrossRefGoogle 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
Kruer, W.L. (1988). The Physics of Laser Plasma Interaction. New York: Additison-Wesley Publishing Company.Google Scholar
Kruer, W.L., Ruffina, U. & Westerhof, E. (1985). Ponderomotive and thermal filamentation of laser light. Comments Plasma Phys. Contr. Fusion 9, 63–72.Google Scholar
Kumar, A., Gupta, M.K. & Sharma, R.P. (2006). Effect of ultra intense laser pulse on the propagation of electron plasma wave in relativistic and ponderomotive regime and particle acceleration. Laser Part. Beams 24, 403–409.CrossRefGoogle Scholar
Liu, M.P., Xie, B.S., Huang, Y.S., et al. (2009). Enhanced ion acceleration by collisionless electrostatic shock in thin foils irradiated by ultra-intense laser pulse. Laser Part. Beams 27, 327–333.CrossRefGoogle Scholar
Loy, M.M.T. & Shen, Y.R. (1969). Small-scale filaments in liquids and tracks of moving foci. Phys. Rev. Lett. 22, 994–997.CrossRefGoogle Scholar
Misra, S. & Mishra, S.K. (2008). On focusing of a ring ripple on a Gaussian electromagnetic beam in a plasma. Phys. Plasmas 15, 0923071/8.CrossRefGoogle Scholar
Misra, S. & Mishra, S.K. (2009). On focusing of a ring ripple on a Gaussian electromagnetic beam in a magnetoplasma. J. Plasma Phys. 15, 1–16.Google Scholar
Mulser, P. & Bauer, D. (2004). Fast ignition of fusion pellets with superintense lasers: Concepts problems and prospectives. Laser Part. Beams 22, 5–12.CrossRefGoogle Scholar
Osman, F., Castillo, R. & Hora, H. (1999). Relativistic and ponderomotive self-focusing at laser-plasma interaction. J. Plasma Phys. 61, 263–273.CrossRefGoogle Scholar
Pandey, H.D. & Tripathi, V.K. (1990). Growth of a spike on a laser beam in a plasma. Phys. Fluids B2, 1221–1223.CrossRefGoogle Scholar
Perkins, F.W. & Valeo, E. (1974). Thermal self-focusing of electromagnetic waves in plasmas. Phys. Rev. Lett. 32, 1234–1237.CrossRefGoogle Scholar
Perkins, F.W. & Goldman, M.V. (1981). Self-focusing of radio waves in an underdense ionosphere. J. Geophys. Res. 86, 600–608.CrossRefGoogle Scholar
Pukhov, A. & Meyer-Ter-vehn, J. (1996). Multi MeV electron beam generation by direct laser acceleration in high density plasma channels. Phys. Rev. Lett. 76, 3975–3978.CrossRefGoogle Scholar
Purohit, G., Chauhan, P.K., Sharma, R.P. & Pandey, H.D. (2005). Effect of relativistic mutual interaction of two laser beams on growth of laser ripple in a plasma. Laser Part. Beams 23, 69–77.CrossRefGoogle Scholar
Purohit, G., Pandey, H.D., Mahmoud, S. & Sharma, R.P. (2004). Growth of high power laser ripple in plasma and its effect on plasma wave excitation: relativistic effects. J. Plasma Phys. 70, 25–40.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. & Willi, 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
Sharma, A., Verma, M.P., Prakash, G. & Sodha, M.S. (2004 a). Three regimes of growth of a Gaussian ripple on a uniform plane electromagnetic wavefront in a plasma. J. Appl. Phys. 95, 2963–2968.CrossRefGoogle Scholar
Sodha, M.S. & Sharma, A. (2007). Comparison of two approaches to the study of filamentation in plasmas. Phys. Plasmas 14, 044501/4.CrossRefGoogle Scholar
Sodha, M.S. & Tripathi, V.K. (1977). Steady state self focusing and filamentation of whistlers in plasmas. J. Appl. Phys. 48, 1078–1084.CrossRefGoogle Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1976). Self focusing of laser beams in plasmas in plasmas and semiconductors. Prog. Opt. 13, 169–265.CrossRefGoogle Scholar
Sodha, M.S., Ghatak, A.K. & Tripathi, V.K. (1974). Self focusing of laser beams in Dielectrics, Semiconductors and Plasmas. Delhi, India: Tata-Mc.Graw-Hills.Google Scholar
Sodha, M.S., Konar, S. & Maheshwari, K.P. (1992). Steady state self focusing of rippled laser beam in plasma: arbitrary nonlinearity. J. Plasma Phys. 48, 107–118.CrossRefGoogle Scholar
Sodha, M.S., Sharma, A., Verma, M.P. & Faisal, M.D. (2007). Self focusing instability in ionospheric plasma with thermal conduction. Phys. Plasmas 14, 052901-906.CrossRefGoogle Scholar
Sodha, M.S., Sharma, A., Prakash, G. & Verma, M.P. (2004). Growth of a ring ripple on a Gaussian beam in a plasma. Phys. Plasmas 11, 3023–3027.CrossRefGoogle Scholar
Sodha, M.S., Sharma, J.K., Tewari, D.P., Sharma, R.P. & Kaushik, S.C. (1979 a). Growth of Gaussian ripple on a uniform plane wave front of electromagnetic wave in plasmas. J. Appl. Phys 50, 6214–6221.CrossRefGoogle Scholar
Sodha, M.S., Sharma, R.P., Maheshwari, K.P. & Kausik, S.C. (1978). Filamentation instability of extraordinary and ordinary modes in a magnetoplasma. Plasma Phys. 20, 585–595.CrossRefGoogle Scholar
Sodha, M.S., Singh, D.P. & Sharma, R.P. (1979 b). Growth of nonuniform ripple on a Gaussian beam in a plasma. Appl. Phys. 18, 97–103.CrossRefGoogle Scholar
Sodha, M.S., Singh, T., Singh, D.P. & Sharma, R.P. (1981). Growth of laser ripple in a plasma and its effect on plasma wave excitation. Phys. Fluids 24, 914–919.CrossRefGoogle Scholar
Sprangle, P. & Esarey, E. (1991). Stimulated back scattered harmonic generation from intense laser interaction with beams and plasmas. Phys. Rev. Lett. 67, 2021–2024.CrossRefGoogle Scholar
Sprangle, P. & Esarey, E. (1992). Interaction of ultrahigh laser fields with beams and plasmas. Phys. Fluids. B4, 2241–2248.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 ultrapowerful lasers. Phys. Plasmas 1, 1626–1634.CrossRefGoogle Scholar
Talanov, V.I. (1966). Self modeling wave beams in a nonlinear dielectric. Sov. Radiophys. 9, 260–261.CrossRefGoogle Scholar
Vidal, F.W. & Johnston, T.W. (1996). Electromagnetic beam breakup: Multiple filaments, single beam equilibria, and radiation. Phys. Rev. Lett. 77, 1282–1285.CrossRefGoogle ScholarPubMed
Wilks, S., Young, P.E., Hammer, J., Tabak, M. & Kruer, W.L. (1994). Spreading of Intense Laser Beams Due to Filamentation. Phys. Rev. Lett. 73, 2994–2997.CrossRefGoogle ScholarPubMed
Winterberg, F. (2008). Laser for inertial confinement fusion driven by high explosives. Laser Part. Beams 26, 127–135.CrossRefGoogle Scholar
Wyrtele, J.S. (1993). Advanced Accelerator Concepts. New York: AIP.Google Scholar
Xie, B.S., Aimidula, A., Niu, J.S., Liu, J. & Yu, M.Y. (2009). Electron acceleration in the wakefield of asymmetric laser pulses. Laser Part. Peams 27, 27–32.CrossRefGoogle Scholar