Skip to main content
SpringerLink
Log in

Nonlinear Effect of Expansion of Laser Produced Plasmas

  • Conference paper
Book cover Laser Interaction and Related Plasma Phenomena

Abstract

At light intensities exceeding I* = 1014W/cm2 (for ruby and neodymium glass lasers), nonlinear effects start to become efficient. One of these effects at plasma densities close to the cut-off-case is the creation of a force, directed towards lower plasma density which exceeds the thermokinetic forces. An elementary description of the force is given showing a drift of the oscillating electrons where only the nonlinear longitudinal oscillation has to be included. The general derivation of the force is given by the equation of motion of the Lorentz theory for nonrelativistic plasma with or without collisions at oblique incidence of the radiation and at total reflection. The transferred momentum can be expressed by a nonlinearly increased radiation pressure, and the resulting ion energy of translatory motion is equal to the increased oscillation energy of the electrons in the plasma. The evaluation of the threshold I* for the nonlinear effect is based on a nonlinear intensity dependence of the inverse bremstrahlung. A self-focusing mechanism in plasma has a threshold at laser powers of only 1 MW. It results in light filaments with electromagnetic energy densities exceeding the thermokinetic values (I> I*) which can explain measured filament diameters in gas breakdown and nonlinear effects in the usual cases of laser produced plasma. It cannot be excluded that the high energy, nonthermal ions at laser produced plasmas (Linlor effect) are due to the described nonlinear acceleration after self-focusing occurred.

Presented at the Workshop on “Laser Interaction and Related Plasma Phenomena”, Rensselaer Polytechnic Institute, Hartford Graduate Center, June 9–13, 1969.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. E. Honig, Mass Spectrometric Studies of the Interaction of Laser Beams with Solids, these Proceedings, p.

    Google Scholar 

  2. J. M. Dawson, C. R. Oberman, Phys. Fluids 5, 517 (1962)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. H. Hora Institut für Plasmaphysik, Garching, Rept. 6 /27 (1964)

    Google Scholar 

  4. P.K. Kaw and A. R. Salat Phys. Fluids, 11, 2223 (1968)

    Article  ADS  Google Scholar 

  5. R. E. Kidder, AIAA Symposium on Fluid Dynamics, Los Angeles, Calif. June 1968

    Google Scholar 

  6. F. J. Allen, Ballistic Research Laboratories Report, 1448-AD 681510 (1969)

    Google Scholar 

  7. N. G. Basov, O. N. Krokhin Zh. Eksp. Teor. Fis. 66, 171 (1964)

    Google Scholar 

  8. J. M. Dawson, Phys. Fluids 7, 981 (1964)

    Article  ADS  Google Scholar 

  9. A. G. Engelhardt, Bull. Amer. Phys. Soc. 9, 305 (1964)

    Google Scholar 

  10. H. Hora, Institut für Plasmaphysik, Garching, Rept. 6 /23 (1964)

    Google Scholar 

  11. H. Hora, Nucl. Sci. Abstr. 20, 394 (1966);

    Google Scholar 

  12. H. Hora, Application of Laser Produced Plasmas for Controlled Thermonuclear Fusion, these Proceedings, p. 427.

    Google Scholar 

  13. A. F. Haught, and D. H. Polk Phys. Fluids 9, 2047 (1966)

    Article  ADS  Google Scholar 

  14. A. F. Naught, D. H. Polk, and W. J. Fader Conference Proceedings Novosibirsk, Aug. 1968, IAEA Vienna, 1969,(Vol. I, p. 925 )

    Google Scholar 

  15. T. V. George. A. G. Engelhardt, J. L. Pack, H. Hora, G. Cox Bull. Amer. Phys. Soc. 13, 1553 (1968);

    Google Scholar 

  16. H. Hora, dome Results of the Self-Similarity Model, these Proceedings, p.

    Google Scholar 

  17. A. Mattioli, Euratom-CEA-Fontenay, Report-FC-477 (1968)

    Google Scholar 

  18. W. J. Fader, Phys. Fluids 11, 2200 (1968)

    Article  ADS  Google Scholar 

  19. N. G. Basov, O. N. Krokhin, and G. V. Sklizkov, IEEE J. QE-4, 988 (1968)

    Google Scholar 

  20. A. Caruso, G. Gratton, Plasma Physics 10, 867 (1968)

    Article  ADS  Google Scholar 

  21. R. G. Rehm, Bull. Amer. Phys. Soc. 13, 879 (1968)

    Google Scholar 

  22. R. E. Kidder, Nucl. Fusion, 8, 3 (1968)

    Article  Google Scholar 

  23. P. Mulser Institut für Plasmaphysik, Garching, Rept. 3/95 (1969) Theses, TH Munich, 1969

    Google Scholar 

  24. J. W. Shearer, and W. S. Barnes, Numerical Calculations of Plasma Heating by Means of Subnanosecond Laser Pulses, these Proceedings, P.

    Google Scholar 

  25. E. Fabre, Ecole Polytechnique, Paris, Rept. PMI 391 R (1969)

    Google Scholar 

  26. W. König, Handbuch der Physik, Ed. by Geiger and Scheel, Vol. 20, Springer Berlin 1928, p. 253.

    Google Scholar 

  27. W. I. Linlor, Appl. Phys. Letters 3, 210 (1963);

    Google Scholar 

  28. W. I. Linlor, Phys. Rev. Letters 12, 383 (1964)

    Article  Google Scholar 

  29. N. R. Isenor, Appl. Phys. Letters 4, 152 (1964)

    Google Scholar 

  30. N. R. Isenor, Can. J. Phys. 42, 1413 (1964)

    Google Scholar 

  31. H. Opower, and E. Burlefinger, Phys. Letters 16, 37 (1965);

    Article  ADS  Google Scholar 

  32. H. Opower, and W. Press, Z. Naturforsch, 21a, 344 (1966);

    ADS  Google Scholar 

  33. H. Opower, W. Kaiser, H. Puell, and W. Heinicke Z. Naturforsch, 22a, 1392 (1967)

    ADS  Google Scholar 

  34. D. W. Gregg, and S. J. Thomas, J. Appl. Phys. 37, 4313 (1966)

    Article  ADS  Google Scholar 

  35. S. Namba, P. H. Kim, and A. Mitsuyama, J.Appl. Phys. 37, 3330 (1966)

    Article  ADS  Google Scholar 

  36. S. Namba, H. Schwarz, Proc. IEEE Symposium on Electron, Ion and Laser Beam Technology, Berkeley, May 1967, p. 861;

    Google Scholar 

  37. S. Namba, P. H. Kim and Helmut Schwarz, Transactions 8th Internat. Conf. on Phenomena in Ionized Gases, Vienna, Austria, Aug. 27-Sept. 2, 1967, P. 59;

    Google Scholar 

  38. S. Namba, Helmut Schwarz, Scientific Papers of the Institute of Phys. andChem. Research, Tokyo, Japan, Vol. 60, 101–106 (1966)

    Google Scholar 

  39. J. Brunteneau, E. Fabre, H. Lamain, and P. Vasseur Phys. Letters, 26A, 37 (1967);

    Article  Google Scholar 

  40. A. W. Ehler, J. Appl. Phys. 37, 4962 (1966);

    Article  ADS  Google Scholar 

  41. H. Weichel, and P. V. Avizonis, Appl. Phys. Letters, 9, 334 (1966);

    Article  ADS  Google Scholar 

  42. P. A. H. Saunders, P. Avivi, and W. Millar Phys. Letters, 5, 290 (1967)

    Article  Google Scholar 

  43. A. Ducauze, G. Tonon, and P. Veyrie, Compt. Rend. 261, 4039 (1965);

    Google Scholar 

  44. G. Tonon, Compt. Rend. 262B, 106 (1966)

    Google Scholar 

  45. D. Bize, T. Consoli, L. Slama, P. Stevenin, and M. Zymanski,Compt. Rend. 264B, 1235 (1967)

    Google Scholar 

  46. E. W. Sucov, J. L. Pack, A. V. Phelps, and A. G. Engelhardt, Phys. Fluids 10, 2035 (1967)

    Article  ADS  Google Scholar 

  47. H. Hirono, and J. Iwamoto, Japan J. Appl. Phsy. 6, 1006 (1967)

    Article  ADS  Google Scholar 

  48. J. C. Bryner, and G. H. Sichling, Bull. Amer. Phys. Soc. 12, 1161 (1967)

    Google Scholar 

  49. H. Weichel, C. D. David, and P. V. Avizonis Appl. Phys. Letters, 13, 316 (1968)

    Google Scholar 

  50. H. Hora, D. Pfirsch, and A. Schlüter, Z. Naturforschung, 22a, 278 (1967)

    ADS  Google Scholar 

  51. A. Schlüter, Z. Naturforschung, 5a, 72 (1950)

    ADS  MATH  Google Scholar 

  52. A. Schlüter, Plasma Physics 10, 471 (1968)

    Google Scholar 

  53. H. Hora, Phys. Fluids 12, 182 (1969)

    Article  ADS  Google Scholar 

  54. T. Consoli, Compt. Rend. Paris 260, 4163 (1965)

    Google Scholar 

  55. P. Javel, (private communication, 1969 )

    Google Scholar 

  56. H. Hora, Ann. Phys. 22, 402 (1969);

    Article  Google Scholar 

  57. H. Hora, Institut fur Plasmaphysik, Garching, Rept. 3 /87 (1969);

    Google Scholar 

  58. H. Hora, Verhandl. Deutsch. Phys. Ges. (IV) 4, 296 (1969)

    Google Scholar 

  59. M. J. Lubin, H. J. Dunn, and W. Friedman, Conference Proceedings, Novosibirsk, Aug. 1968

    Google Scholar 

  60. M. J. Lubin, H. J. Dunn, and W. Friedman,IAEA, Vienna 1969, Vol. I, P. 945.

    Google Scholar 

  61. P. P. Ljamo’r, L. G. Sapogin Zh. Tekh. Fiz. 37, 629 (1967)

    Google Scholar 

  62. H. Hora, and H. Müller, Nuclear Fusion 10, No. 1 (1970)

    Google Scholar 

  63. L. D. Landau, and E. M. Lifshitz Electrodynamics of Continuous Media ( Pergamon Press, Oxford, 1966 ) p. 242

    Google Scholar 

  64. H. Hora, Jenaer Jahrbuch, 1967, p. 131;

    Google Scholar 

  65. H. Hora, Institut für Plasmaphysik, Garching, Rept. 6 /5 (1963)

    Google Scholar 

  66. L. Spitzer, Jr. Physics of Fully Ionized Gases ( Interscience Publ., New York, 1950 )

    Google Scholar 

  67. H. Motz, and C. J. H. Watson Advances in Electronics and Electron Physics 23, 153 (1967)

    Article  Google Scholar 

  68. V. L. Ginsburg, The Propagation of Electromagnetic Waves in Plasmas ( Pergamon Press, Oxford, 1964 ), p. 205

    Google Scholar 

  69. H. L. Berk, D. L. Book, and D. Pfirsch J. Math. Phys. 8, 1611 (1967)

    Article  ADS  MATH  Google Scholar 

  70. S. L. Shapiro, M. A. Duguay, and L. B. Kreuzer, Appl. Phys. Letters 12, 36 (1968)

    Article  ADS  Google Scholar 

  71. D. W. Gregg, and S. J. Thomas J. Appl. Phys. 37, 2787 (1966)

    Article  ADS  Google Scholar 

  72. E. Panarella, and P. Savic Can. J. Phys. 46, 183 (1968)

    ADS  Google Scholar 

  73. Rand, Phys. Rev. 136, B231 (1964); T.P. Hughes, and M. B. Nicholson-Florence, J. Phys. Al, 588 (1968)

    Google Scholar 

  74. M. Bornatici, A. Cavaliere, and F. Engelmann, Phys. Fluids, 12, 2362 (1969).

    Article  ADS  MATH  Google Scholar 

  75. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Letters 13, 479 (1964)

    Article  ADS  Google Scholar 

  76. N. Bloembergen, Topics in Nonlinear Physics, Proc. Intern. School NATO, Munich, 1966, ( Springer, New York, 1968 ) p. 425

    Google Scholar 

  77. Yu. P. Raizer, zh. Eks. Teor. Fiz. 52, 470 (1967);

    Google Scholar 

  78. Yu. P. Raizer, Sov. Phys. JETP 25, 308 (1967)

    ADS  Google Scholar 

  79. W. Engelhardt, Appl. Phys. Letters, 15, 216 (1969);

    Google Scholar 

  80. H. DuPont, A. Donzel, and J. Ernest, Appl. Phys. Letters 11 (1967);

    Google Scholar 

  81. S. R. Winkler, Verhandl. DPG (IV) 4, 256 (1969)

    Google Scholar 

  82. A. G. Litvak, Izvestiya VUZ. Radifizika, 8, 1148 (1965)

    Google Scholar 

  83. V. V. Korobkin, and A. J. A.cock Phys. Rev. Letters 21, 1433 (1968)

    Article  ADS  Google Scholar 

  84. H. Hora, Z. Physik 226. 156 (1969)

    Article  ADS  Google Scholar 

  85. A. R. M. Rashad, 6th Microwave and Opt. Generation and Amplification Conf., Cambridge, Mass. 1966 (Proceedings) p. 445

    Google Scholar 

  86. A. J. Alcock, C. DeMichelis, V. V. Korobkin, and M. C. Richardson Appl. Phys. Letters, 14, 445 (1969)

    Google Scholar 

  87. P. D. Maker, R. W. Terhune, and C. M. Savage, Proc. 3rd Int. Quantum Electr. Conf. Paris, Febr. 1963;

    Google Scholar 

  88. P. D. Maker, R. W. Terhune, and C. M. Savage, Dunod Paris, 1964, Vol. I p. 1559

    Google Scholar 

  89. E. K. Damon, and R. G. Tomlinson Appl. Opt. 2, 546 (1963)

    ADS  Google Scholar 

  90. R. W. Minck, J. Appl. Phys. 35 252 (1964)

    Article  ADS  Google Scholar 

  91. R. G. Meyerand, and A. F. Haught Phys. Rev. Letters 11, 401 (1963)

    Article  ADS  Google Scholar 

  92. S. A. Ramsden, and W. E. Davis Phys. Rev. Letters 13, 227 (1964)

    Article  ADS  Google Scholar 

  93. S. L. Mandelstam, P. P. Pashinin, A. V. Prokhindeev, A. M. Prokhorov, and N. K. Sukhodrev Zh. Exp. Teor. Fiz. (USSR) 47, 2003 (1964) (Soy. Phys. JETP (USA) 20, 1344 (1965)).

    Google Scholar 

  94. B. C. Boland, E. E. Irons, and R. W. McWhirter, J. Phys. 1B, 1180 (1968)

    ADS  Google Scholar 

  95. A. G. Engelhardt, T. V. George, H. Hora and J. L. Pack Phys. Fluids 13, No. 1 (1970)

    Google Scholar 

  96. B. E. Paton, and N. R. Isenor Can. J. Phys. 46, 1237 (1968)

    ADS  Google Scholar 

  97. R. W. Minck, and W. G. Rado, J. Appl. Phys. 37, 355 (1966)

    Article  ADS  Google Scholar 

  98. D. H. Gill, and A. A. Dougal Phys. Rev. Letters 15, 845 (1965)

    Article  ADS  Google Scholar 

  99. A. J. Alcock, E. Panarella, and S. A. Ramsden, Proc. 7th Int. Conf. Phen. Ion. Gas, Belgrade (1965) Vol. III, P. 224

    Google Scholar 

  100. O. Vollrath, Verhandl. DPG (IV) 4, 256 (1969)

    Google Scholar 

  101. M. M. Litvak, and P.F. Edwards IEEE J. Q-E 2, 486 (1966)

    Article  Google Scholar 

  102. K. Hohla, Institut fúr Plasmaphysik, Garching, Rep. 3/67 (1968);

    Google Scholar 

  103. K. Büchl, K. Hohla, R. Wienecke, and S.Witkowski, Z. Naturforsch, 24A, 1244 (1969)

    Google Scholar 

  104. P. E. Faugeras, M. Mattioli, and R. Papoular, AIAA Fluid and Plasma Dynamics Conf. Los Angeles, Calif., June 1968

    Google Scholar 

  105. T. Yamanaka, N. Tsuchimori, T. Sasaki, and C. Yamanaka Technol. Reports of the Osaka University 18, 155 (1968)

    Google Scholar 

  106. P. Kaw, Appl. Phys. Letters 15, 16 (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Plasmaphysik, Rensselaer Polytechnic Institute, Garching, Germany West

    Heinrich Hora

Authors
  1. Heinrich Hora
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Rensselaer Polytechnic Institute, USA

    Helmut J. Schwarz (Professor of Physics) (Professor of Physics)

  2. Institut für Plasmaphysik (Max Planck Society), Rensselaer Polytechnic Institute, Garching, Germany

    Heinrich Hora (Adjunct Associate Professor of Physics) (Adjunct Associate Professor of Physics)

Rights and permissions

Reprints and permissions

Copyright information

© 1971 Springer Science+Business Media New York

About this paper

Cite this paper

Hora, H. (1971). Nonlinear Effect of Expansion of Laser Produced Plasmas. In: Schwarz, H.J., Hora, H. (eds) Laser Interaction and Related Plasma Phenomena. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-0901-7_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0901-7_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-0903-1

  • Online ISBN: 978-1-4684-0901-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation