Nonlinear Forces in Laser Produced Plasmas

  • Heinrich Hora


The very recent observation of a correlation of the increase of reflectivity from laser produced plasmas with the onset of nuclear fusion reactions indicates a nonlinear mechanism. Numerical calculations of Shearer, Kidder and Zink of the plasma dynamics on interaction with light that allow for the nonlinear force, described before, on the basis of the ponderomotive interaction for collisionless dispersion effects indicated the increase of reflectivity due to this force. A review on this force is given and an exact numerical example of 1015 W/cm2 laser intensity (Nd glass) in a plasma with a temperature of 103 eV and with a WBK-like density profile shows the predominance of the nonlinear force over the thermokinetic force. More detailed calculations of the threshold intensities I for the predominance of this force for a net plasma acceleration around I* = 1014 W/cm2 are reported. These include the calculation of Steinhauer and Ahlstrom, where this threshold was given even for lower intensities but so that temperatures exceeding 10 keV are then needed. The non-WBK-like density profile as treated analytically by Lindi and Kaw, resulted in the same net acceleration of the layer as in the WBK case, and the acceleration towards the nodes of the created standing wave was again very similar to the WBK case treated before by the author. For oblique incidence, where a Brillouin turbulence can occur, Lindi and Kaw found the possibility of a polarization dependent increase of the nonlinear force due to a Ginzburg-Denisov coupling of electromagnetic and electrostatic waves. Numerical calculations for non-WBK cases are reviewed, showing the predominance of the net acceleration and the increase of reflectivity. The forces in standing waves can exceed the thermokinetic forces even at intensities appreciably below I*, as Mulser found from a dynamic numerical calculation. This fact allows the assumption that this mechanism may be one reason for the correlation of reflectivity and neutron production.


Electron Temperature Standing Wave Density Profile Laser Intensity Oblique Incidence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.W. Minck and W.G. Rado, J. Appl. Phys. 37, 355 (1966).ADSCrossRefGoogle Scholar
  2. 2.
    A.G. Engelhardt, T.V. George, H. Hora and J.L. Pack, Phys. Fluids 13, 212 (1970).ADSCrossRefGoogle Scholar
  3. 3.
    R. Sigel, Z. Naturforsch. 25a, 488 (1970).ADSGoogle Scholar
  4. 4.
    H. Salzmann, K. Eidmann and R. Sigel, Verhndl. Dtsch. Phys. Ges. (VI) 6, 407 (1971).Google Scholar
  5. 5.
    N.G. Basov, P.G. Kriukov, S.D. Zakharov, Yu.V. Senatsky and S.V. Tchekalin, IEEE J. Quantum Electronics QE-4, 864 (1968).ADSCrossRefGoogle Scholar
  6. 6.
    F. Floux, Laser Interaction and Related Plasma Phenomena (H. Schwarz and H. Hora, Eds.) Plenum 1971.Google Scholar
  7. 7.
    F. Floux, J.F. Bernard, D. Cognard and A. Saleres, Second Workshop Laser Interaction and Related Plasma Phenomena, these Proceedings, p. 409.Google Scholar
  8. 8.
    K. Büchl, K. Eidmann, P. Mulser, H. Salzmann, R. Sigel and S. Witkowski, Paper CN 28-D-11, 4th Conf. on Plasma Physics and Controlled Thermonuclear Fusion Research, Madison, Wisc., June 1971.Google Scholar
  9. 9.
    S.W. Mead, R.E. Kidder and J.E. Swain, Report UCRL-73356, August 17, 1971, IEEE J. Quantum Electronics (submitted).Google Scholar
  10. 10.
    J.W. Shearer, R.E. Kidder and J.W. Zink, Bull. Am. Phys. Soc. 15, 1483 (1970).Google Scholar
  11. 11.
    H. Hora, D. Pfirsch and A. Schlüter, Z. Naturforsch. 22a, 278 (1967); A. Schlüter, Plasma Physics 10, 471 (1968).ADSGoogle Scholar
  12. 12.
    H. Hora, Phys. Fluids 12, 182 ( 1969); H. Hora, Laser Interaction and Related Plasma Phenomena (H. Schwarz and H. Hora Eds.) Plenum, New York 1971, p. 383.ADSCrossRefGoogle Scholar
  13. 13.
    H. Hora, Opto-Electronics 2, 201 (1970).CrossRefGoogle Scholar
  14. 14.
    S. Rand, Phys. Rev. 136, B 231 (1964).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    T.B. Hughes and M.B. Nicholson-Florence, J. Phys. A (2) 588 (1968).Google Scholar
  16. 16.
    R. Kidder, paper presented at the Varenna Summer School (July 1969), UCRL-Preprint 71775 (1969).Google Scholar
  17. 17.
    A. Caruso, A. de Angelis, G. Gatti, R. Gratton and S. Martellucci, Phys. Lett. 33A, 29 (1970.ADSCrossRefGoogle Scholar
  18. 18.
    H. Hora, Z. Physik 226, 156 (1969).ADSCrossRefGoogle Scholar
  19. 19.
    P.K. Kaw, Appl. Phys. Lett. 15, 16 (1969).ADSCrossRefGoogle Scholar
  20. 20.
    P.K. Kaw and J.M. Dawson, Phys. Fluids 12, 2586 (1969).ADSCrossRefGoogle Scholar
  21. 21.
    W.L. Kruer and J.M. Dawson, Phys. Fluids 14, 1003 (1971); Second Workshop Laser Interaction and Related Plasma Phenomena, these Proceedings, p. 317.ADSCrossRefGoogle Scholar
  22. 22.
    see for example H. Motz and C.J.H. Watson, in Advances in Electronics and Electron Physics (L. Marton, Ed.) Academic Press, New York, Vol. 23, p. 153.Google Scholar
  23. 23.
    A.V. Gorbunov and M.A. Miller, ZhETF 34, 242; 751 (1958) (Sov. Phys. JETP 7, 168; 515 (1958)).Google Scholar
  24. 25.
    J. Lindl and P. Kaw, Phys. Fluids 14, 371 (1971).ADSCrossRefGoogle Scholar
  25. 25.
    L.C. Steinhauer and H.G. Ahlstrom, Phys. Fluids 13, 1103 (1970).ADSCrossRefGoogle Scholar
  26. 26.
    B. Green and P. Mulser, Verhandl. Dtsch. Phys. Ges. (IV) 6, 405 (1971).Google Scholar
  27. 27.
    P. Mulser, Second Workshop Laser Interaction and Related Plasma Phenomena, these Proceedings, p. 381.Google Scholar
  28. 28.
    L.D. Landau and E.M. Lifshitz, Electrodynamic of Continuous Media (Pergamon Press, Oxford, 1966) p. 242.Google Scholar
  29. 29.
    see e.g. C.W. Allen, Astrophysical Quantities, Athlon Press, London 1955.Google Scholar
  30. 30.
    J.M. Dawson and C. Oberman, Phys. Fluids 5, 517 (1962).MathSciNetADSCrossRefMATHGoogle Scholar
  31. 31.
    H. Hora and H. Wilhelm, Nuclear Fusion 10, 111 (1970).CrossRefGoogle Scholar
  32. 32.
    L. Spitzer, Jr., Physics of Fully Ionized Gases, Interscience, New York (1956).MATHGoogle Scholar
  33. 33.
    V.L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Addison-Wesley, Reading, Mass. 1969), pp. 193–198 and 213–228.Google Scholar
  34. 34.
    P. Kaw, (private communication, July 1969).Google Scholar
  35. 35.
    N.G. Denisov, ZhETF 31, 609 (1956); Sov. Phys. JETP 4, 544 (1957).Google Scholar
  36. 36.
    H. Hora, Ann. Physik (7) 22, 402 (1969).ADSCrossRefGoogle Scholar
  37. 37.
    J.W. Shearer and W.S. Barnes, Laser Interaction and Related Plasma Phenomena (H. Schwarz and H. Hora Eds.) Plenum, New York 1971, p. 307.Google Scholar
  38. 38.
    J.W. Shearer, Report Livermore Rad. Lab. UCID-15745 (Dec. 7, 1970).Google Scholar

Copyright information

© Springer Science+Business Media New York 1972

Authors and Affiliations

  • Heinrich Hora
    • 1
    • 2
  1. 1.Max-Planck-Institut für PlasmaphysikEuratom AssociationGarchingGermany
  2. 2.Rensselaer Polytechnic InstituteHartfordUSA

Personalised recommendations