Abstract

The force exerted by a high-frequency electric field on a macroscopic body is calculated. Starting from total momentum conservation, a rigorous definition of radiation force density is given, and the relationship between a time-averaged Maxwellian stress tensor and radiation pressure is clarified. Formulas are presented for calculating the volume force density of the radiation-force term. It is further shown that all resonant wave–wave interactions of nonlinear optics, such as stimulated Brillouin and Raman scattering, are driven by radiation pressure. The limits of validity of the radiation-pressure concept are discussed.

© 1985 Optical Society of America

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  1. J. C. Maxwell, A Treatise on Electricity and Magnetism (Oxford U. Press, Oxford, 1871).
  2. A. Bartoli, Nuovo Cimento 15, 195 (1883). According to Debye, Bartoli published his formula first in 1875 (see Ref. 80, p. 79).
  3. P. N. Lebedev, “Untersuchungen über die Druckkräfte des Lichtes (Investigations on the pressure forces of light),” Ann. Phys. 6, 433–458 (1901).
    [CrossRef]
  4. E. Nichols, G. F. Hull, “Über Strahlungsdruck (On radiation pressure),” Ann. Phys. 12, 225–263 (1903).
    [CrossRef]
  5. W. Gerlach, A. Golsen, “Untersuchung an Radiometern. II. Eine neue Messung des Strahlungsdruckes (Investigations with radiometers. II. A new measurement of the radiation pressure),” Z. Phys. 15, 1–7 (1923).
    [CrossRef]
  6. L. Boltzmann, “Ableitung des Stefanschen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der elektromagnetischen Lichttheorie (Derivation of Stefan’s law concerning the temperature dependence of thermal radiation from the electromagnetic theory of light),” Wied. Ann. 22, 291–293 (1884).
    [CrossRef]
  7. A. S. Eddington, “On the radiative equilibrium of stars,” Mon. Not. R. Astron. Soc. 77, 16 (1917).
  8. M. Schwarzschild, R. Härm, “On the maximum mass of stable stars,” Astrophys. J. 129, 637–646 (1959) (the upper limit for M given here is 60 sun masses); J. P. Cox, R. Th. Giuli, Stellar Structure (Gordon & Breach, New York, 1968), Vol. I, Chap. 11.
    [CrossRef]
  9. F. L. Whipple, W. F. Huebner, “Physical processes in comets,” Ann. Rev. Astron. Astrophys. 14, 143–172 (1976), p. 166.
    [CrossRef]
  10. J. C. Brandt, “The physics of comet tails,” Ann. Rev. Astron. Astrophys. 6, 267–286 (1968).
    [CrossRef]
  11. J. G. Hills, “The formation of comets by radiation pressure in the outer protosun,” Astron. J. 87, 906–910 (1982); J. G. Hills, M. T. Sandford, “Dependence on the radiation-grain coupling,” Astron. J. 88, 1519–1521 (1983); “Dependence on the anistropy of the radiation field,” Astron J. 88, 1522–1530 (1983).
    [CrossRef]
  12. P. N. Lebedev, Astrophys. J. 14, 155–163 (1902).
    [CrossRef]
  13. E. E. Salpeter, “Central stars of planetary nebulae,” Ann. Rev. Astron. Astrophys. 9, 127–146 (1971) p. 141.
    [CrossRef]
  14. W. G. Mathews, C. R. O’Dell, “Evolution of diffuse nebulae,” Ann. Rev. Astron. Astrophys. 7, 67–98 (1969) p. 85.
    [CrossRef]
  15. L. Spitzer, Diffuse Matter in Space (Wiley/Interscience, New York, 1968), pp. 207–212.
  16. B. Baud, H. J. Habing, “The maser strength of OH/IR stars, evolution of mass loss and the creation of superwind,” Astron. Astrophys. 127, 73–83 (1983).
  17. H. E. Fröhlich, “Der Druck des ultravioletten Strahlungsfeldes auf interstellare Staubteilchen (The pressure of the UV radiation field on interstellar dust particles),” Astron. Nachr. 302, 15–28 (1981).
    [CrossRef]
  18. A. E. Roy, Orbital Motion (Adam Hilger, Bristol, England, 1978), Chap. 12.
  19. W. J. Boulton, “The effect of solar radiation pressure on the orbit of a cylindrical satellite,” Planet Space Sci. 32, 287–296 (1984).
    [CrossRef]
  20. S. Weinberg, The First Three Minutes (Basic, New York, 1977).
  21. W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1975), Chap. 11.
  22. H. A. Lorentz, “Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern (Attempt to establish a theory of the electrical and optical phenomena in moving bodies),” (Brill, Leiden, 1895; reprint Teubner, Leipzig, 1906), pp. 21–29; H. A. Lorentz, The Theory of Electrons (1909; republished by Dover, New York, 1952).
  23. P. Penfield, H. A. Haus, Electrodynamics of Moving Media (MIT Press, Cambridge, Mass.1967), Chaps. 1, 7, 8. For additional references see also M. M. Novak, “Interaction of photons with electrons in dielectric media,” Fortschr. Phys. 28, 285–355 (1980).
    [CrossRef]
  24. A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (On a heuristic point of view concerning the generation and transformation of light),” Ann. Phys. 17, 132–148 (1905); “Zum gegenwärtigen Stand des Strahlungsproblems (additional new opinions on radiation problems),” Phys. Z. 10, 185–193 (1909); “Zur Quantentheorie der Strahlung (On quantum theory of radiation),” Phys. Z. 18, 121–128 (1917).
    [CrossRef]
  25. J. M. Jauch, F. Rohrlich, The Theory of Photons and Electrons (Springer, New York, 1976); J. Schwinger, Quantum Electrodynamics (Dover, New York, 1958) (contains a collection of original papers since 1927); C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
    [CrossRef]
  26. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1950).
  27. B. Guillame, A. Delfour, D. Bize, “10.6 μ m Mie scattering by a single particle in optical levitation,” Proc. Soc. PhotoOpt. Eng. 384, 66–72 (1983).
  28. R. Thurn, W. Kiefer, “Raman microsampling technique applying optical levitation by radiation pressure,” Appl. Spectrosc. 38, 78–83 (1984).
    [CrossRef]
  29. Proceedings of the Workshop on Laser-Cooled and Trapped Atoms, Washington, April 14-15, 1983 [Nat. Bur. Stand. (U.S.) Spec. Publ. 653 (1983); contains 20 papers].
  30. W. Neuhauser, M. Hohenstatt, P. Toschek, “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233–236 (1978).
    [CrossRef]
  31. D. W. Wineland, R. E. Drullinger, F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639–1642 (1978).
    [CrossRef]
  32. J. Javanainen, M. Lindberg, S. Stenholm, “Laser cooling of trapped ions: dynamics of the final stages,” J. Opt. Soc. Am. B 1, 111–115 (1984).
    [CrossRef]
  33. V. S. Letokhov, V. G. Minogin, “Laser cooling of atoms and its application in frequency standards,” J. Phys. Colloq. C8, 42, 347–355 (1981).
  34. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1978).
  35. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
  36. J. J. Duderstadt, G. A. Moses, Inertial Confinement Fusion (Wiley, New York, 1982), Chaps. 4 and 5.
  37. Th. M. Johnson, “Inertial confinement fusion: review and perspective,” Proc. IEEE 72, 548–594 (1984).
    [CrossRef]
  38. F. F. Chen, “Physical mechanisms for laser-plasma parametric instabilities,” in Laser Interaction and Related Plasma Phenomena, H. J. Schwarz, H. Hora, eds. (Plenum, New York, 1974), p. 294; Introduction to Plasma Physics (Plenum, New York, 1976), p. 264.
  39. V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1–65 (1981).
    [CrossRef]
  40. See, for example, L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1979), Chaps. 1 and 2.
  41. H. A. H. Boot, S. A. Self, R. B. R. Shersby-Harvie, “Containment of a fully ionized plasma by radio frequency fields,” J. Electron. Control 4, 434–453 (1958); A. V. Gapunov, M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” Sov. Phys. JETP 7, 168–169 (1958).
    [CrossRef]
  42. H. Hora, D. Pfirsch, A. Schlüter, “Beschleunigung von inhomogenen Plasmen durch Laserlicht (Acceleration of inhomogeneous plasmas by laser light),” Z. Naturforsch. 22a, 278–280 (1967).
  43. A. Zeidler, H. Schnabl, P. Mulser, “Light pressure of time-dependent fields in plasmas,” Phys. Fluids 28, 372–376 (1985). The time-dependent expression of π was found in 1982 (see Annual Report 1982, Institute of Applied Physics, Technical University, 6100 Darmstadt, p. 55). For a homogeneous plasma it is also obtained by summing up all terms for B0= 0 in Ref. 44.
    [CrossRef]
  44. G. Stratham, D. ter Haar, “Strong turbulence of a magnetized plasma. II. The ponderomotive force,” Plasma Phys. 25, 681–698 (1983).
    [CrossRef]
  45. A. B. Langdon, “Nonlinear inverse bremsstrahlung and heated-electron distributions,” Phys. Rev. Lett. 44, 575–579 (1980).
    [CrossRef]
  46. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1981), Secs. 15 and 16; R. Becker, F. Sauter, Electromagnetic Fields and Interactions (Dover, New York, 1982), Vol. I, Sec. 35. See also Ref. 21, Chap. 6.
  47. V. S. Starunov, I. L. Fabelinskii, “Stimulated Mandel’shtam–Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463–489 (1969–70) [Usp. Fiz. Nauk 98, 441–491 (1969)].
    [CrossRef]
  48. B. J. B. Crowley, “Dispersive effects in radiation transport and radiation hydrodynamics in matter at high density,” J. Phys. Colloq. C8 44, 25–38 (1983).
  49. R. L. Carmen, D. W. Forslund, J. M. Kindel, “Visible harmonic emission as a way of measuring profile steepening,” Phys. Rev. Lett. 46, 29–32 (1981).
    [CrossRef]
  50. R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
    [CrossRef]
  51. O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 1–51.
    [CrossRef]
  52. K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
    [CrossRef]
  53. P. Mulser, C. van Kessel, “Profile modifications and plateau formation due to light pressure in laser irradiated targets,” Phys. Rev. Lett. 38, 902–905 (1977).
    [CrossRef]
  54. P. Mulser, G. Spindler, “Radiation pressure dominated plasma flow,” Z. Naturforsch. 34a, 1059–1062 (1979).
  55. H. Takabe, P. Mulser, “Self consistent treatment of resonance absorption in a streaming plasma,” Phys. Fluids 25, 2304–2306 (1982); W. L. Kruer, “Model of resonance absorption with profile modification,” Phys. Fluids 25, 2324–2325 (1982).
    [CrossRef]
  56. R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
    [CrossRef]
  57. M. D’Evelyn, G. M. Morales, “Properties of large amplitude Langmuir solitons,” Phys. Fluids 21, 1997–2008 (1978).
    [CrossRef]
  58. H. H. Chen, Ch. S. Liu, “Soliton generation at resonance and density modification in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1147–1151 (1977); G. D. Doolen, D. F. DuBois, H. A. Rose, “Nucleation of cavitons in strong Langmuir turbulence,” Phys. Rev. Lett. 54, 804–807 (1985).
    [CrossRef] [PubMed]
  59. H. C. Kim, R. L. Stenzel, A. Y. Wong, “Development of cavitons and trapping of rf fields,” Phys. Rev. Lett. 33, 886–889 (1974).
    [CrossRef]
  60. J. A. Stamper, E. A. McLean, B. H. Ripin, “Studies of spontaneous magnetic fields in laser-produced plasmas by Faraday rotation,” Phys. Rev. Lett. 40, 1177–1180 (1978); A. Raven, O. Willi, P. T. Rumsby, “Megagauss magnetic field profiles in laser-produced plasmas,” Phys. Rev. Lett. 41, 554–557 (1979).
    [CrossRef]
  61. D. G. Colombant, N. K. Winsor, “Thermal-force terms and self-generated magnetic fields in laser-produced plasmas,” Phys. Rev. Lett. 38, 697–701 (1977).
    [CrossRef]
  62. J. J. Thomson, C. E. Max, K. Estabrook, “Magnetic fields due to resonance absorption of laser light,” Phys. Rev. Lett. 35, 663–667 (1975); W. Woo, J. S. DeGroot, “Magnetic fields due to laser light absorption,” Phys. Fluids 21, 2072–2075 (1978).
    [CrossRef]
  63. O. Willi, P. T. Rumsby, “Filamentation on laser irradiated spherical targets,” Opt. Commun. 37, 45–48 (1981).
    [CrossRef]
  64. A. Bers, “Space–time evolution of plasma instabilities—absolute and convective,” in Handbook of Plasma Physics, M. N. Rosenbluth, R. Z. Sagdeev, eds. (North-Holland, Amsterdam, 1983), pp. 451–517.
  65. C. S. Liu, “Parametric instabilities in homogeneous unmagnetized plasmas,” in Advances in Plasma Physics (Wiley, New York, 1976), pp. 83–120.
  66. L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).
  67. R. C. Davidson, Methods in Nonlinear Plasma Theory (Academic, New York, 1972), p. 125.
  68. P. Mulser, A. Giulietti, M. Vaselli, “Quantitative explanation of oscillating two-stream and parametric decay instabilities in terms of wave pressure,” Phys. Fluids 27, 2035–2038 (1984).
    [CrossRef]
  69. N. Bloembergen, “Nonlinear optics and spectroscopy,” Rev. Mod. Phys. 54, 685–695 (1982).
    [CrossRef]
  70. P. Mulser, “Nonlinear optics and wave pressure in laser plasmas,” in Laser–Plasma Interactions 2, R. A. Cairns, ed. (SUSSP, Edinburgh, U.K., 1983), pp. 29–54.
  71. A. Reiman, “Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium,” Rev. Mod. Phys. 51, 311–330 (1979).
    [CrossRef]
  72. P. Kaw, G. Schmidt, T. Wilcox, “Filamentation and trapping of electromagnetic radiation in plasmas,” Phys. Fluids16, 1522–1525 (1973); R. W. Short, R. Bingham, E. A. Williams, “Filamentation of laser light in flowing plasmas,” Phys. Fluids 25, 2302–2305 (1982); M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 171–265.
    [CrossRef]
  73. P. Mulser, H. Schnabl, “Excitation of large amplitude electron plasma waves by laser,” Laser Particle Beams 1, 379–394 (1983); Erratum 2, 254 (1984).
    [CrossRef]
  74. W. Schneider, “Elektronenbeschleunigung durch inhomogene Langmuirwellen hoher Amplitude (Electron acceleration in inhomogeneous high-amplitude Langmuir waves),” Phys. Fluids (to be published).
  75. For V see M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 194–212. For π see Ref. 44.
  76. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 122.
  77. G. C. Pomraning, Radiation Hydrodynamics (Pergamon, Oxford, 1973); M. S. Zubairy, “Radiative energy transfer in presence of random source distributions,” in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York, 1978), pp. 459–467.
  78. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), pp. 247–251; V. A. Kulkarny, B. S. White, “Focusing and waves in turbulent inhomogeneous media,” Phys. Fluids 25, 1770–1784 (1982); M. J. Beran, “Coherence theory and caustic corrections,” Proc. Soc. Photo-Opt. Eng. 358, 176–183 (1982).
    [CrossRef]
  79. K. Rawer, “Elektrische Wellen in einem geschichteten Medium (Electric waves in a stratified medium),” Ann. Phys. 35, 385–416 (1939); Erratum 42, 294–296 (1942).
    [CrossRef]
  80. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material (The light pressure on spheres of arbitrary material),” Ann. Phys. 30, 57–136 (1909).
    [CrossRef]
  81. W. M. Irvine, “Light scattering by spherical particles: radiation pressure, asymmetry factor, and extinction cross section,” J. Opt. Soc. Am. 55, 16–21 (1965); H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
    [CrossRef]
  82. N. V. Voshchinnikov, V. B. Il’in, “Planck mean cross sections for radiation pressure for nonspherical grains. I and II,” Astrophys. 18, 353–360 (1982); Astrophys. 19, 347–357 (1983).
  83. J. H. Poynting, “Radiation in the solar system: its effect on temperature and its pressure on small bodies,” Phil. Trans. R. Soc. London Ser. A 202, 525–552 (1904); H. P. Robertson, “Dynamical effects on radiation in the solar system,” Mon. Not. R. Astron. Soc. 97, 423–438 (1937).
    [CrossRef]
  84. I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
    [CrossRef]
  85. R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London Ser. A 347, 475–491 (1976). The following paper contains a comment on Peierls result: H. M. Lai, W. M. Suen, K. Young, “Microscopic derivation of a force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
    [CrossRef]

1985 (1)

A. Zeidler, H. Schnabl, P. Mulser, “Light pressure of time-dependent fields in plasmas,” Phys. Fluids 28, 372–376 (1985). The time-dependent expression of π was found in 1982 (see Annual Report 1982, Institute of Applied Physics, Technical University, 6100 Darmstadt, p. 55). For a homogeneous plasma it is also obtained by summing up all terms for B0= 0 in Ref. 44.
[CrossRef]

1984 (5)

R. Thurn, W. Kiefer, “Raman microsampling technique applying optical levitation by radiation pressure,” Appl. Spectrosc. 38, 78–83 (1984).
[CrossRef]

J. Javanainen, M. Lindberg, S. Stenholm, “Laser cooling of trapped ions: dynamics of the final stages,” J. Opt. Soc. Am. B 1, 111–115 (1984).
[CrossRef]

Th. M. Johnson, “Inertial confinement fusion: review and perspective,” Proc. IEEE 72, 548–594 (1984).
[CrossRef]

W. J. Boulton, “The effect of solar radiation pressure on the orbit of a cylindrical satellite,” Planet Space Sci. 32, 287–296 (1984).
[CrossRef]

P. Mulser, A. Giulietti, M. Vaselli, “Quantitative explanation of oscillating two-stream and parametric decay instabilities in terms of wave pressure,” Phys. Fluids 27, 2035–2038 (1984).
[CrossRef]

1983 (5)

P. Mulser, H. Schnabl, “Excitation of large amplitude electron plasma waves by laser,” Laser Particle Beams 1, 379–394 (1983); Erratum 2, 254 (1984).
[CrossRef]

B. Baud, H. J. Habing, “The maser strength of OH/IR stars, evolution of mass loss and the creation of superwind,” Astron. Astrophys. 127, 73–83 (1983).

B. Guillame, A. Delfour, D. Bize, “10.6 μ m Mie scattering by a single particle in optical levitation,” Proc. Soc. PhotoOpt. Eng. 384, 66–72 (1983).

G. Stratham, D. ter Haar, “Strong turbulence of a magnetized plasma. II. The ponderomotive force,” Plasma Phys. 25, 681–698 (1983).
[CrossRef]

B. J. B. Crowley, “Dispersive effects in radiation transport and radiation hydrodynamics in matter at high density,” J. Phys. Colloq. C8 44, 25–38 (1983).

1982 (4)

J. G. Hills, “The formation of comets by radiation pressure in the outer protosun,” Astron. J. 87, 906–910 (1982); J. G. Hills, M. T. Sandford, “Dependence on the radiation-grain coupling,” Astron. J. 88, 1519–1521 (1983); “Dependence on the anistropy of the radiation field,” Astron J. 88, 1522–1530 (1983).
[CrossRef]

N. V. Voshchinnikov, V. B. Il’in, “Planck mean cross sections for radiation pressure for nonspherical grains. I and II,” Astrophys. 18, 353–360 (1982); Astrophys. 19, 347–357 (1983).

N. Bloembergen, “Nonlinear optics and spectroscopy,” Rev. Mod. Phys. 54, 685–695 (1982).
[CrossRef]

H. Takabe, P. Mulser, “Self consistent treatment of resonance absorption in a streaming plasma,” Phys. Fluids 25, 2304–2306 (1982); W. L. Kruer, “Model of resonance absorption with profile modification,” Phys. Fluids 25, 2324–2325 (1982).
[CrossRef]

1981 (5)

O. Willi, P. T. Rumsby, “Filamentation on laser irradiated spherical targets,” Opt. Commun. 37, 45–48 (1981).
[CrossRef]

H. E. Fröhlich, “Der Druck des ultravioletten Strahlungsfeldes auf interstellare Staubteilchen (The pressure of the UV radiation field on interstellar dust particles),” Astron. Nachr. 302, 15–28 (1981).
[CrossRef]

R. L. Carmen, D. W. Forslund, J. M. Kindel, “Visible harmonic emission as a way of measuring profile steepening,” Phys. Rev. Lett. 46, 29–32 (1981).
[CrossRef]

V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1–65 (1981).
[CrossRef]

V. S. Letokhov, V. G. Minogin, “Laser cooling of atoms and its application in frequency standards,” J. Phys. Colloq. C8, 42, 347–355 (1981).

1980 (2)

R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
[CrossRef]

A. B. Langdon, “Nonlinear inverse bremsstrahlung and heated-electron distributions,” Phys. Rev. Lett. 44, 575–579 (1980).
[CrossRef]

1979 (4)

P. Mulser, G. Spindler, “Radiation pressure dominated plasma flow,” Z. Naturforsch. 34a, 1059–1062 (1979).

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
[CrossRef]

R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
[CrossRef]

A. Reiman, “Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium,” Rev. Mod. Phys. 51, 311–330 (1979).
[CrossRef]

1978 (4)

J. A. Stamper, E. A. McLean, B. H. Ripin, “Studies of spontaneous magnetic fields in laser-produced plasmas by Faraday rotation,” Phys. Rev. Lett. 40, 1177–1180 (1978); A. Raven, O. Willi, P. T. Rumsby, “Megagauss magnetic field profiles in laser-produced plasmas,” Phys. Rev. Lett. 41, 554–557 (1979).
[CrossRef]

M. D’Evelyn, G. M. Morales, “Properties of large amplitude Langmuir solitons,” Phys. Fluids 21, 1997–2008 (1978).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. Toschek, “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233–236 (1978).
[CrossRef]

D. W. Wineland, R. E. Drullinger, F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639–1642 (1978).
[CrossRef]

1977 (4)

K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
[CrossRef]

P. Mulser, C. van Kessel, “Profile modifications and plateau formation due to light pressure in laser irradiated targets,” Phys. Rev. Lett. 38, 902–905 (1977).
[CrossRef]

H. H. Chen, Ch. S. Liu, “Soliton generation at resonance and density modification in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1147–1151 (1977); G. D. Doolen, D. F. DuBois, H. A. Rose, “Nucleation of cavitons in strong Langmuir turbulence,” Phys. Rev. Lett. 54, 804–807 (1985).
[CrossRef] [PubMed]

D. G. Colombant, N. K. Winsor, “Thermal-force terms and self-generated magnetic fields in laser-produced plasmas,” Phys. Rev. Lett. 38, 697–701 (1977).
[CrossRef]

1976 (2)

R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London Ser. A 347, 475–491 (1976). The following paper contains a comment on Peierls result: H. M. Lai, W. M. Suen, K. Young, “Microscopic derivation of a force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

F. L. Whipple, W. F. Huebner, “Physical processes in comets,” Ann. Rev. Astron. Astrophys. 14, 143–172 (1976), p. 166.
[CrossRef]

1975 (1)

J. J. Thomson, C. E. Max, K. Estabrook, “Magnetic fields due to resonance absorption of laser light,” Phys. Rev. Lett. 35, 663–667 (1975); W. Woo, J. S. DeGroot, “Magnetic fields due to laser light absorption,” Phys. Fluids 21, 2072–2075 (1978).
[CrossRef]

1974 (1)

H. C. Kim, R. L. Stenzel, A. Y. Wong, “Development of cavitons and trapping of rf fields,” Phys. Rev. Lett. 33, 886–889 (1974).
[CrossRef]

1971 (1)

E. E. Salpeter, “Central stars of planetary nebulae,” Ann. Rev. Astron. Astrophys. 9, 127–146 (1971) p. 141.
[CrossRef]

1969 (1)

W. G. Mathews, C. R. O’Dell, “Evolution of diffuse nebulae,” Ann. Rev. Astron. Astrophys. 7, 67–98 (1969) p. 85.
[CrossRef]

1968 (1)

J. C. Brandt, “The physics of comet tails,” Ann. Rev. Astron. Astrophys. 6, 267–286 (1968).
[CrossRef]

1967 (1)

H. Hora, D. Pfirsch, A. Schlüter, “Beschleunigung von inhomogenen Plasmen durch Laserlicht (Acceleration of inhomogeneous plasmas by laser light),” Z. Naturforsch. 22a, 278–280 (1967).

1965 (1)

1959 (1)

M. Schwarzschild, R. Härm, “On the maximum mass of stable stars,” Astrophys. J. 129, 637–646 (1959) (the upper limit for M given here is 60 sun masses); J. P. Cox, R. Th. Giuli, Stellar Structure (Gordon & Breach, New York, 1968), Vol. I, Chap. 11.
[CrossRef]

1958 (1)

H. A. H. Boot, S. A. Self, R. B. R. Shersby-Harvie, “Containment of a fully ionized plasma by radio frequency fields,” J. Electron. Control 4, 434–453 (1958); A. V. Gapunov, M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” Sov. Phys. JETP 7, 168–169 (1958).
[CrossRef]

1939 (1)

K. Rawer, “Elektrische Wellen in einem geschichteten Medium (Electric waves in a stratified medium),” Ann. Phys. 35, 385–416 (1939); Erratum 42, 294–296 (1942).
[CrossRef]

1923 (1)

W. Gerlach, A. Golsen, “Untersuchung an Radiometern. II. Eine neue Messung des Strahlungsdruckes (Investigations with radiometers. II. A new measurement of the radiation pressure),” Z. Phys. 15, 1–7 (1923).
[CrossRef]

1917 (1)

A. S. Eddington, “On the radiative equilibrium of stars,” Mon. Not. R. Astron. Soc. 77, 16 (1917).

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material (The light pressure on spheres of arbitrary material),” Ann. Phys. 30, 57–136 (1909).
[CrossRef]

1905 (1)

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (On a heuristic point of view concerning the generation and transformation of light),” Ann. Phys. 17, 132–148 (1905); “Zum gegenwärtigen Stand des Strahlungsproblems (additional new opinions on radiation problems),” Phys. Z. 10, 185–193 (1909); “Zur Quantentheorie der Strahlung (On quantum theory of radiation),” Phys. Z. 18, 121–128 (1917).
[CrossRef]

1904 (1)

J. H. Poynting, “Radiation in the solar system: its effect on temperature and its pressure on small bodies,” Phil. Trans. R. Soc. London Ser. A 202, 525–552 (1904); H. P. Robertson, “Dynamical effects on radiation in the solar system,” Mon. Not. R. Astron. Soc. 97, 423–438 (1937).
[CrossRef]

1903 (1)

E. Nichols, G. F. Hull, “Über Strahlungsdruck (On radiation pressure),” Ann. Phys. 12, 225–263 (1903).
[CrossRef]

1902 (1)

P. N. Lebedev, Astrophys. J. 14, 155–163 (1902).
[CrossRef]

1901 (1)

P. N. Lebedev, “Untersuchungen über die Druckkräfte des Lichtes (Investigations on the pressure forces of light),” Ann. Phys. 6, 433–458 (1901).
[CrossRef]

1884 (1)

L. Boltzmann, “Ableitung des Stefanschen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der elektromagnetischen Lichttheorie (Derivation of Stefan’s law concerning the temperature dependence of thermal radiation from the electromagnetic theory of light),” Wied. Ann. 22, 291–293 (1884).
[CrossRef]

1883 (1)

A. Bartoli, Nuovo Cimento 15, 195 (1883). According to Debye, Bartoli published his formula first in 1875 (see Ref. 80, p. 79).

Allen, L.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Bartoli, A.

A. Bartoli, Nuovo Cimento 15, 195 (1883). According to Debye, Bartoli published his formula first in 1875 (see Ref. 80, p. 79).

Baud, B.

B. Baud, H. J. Habing, “The maser strength of OH/IR stars, evolution of mass loss and the creation of superwind,” Astron. Astrophys. 127, 73–83 (1983).

Bers, A.

A. Bers, “Space–time evolution of plasma instabilities—absolute and convective,” in Handbook of Plasma Physics, M. N. Rosenbluth, R. Z. Sagdeev, eds. (North-Holland, Amsterdam, 1983), pp. 451–517.

Bize, D.

B. Guillame, A. Delfour, D. Bize, “10.6 μ m Mie scattering by a single particle in optical levitation,” Proc. Soc. PhotoOpt. Eng. 384, 66–72 (1983).

Bloembergen, N.

N. Bloembergen, “Nonlinear optics and spectroscopy,” Rev. Mod. Phys. 54, 685–695 (1982).
[CrossRef]

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

Boltzmann, L.

L. Boltzmann, “Ableitung des Stefanschen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der elektromagnetischen Lichttheorie (Derivation of Stefan’s law concerning the temperature dependence of thermal radiation from the electromagnetic theory of light),” Wied. Ann. 22, 291–293 (1884).
[CrossRef]

Boot, H. A. H.

H. A. H. Boot, S. A. Self, R. B. R. Shersby-Harvie, “Containment of a fully ionized plasma by radio frequency fields,” J. Electron. Control 4, 434–453 (1958); A. V. Gapunov, M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” Sov. Phys. JETP 7, 168–169 (1958).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 122.

Boulton, W. J.

W. J. Boulton, “The effect of solar radiation pressure on the orbit of a cylindrical satellite,” Planet Space Sci. 32, 287–296 (1984).
[CrossRef]

Brandt, J. C.

J. C. Brandt, “The physics of comet tails,” Ann. Rev. Astron. Astrophys. 6, 267–286 (1968).
[CrossRef]

Brevik, I.

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
[CrossRef]

Burgess, M. D. J.

R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
[CrossRef]

Carmen, R. L.

R. L. Carmen, D. W. Forslund, J. M. Kindel, “Visible harmonic emission as a way of measuring profile steepening,” Phys. Rev. Lett. 46, 29–32 (1981).
[CrossRef]

Chen, F. F.

F. F. Chen, “Physical mechanisms for laser-plasma parametric instabilities,” in Laser Interaction and Related Plasma Phenomena, H. J. Schwarz, H. Hora, eds. (Plenum, New York, 1974), p. 294; Introduction to Plasma Physics (Plenum, New York, 1976), p. 264.

Chen, H. H.

H. H. Chen, Ch. S. Liu, “Soliton generation at resonance and density modification in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1147–1151 (1977); G. D. Doolen, D. F. DuBois, H. A. Rose, “Nucleation of cavitons in strong Langmuir turbulence,” Phys. Rev. Lett. 54, 804–807 (1985).
[CrossRef] [PubMed]

Colombant, D. G.

D. G. Colombant, N. K. Winsor, “Thermal-force terms and self-generated magnetic fields in laser-produced plasmas,” Phys. Rev. Lett. 38, 697–701 (1977).
[CrossRef]

Cook, R. J.

R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
[CrossRef]

Crowley, B. J. B.

B. J. B. Crowley, “Dispersive effects in radiation transport and radiation hydrodynamics in matter at high density,” J. Phys. Colloq. C8 44, 25–38 (1983).

D’Evelyn, M.

M. D’Evelyn, G. M. Morales, “Properties of large amplitude Langmuir solitons,” Phys. Fluids 21, 1997–2008 (1978).
[CrossRef]

Davidson, R. C.

R. C. Davidson, Methods in Nonlinear Plasma Theory (Academic, New York, 1972), p. 125.

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material (The light pressure on spheres of arbitrary material),” Ann. Phys. 30, 57–136 (1909).
[CrossRef]

Delfour, A.

B. Guillame, A. Delfour, D. Bize, “10.6 μ m Mie scattering by a single particle in optical levitation,” Proc. Soc. PhotoOpt. Eng. 384, 66–72 (1983).

Drullinger, R. E.

D. W. Wineland, R. E. Drullinger, F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639–1642 (1978).
[CrossRef]

Duderstadt, J. J.

J. J. Duderstadt, G. A. Moses, Inertial Confinement Fusion (Wiley, New York, 1982), Chaps. 4 and 5.

Eberly, J. H.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Eddington, A. S.

A. S. Eddington, “On the radiative equilibrium of stars,” Mon. Not. R. Astron. Soc. 77, 16 (1917).

Einstein, A.

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (On a heuristic point of view concerning the generation and transformation of light),” Ann. Phys. 17, 132–148 (1905); “Zum gegenwärtigen Stand des Strahlungsproblems (additional new opinions on radiation problems),” Phys. Z. 10, 185–193 (1909); “Zur Quantentheorie der Strahlung (On quantum theory of radiation),” Phys. Z. 18, 121–128 (1917).
[CrossRef]

Enright, G. D.

R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
[CrossRef]

Estabrook, K.

J. J. Thomson, C. E. Max, K. Estabrook, “Magnetic fields due to resonance absorption of laser light,” Phys. Rev. Lett. 35, 663–667 (1975); W. Woo, J. S. DeGroot, “Magnetic fields due to laser light absorption,” Phys. Fluids 21, 2072–2075 (1978).
[CrossRef]

Fabelinskii, I. L.

V. S. Starunov, I. L. Fabelinskii, “Stimulated Mandel’shtam–Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463–489 (1969–70) [Usp. Fiz. Nauk 98, 441–491 (1969)].
[CrossRef]

Fedosejevs, R.

R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
[CrossRef]

Forslund, D. W.

R. L. Carmen, D. W. Forslund, J. M. Kindel, “Visible harmonic emission as a way of measuring profile steepening,” Phys. Rev. Lett. 46, 29–32 (1981).
[CrossRef]

K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
[CrossRef]

Fröhlich, H. E.

H. E. Fröhlich, “Der Druck des ultravioletten Strahlungsfeldes auf interstellare Staubteilchen (The pressure of the UV radiation field on interstellar dust particles),” Astron. Nachr. 302, 15–28 (1981).
[CrossRef]

Gerlach, W.

W. Gerlach, A. Golsen, “Untersuchung an Radiometern. II. Eine neue Messung des Strahlungsdruckes (Investigations with radiometers. II. A new measurement of the radiation pressure),” Z. Phys. 15, 1–7 (1923).
[CrossRef]

Ghatak, A. K.

For V see M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 194–212. For π see Ref. 44.

Giulietti, A.

P. Mulser, A. Giulietti, M. Vaselli, “Quantitative explanation of oscillating two-stream and parametric decay instabilities in terms of wave pressure,” Phys. Fluids 27, 2035–2038 (1984).
[CrossRef]

Golsen, A.

W. Gerlach, A. Golsen, “Untersuchung an Radiometern. II. Eine neue Messung des Strahlungsdruckes (Investigations with radiometers. II. A new measurement of the radiation pressure),” Z. Phys. 15, 1–7 (1923).
[CrossRef]

Guillame, B.

B. Guillame, A. Delfour, D. Bize, “10.6 μ m Mie scattering by a single particle in optical levitation,” Proc. Soc. PhotoOpt. Eng. 384, 66–72 (1983).

Habing, H. J.

B. Baud, H. J. Habing, “The maser strength of OH/IR stars, evolution of mass loss and the creation of superwind,” Astron. Astrophys. 127, 73–83 (1983).

Härm, R.

M. Schwarzschild, R. Härm, “On the maximum mass of stable stars,” Astrophys. J. 129, 637–646 (1959) (the upper limit for M given here is 60 sun masses); J. P. Cox, R. Th. Giuli, Stellar Structure (Gordon & Breach, New York, 1968), Vol. I, Chap. 11.
[CrossRef]

Haus, H. A.

P. Penfield, H. A. Haus, Electrodynamics of Moving Media (MIT Press, Cambridge, Mass.1967), Chaps. 1, 7, 8. For additional references see also M. M. Novak, “Interaction of photons with electrons in dielectric media,” Fortschr. Phys. 28, 285–355 (1980).
[CrossRef]

Hills, J. G.

J. G. Hills, “The formation of comets by radiation pressure in the outer protosun,” Astron. J. 87, 906–910 (1982); J. G. Hills, M. T. Sandford, “Dependence on the radiation-grain coupling,” Astron. J. 88, 1519–1521 (1983); “Dependence on the anistropy of the radiation field,” Astron J. 88, 1522–1530 (1983).
[CrossRef]

Hohenstatt, M.

W. Neuhauser, M. Hohenstatt, P. Toschek, “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233–236 (1978).
[CrossRef]

Hora, H.

H. Hora, D. Pfirsch, A. Schlüter, “Beschleunigung von inhomogenen Plasmen durch Laserlicht (Acceleration of inhomogeneous plasmas by laser light),” Z. Naturforsch. 22a, 278–280 (1967).

Huebner, W. F.

F. L. Whipple, W. F. Huebner, “Physical processes in comets,” Ann. Rev. Astron. Astrophys. 14, 143–172 (1976), p. 166.
[CrossRef]

Hull, G. F.

E. Nichols, G. F. Hull, “Über Strahlungsdruck (On radiation pressure),” Ann. Phys. 12, 225–263 (1903).
[CrossRef]

Il’in, V. B.

N. V. Voshchinnikov, V. B. Il’in, “Planck mean cross sections for radiation pressure for nonspherical grains. I and II,” Astrophys. 18, 353–360 (1982); Astrophys. 19, 347–357 (1983).

Irvine, W. M.

Jauch, J. M.

J. M. Jauch, F. Rohrlich, The Theory of Photons and Electrons (Springer, New York, 1976); J. Schwinger, Quantum Electrodynamics (Dover, New York, 1958) (contains a collection of original papers since 1927); C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
[CrossRef]

Javanainen, J.

Johnson, Th. M.

Th. M. Johnson, “Inertial confinement fusion: review and perspective,” Proc. IEEE 72, 548–594 (1984).
[CrossRef]

Kaw, P.

P. Kaw, G. Schmidt, T. Wilcox, “Filamentation and trapping of electromagnetic radiation in plasmas,” Phys. Fluids16, 1522–1525 (1973); R. W. Short, R. Bingham, E. A. Williams, “Filamentation of laser light in flowing plasmas,” Phys. Fluids 25, 2302–2305 (1982); M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 171–265.
[CrossRef]

Kiefer, W.

Kim, H. C.

H. C. Kim, R. L. Stenzel, A. Y. Wong, “Development of cavitons and trapping of rf fields,” Phys. Rev. Lett. 33, 886–889 (1974).
[CrossRef]

Kindel, J. M.

R. L. Carmen, D. W. Forslund, J. M. Kindel, “Visible harmonic emission as a way of measuring profile steepening,” Phys. Rev. Lett. 46, 29–32 (1981).
[CrossRef]

K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1981), Secs. 15 and 16; R. Becker, F. Sauter, Electromagnetic Fields and Interactions (Dover, New York, 1982), Vol. I, Sec. 35. See also Ref. 21, Chap. 6.

See, for example, L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1979), Chaps. 1 and 2.

Langdon, A. B.

A. B. Langdon, “Nonlinear inverse bremsstrahlung and heated-electron distributions,” Phys. Rev. Lett. 44, 575–579 (1980).
[CrossRef]

Lebedev, P. N.

P. N. Lebedev, Astrophys. J. 14, 155–163 (1902).
[CrossRef]

P. N. Lebedev, “Untersuchungen über die Druckkräfte des Lichtes (Investigations on the pressure forces of light),” Ann. Phys. 6, 433–458 (1901).
[CrossRef]

Lee, K.

K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
[CrossRef]

Letokhov, V. S.

V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1–65 (1981).
[CrossRef]

V. S. Letokhov, V. G. Minogin, “Laser cooling of atoms and its application in frequency standards,” J. Phys. Colloq. C8, 42, 347–355 (1981).

Lifshitz, E. M.

See, for example, L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1979), Chaps. 1 and 2.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1981), Secs. 15 and 16; R. Becker, F. Sauter, Electromagnetic Fields and Interactions (Dover, New York, 1982), Vol. I, Sec. 35. See also Ref. 21, Chap. 6.

Lindberg, M.

Lindman, E. L.

K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
[CrossRef]

Liu, C. S.

C. S. Liu, “Parametric instabilities in homogeneous unmagnetized plasmas,” in Advances in Plasma Physics (Wiley, New York, 1976), pp. 83–120.

Liu, Ch. S.

H. H. Chen, Ch. S. Liu, “Soliton generation at resonance and density modification in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1147–1151 (1977); G. D. Doolen, D. F. DuBois, H. A. Rose, “Nucleation of cavitons in strong Langmuir turbulence,” Phys. Rev. Lett. 54, 804–807 (1985).
[CrossRef] [PubMed]

Lorentz, H. A.

H. A. Lorentz, “Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern (Attempt to establish a theory of the electrical and optical phenomena in moving bodies),” (Brill, Leiden, 1895; reprint Teubner, Leipzig, 1906), pp. 21–29; H. A. Lorentz, The Theory of Electrons (1909; republished by Dover, New York, 1952).

Loudon, R.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1978).

Mathews, W. G.

W. G. Mathews, C. R. O’Dell, “Evolution of diffuse nebulae,” Ann. Rev. Astron. Astrophys. 7, 67–98 (1969) p. 85.
[CrossRef]

Max, C. E.

J. J. Thomson, C. E. Max, K. Estabrook, “Magnetic fields due to resonance absorption of laser light,” Phys. Rev. Lett. 35, 663–667 (1975); W. Woo, J. S. DeGroot, “Magnetic fields due to laser light absorption,” Phys. Fluids 21, 2072–2075 (1978).
[CrossRef]

Maxwell, J. C.

J. C. Maxwell, A Treatise on Electricity and Magnetism (Oxford U. Press, Oxford, 1871).

McLean, E. A.

J. A. Stamper, E. A. McLean, B. H. Ripin, “Studies of spontaneous magnetic fields in laser-produced plasmas by Faraday rotation,” Phys. Rev. Lett. 40, 1177–1180 (1978); A. Raven, O. Willi, P. T. Rumsby, “Megagauss magnetic field profiles in laser-produced plasmas,” Phys. Rev. Lett. 41, 554–557 (1979).
[CrossRef]

Minogin, V. G.

V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1–65 (1981).
[CrossRef]

V. S. Letokhov, V. G. Minogin, “Laser cooling of atoms and its application in frequency standards,” J. Phys. Colloq. C8, 42, 347–355 (1981).

Morales, G. M.

M. D’Evelyn, G. M. Morales, “Properties of large amplitude Langmuir solitons,” Phys. Fluids 21, 1997–2008 (1978).
[CrossRef]

Moses, G. A.

J. J. Duderstadt, G. A. Moses, Inertial Confinement Fusion (Wiley, New York, 1982), Chaps. 4 and 5.

Mulser, P.

A. Zeidler, H. Schnabl, P. Mulser, “Light pressure of time-dependent fields in plasmas,” Phys. Fluids 28, 372–376 (1985). The time-dependent expression of π was found in 1982 (see Annual Report 1982, Institute of Applied Physics, Technical University, 6100 Darmstadt, p. 55). For a homogeneous plasma it is also obtained by summing up all terms for B0= 0 in Ref. 44.
[CrossRef]

P. Mulser, A. Giulietti, M. Vaselli, “Quantitative explanation of oscillating two-stream and parametric decay instabilities in terms of wave pressure,” Phys. Fluids 27, 2035–2038 (1984).
[CrossRef]

P. Mulser, H. Schnabl, “Excitation of large amplitude electron plasma waves by laser,” Laser Particle Beams 1, 379–394 (1983); Erratum 2, 254 (1984).
[CrossRef]

H. Takabe, P. Mulser, “Self consistent treatment of resonance absorption in a streaming plasma,” Phys. Fluids 25, 2304–2306 (1982); W. L. Kruer, “Model of resonance absorption with profile modification,” Phys. Fluids 25, 2324–2325 (1982).
[CrossRef]

P. Mulser, G. Spindler, “Radiation pressure dominated plasma flow,” Z. Naturforsch. 34a, 1059–1062 (1979).

P. Mulser, C. van Kessel, “Profile modifications and plateau formation due to light pressure in laser irradiated targets,” Phys. Rev. Lett. 38, 902–905 (1977).
[CrossRef]

P. Mulser, “Nonlinear optics and wave pressure in laser plasmas,” in Laser–Plasma Interactions 2, R. A. Cairns, ed. (SUSSP, Edinburgh, U.K., 1983), pp. 29–54.

Neuhauser, W.

W. Neuhauser, M. Hohenstatt, P. Toschek, “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233–236 (1978).
[CrossRef]

Nichols, E.

E. Nichols, G. F. Hull, “Über Strahlungsdruck (On radiation pressure),” Ann. Phys. 12, 225–263 (1903).
[CrossRef]

O’Dell, C. R.

W. G. Mathews, C. R. O’Dell, “Evolution of diffuse nebulae,” Ann. Rev. Astron. Astrophys. 7, 67–98 (1969) p. 85.
[CrossRef]

Panofsky, W. K. H.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1975), Chap. 11.

Peierls, R.

R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London Ser. A 347, 475–491 (1976). The following paper contains a comment on Peierls result: H. M. Lai, W. M. Suen, K. Young, “Microscopic derivation of a force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

Penfield, P.

P. Penfield, H. A. Haus, Electrodynamics of Moving Media (MIT Press, Cambridge, Mass.1967), Chaps. 1, 7, 8. For additional references see also M. M. Novak, “Interaction of photons with electrons in dielectric media,” Fortschr. Phys. 28, 285–355 (1980).
[CrossRef]

Pfirsch, D.

H. Hora, D. Pfirsch, A. Schlüter, “Beschleunigung von inhomogenen Plasmen durch Laserlicht (Acceleration of inhomogeneous plasmas by laser light),” Z. Naturforsch. 22a, 278–280 (1967).

Phillips, M.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1975), Chap. 11.

Pomraning, G. C.

G. C. Pomraning, Radiation Hydrodynamics (Pergamon, Oxford, 1973); M. S. Zubairy, “Radiative energy transfer in presence of random source distributions,” in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York, 1978), pp. 459–467.

Poynting, J. H.

J. H. Poynting, “Radiation in the solar system: its effect on temperature and its pressure on small bodies,” Phil. Trans. R. Soc. London Ser. A 202, 525–552 (1904); H. P. Robertson, “Dynamical effects on radiation in the solar system,” Mon. Not. R. Astron. Soc. 97, 423–438 (1937).
[CrossRef]

Rawer, K.

K. Rawer, “Elektrische Wellen in einem geschichteten Medium (Electric waves in a stratified medium),” Ann. Phys. 35, 385–416 (1939); Erratum 42, 294–296 (1942).
[CrossRef]

Reiman, A.

A. Reiman, “Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium,” Rev. Mod. Phys. 51, 311–330 (1979).
[CrossRef]

Richardson, M. C.

R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
[CrossRef]

Ripin, B. H.

J. A. Stamper, E. A. McLean, B. H. Ripin, “Studies of spontaneous magnetic fields in laser-produced plasmas by Faraday rotation,” Phys. Rev. Lett. 40, 1177–1180 (1978); A. Raven, O. Willi, P. T. Rumsby, “Megagauss magnetic field profiles in laser-produced plasmas,” Phys. Rev. Lett. 41, 554–557 (1979).
[CrossRef]

Rohrlich, F.

J. M. Jauch, F. Rohrlich, The Theory of Photons and Electrons (Springer, New York, 1976); J. Schwinger, Quantum Electrodynamics (Dover, New York, 1958) (contains a collection of original papers since 1927); C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
[CrossRef]

Roy, A. E.

A. E. Roy, Orbital Motion (Adam Hilger, Bristol, England, 1978), Chap. 12.

Rumsby, P. T.

O. Willi, P. T. Rumsby, “Filamentation on laser irradiated spherical targets,” Opt. Commun. 37, 45–48 (1981).
[CrossRef]

Salpeter, E. E.

E. E. Salpeter, “Central stars of planetary nebulae,” Ann. Rev. Astron. Astrophys. 9, 127–146 (1971) p. 141.
[CrossRef]

Schlüter, A.

H. Hora, D. Pfirsch, A. Schlüter, “Beschleunigung von inhomogenen Plasmen durch Laserlicht (Acceleration of inhomogeneous plasmas by laser light),” Z. Naturforsch. 22a, 278–280 (1967).

Schmidt, G.

P. Kaw, G. Schmidt, T. Wilcox, “Filamentation and trapping of electromagnetic radiation in plasmas,” Phys. Fluids16, 1522–1525 (1973); R. W. Short, R. Bingham, E. A. Williams, “Filamentation of laser light in flowing plasmas,” Phys. Fluids 25, 2302–2305 (1982); M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 171–265.
[CrossRef]

Schnabl, H.

A. Zeidler, H. Schnabl, P. Mulser, “Light pressure of time-dependent fields in plasmas,” Phys. Fluids 28, 372–376 (1985). The time-dependent expression of π was found in 1982 (see Annual Report 1982, Institute of Applied Physics, Technical University, 6100 Darmstadt, p. 55). For a homogeneous plasma it is also obtained by summing up all terms for B0= 0 in Ref. 44.
[CrossRef]

P. Mulser, H. Schnabl, “Excitation of large amplitude electron plasma waves by laser,” Laser Particle Beams 1, 379–394 (1983); Erratum 2, 254 (1984).
[CrossRef]

Schneider, W.

W. Schneider, “Elektronenbeschleunigung durch inhomogene Langmuirwellen hoher Amplitude (Electron acceleration in inhomogeneous high-amplitude Langmuir waves),” Phys. Fluids (to be published).

Schwarzschild, M.

M. Schwarzschild, R. Härm, “On the maximum mass of stable stars,” Astrophys. J. 129, 637–646 (1959) (the upper limit for M given here is 60 sun masses); J. P. Cox, R. Th. Giuli, Stellar Structure (Gordon & Breach, New York, 1968), Vol. I, Chap. 11.
[CrossRef]

Self, S. A.

H. A. H. Boot, S. A. Self, R. B. R. Shersby-Harvie, “Containment of a fully ionized plasma by radio frequency fields,” J. Electron. Control 4, 434–453 (1958); A. V. Gapunov, M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” Sov. Phys. JETP 7, 168–169 (1958).
[CrossRef]

Shersby-Harvie, R. B. R.

H. A. H. Boot, S. A. Self, R. B. R. Shersby-Harvie, “Containment of a fully ionized plasma by radio frequency fields,” J. Electron. Control 4, 434–453 (1958); A. V. Gapunov, M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” Sov. Phys. JETP 7, 168–169 (1958).
[CrossRef]

Sodha, M. S.

For V see M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 194–212. For π see Ref. 44.

Spindler, G.

P. Mulser, G. Spindler, “Radiation pressure dominated plasma flow,” Z. Naturforsch. 34a, 1059–1062 (1979).

Spitzer, L.

L. Spitzer, Diffuse Matter in Space (Wiley/Interscience, New York, 1968), pp. 207–212.

Stamper, J. A.

J. A. Stamper, E. A. McLean, B. H. Ripin, “Studies of spontaneous magnetic fields in laser-produced plasmas by Faraday rotation,” Phys. Rev. Lett. 40, 1177–1180 (1978); A. Raven, O. Willi, P. T. Rumsby, “Megagauss magnetic field profiles in laser-produced plasmas,” Phys. Rev. Lett. 41, 554–557 (1979).
[CrossRef]

Starunov, V. S.

V. S. Starunov, I. L. Fabelinskii, “Stimulated Mandel’shtam–Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463–489 (1969–70) [Usp. Fiz. Nauk 98, 441–491 (1969)].
[CrossRef]

Stenholm, S.

Stenzel, R. L.

H. C. Kim, R. L. Stenzel, A. Y. Wong, “Development of cavitons and trapping of rf fields,” Phys. Rev. Lett. 33, 886–889 (1974).
[CrossRef]

Stratham, G.

G. Stratham, D. ter Haar, “Strong turbulence of a magnetized plasma. II. The ponderomotive force,” Plasma Phys. 25, 681–698 (1983).
[CrossRef]

Svelto, O.

O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 1–51.
[CrossRef]

Takabe, H.

H. Takabe, P. Mulser, “Self consistent treatment of resonance absorption in a streaming plasma,” Phys. Fluids 25, 2304–2306 (1982); W. L. Kruer, “Model of resonance absorption with profile modification,” Phys. Fluids 25, 2324–2325 (1982).
[CrossRef]

ter Haar, D.

G. Stratham, D. ter Haar, “Strong turbulence of a magnetized plasma. II. The ponderomotive force,” Plasma Phys. 25, 681–698 (1983).
[CrossRef]

Thomson, J. J.

J. J. Thomson, C. E. Max, K. Estabrook, “Magnetic fields due to resonance absorption of laser light,” Phys. Rev. Lett. 35, 663–667 (1975); W. Woo, J. S. DeGroot, “Magnetic fields due to laser light absorption,” Phys. Fluids 21, 2072–2075 (1978).
[CrossRef]

Thurn, R.

Toschek, P.

W. Neuhauser, M. Hohenstatt, P. Toschek, “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233–236 (1978).
[CrossRef]

Tripathi, V. K.

For V see M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 194–212. For π see Ref. 44.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1950).

van Kessel, C.

P. Mulser, C. van Kessel, “Profile modifications and plateau formation due to light pressure in laser irradiated targets,” Phys. Rev. Lett. 38, 902–905 (1977).
[CrossRef]

Vaselli, M.

P. Mulser, A. Giulietti, M. Vaselli, “Quantitative explanation of oscillating two-stream and parametric decay instabilities in terms of wave pressure,” Phys. Fluids 27, 2035–2038 (1984).
[CrossRef]

Voshchinnikov, N. V.

N. V. Voshchinnikov, V. B. Il’in, “Planck mean cross sections for radiation pressure for nonspherical grains. I and II,” Astrophys. 18, 353–360 (1982); Astrophys. 19, 347–357 (1983).

Walls, F. L.

D. W. Wineland, R. E. Drullinger, F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639–1642 (1978).
[CrossRef]

Weinberg, S.

S. Weinberg, The First Three Minutes (Basic, New York, 1977).

Whipple, F. L.

F. L. Whipple, W. F. Huebner, “Physical processes in comets,” Ann. Rev. Astron. Astrophys. 14, 143–172 (1976), p. 166.
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), pp. 247–251; V. A. Kulkarny, B. S. White, “Focusing and waves in turbulent inhomogeneous media,” Phys. Fluids 25, 1770–1784 (1982); M. J. Beran, “Coherence theory and caustic corrections,” Proc. Soc. Photo-Opt. Eng. 358, 176–183 (1982).
[CrossRef]

Wilcox, T.

P. Kaw, G. Schmidt, T. Wilcox, “Filamentation and trapping of electromagnetic radiation in plasmas,” Phys. Fluids16, 1522–1525 (1973); R. W. Short, R. Bingham, E. A. Williams, “Filamentation of laser light in flowing plasmas,” Phys. Fluids 25, 2302–2305 (1982); M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 171–265.
[CrossRef]

Willi, O.

O. Willi, P. T. Rumsby, “Filamentation on laser irradiated spherical targets,” Opt. Commun. 37, 45–48 (1981).
[CrossRef]

Wineland, D. W.

D. W. Wineland, R. E. Drullinger, F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639–1642 (1978).
[CrossRef]

Winsor, N. K.

D. G. Colombant, N. K. Winsor, “Thermal-force terms and self-generated magnetic fields in laser-produced plasmas,” Phys. Rev. Lett. 38, 697–701 (1977).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 122.

Wong, A. Y.

H. C. Kim, R. L. Stenzel, A. Y. Wong, “Development of cavitons and trapping of rf fields,” Phys. Rev. Lett. 33, 886–889 (1974).
[CrossRef]

Zeidler, A.

A. Zeidler, H. Schnabl, P. Mulser, “Light pressure of time-dependent fields in plasmas,” Phys. Fluids 28, 372–376 (1985). The time-dependent expression of π was found in 1982 (see Annual Report 1982, Institute of Applied Physics, Technical University, 6100 Darmstadt, p. 55). For a homogeneous plasma it is also obtained by summing up all terms for B0= 0 in Ref. 44.
[CrossRef]

Ann. Phys. (5)

P. N. Lebedev, “Untersuchungen über die Druckkräfte des Lichtes (Investigations on the pressure forces of light),” Ann. Phys. 6, 433–458 (1901).
[CrossRef]

E. Nichols, G. F. Hull, “Über Strahlungsdruck (On radiation pressure),” Ann. Phys. 12, 225–263 (1903).
[CrossRef]

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (On a heuristic point of view concerning the generation and transformation of light),” Ann. Phys. 17, 132–148 (1905); “Zum gegenwärtigen Stand des Strahlungsproblems (additional new opinions on radiation problems),” Phys. Z. 10, 185–193 (1909); “Zur Quantentheorie der Strahlung (On quantum theory of radiation),” Phys. Z. 18, 121–128 (1917).
[CrossRef]

K. Rawer, “Elektrische Wellen in einem geschichteten Medium (Electric waves in a stratified medium),” Ann. Phys. 35, 385–416 (1939); Erratum 42, 294–296 (1942).
[CrossRef]

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material (The light pressure on spheres of arbitrary material),” Ann. Phys. 30, 57–136 (1909).
[CrossRef]

Ann. Rev. Astron. Astrophys. (4)

F. L. Whipple, W. F. Huebner, “Physical processes in comets,” Ann. Rev. Astron. Astrophys. 14, 143–172 (1976), p. 166.
[CrossRef]

J. C. Brandt, “The physics of comet tails,” Ann. Rev. Astron. Astrophys. 6, 267–286 (1968).
[CrossRef]

E. E. Salpeter, “Central stars of planetary nebulae,” Ann. Rev. Astron. Astrophys. 9, 127–146 (1971) p. 141.
[CrossRef]

W. G. Mathews, C. R. O’Dell, “Evolution of diffuse nebulae,” Ann. Rev. Astron. Astrophys. 7, 67–98 (1969) p. 85.
[CrossRef]

Appl. Spectrosc. (1)

Astron. Astrophys. (1)

B. Baud, H. J. Habing, “The maser strength of OH/IR stars, evolution of mass loss and the creation of superwind,” Astron. Astrophys. 127, 73–83 (1983).

Astron. J. (1)

J. G. Hills, “The formation of comets by radiation pressure in the outer protosun,” Astron. J. 87, 906–910 (1982); J. G. Hills, M. T. Sandford, “Dependence on the radiation-grain coupling,” Astron. J. 88, 1519–1521 (1983); “Dependence on the anistropy of the radiation field,” Astron J. 88, 1522–1530 (1983).
[CrossRef]

Astron. Nachr. (1)

H. E. Fröhlich, “Der Druck des ultravioletten Strahlungsfeldes auf interstellare Staubteilchen (The pressure of the UV radiation field on interstellar dust particles),” Astron. Nachr. 302, 15–28 (1981).
[CrossRef]

Astrophys. (1)

N. V. Voshchinnikov, V. B. Il’in, “Planck mean cross sections for radiation pressure for nonspherical grains. I and II,” Astrophys. 18, 353–360 (1982); Astrophys. 19, 347–357 (1983).

Astrophys. J. (2)

M. Schwarzschild, R. Härm, “On the maximum mass of stable stars,” Astrophys. J. 129, 637–646 (1959) (the upper limit for M given here is 60 sun masses); J. P. Cox, R. Th. Giuli, Stellar Structure (Gordon & Breach, New York, 1968), Vol. I, Chap. 11.
[CrossRef]

P. N. Lebedev, Astrophys. J. 14, 155–163 (1902).
[CrossRef]

J. Electron. Control (1)

H. A. H. Boot, S. A. Self, R. B. R. Shersby-Harvie, “Containment of a fully ionized plasma by radio frequency fields,” J. Electron. Control 4, 434–453 (1958); A. V. Gapunov, M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” Sov. Phys. JETP 7, 168–169 (1958).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Phys. Colloq. C8 (2)

V. S. Letokhov, V. G. Minogin, “Laser cooling of atoms and its application in frequency standards,” J. Phys. Colloq. C8, 42, 347–355 (1981).

B. J. B. Crowley, “Dispersive effects in radiation transport and radiation hydrodynamics in matter at high density,” J. Phys. Colloq. C8 44, 25–38 (1983).

Laser Particle Beams (1)

P. Mulser, H. Schnabl, “Excitation of large amplitude electron plasma waves by laser,” Laser Particle Beams 1, 379–394 (1983); Erratum 2, 254 (1984).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

A. S. Eddington, “On the radiative equilibrium of stars,” Mon. Not. R. Astron. Soc. 77, 16 (1917).

Nuovo Cimento (1)

A. Bartoli, Nuovo Cimento 15, 195 (1883). According to Debye, Bartoli published his formula first in 1875 (see Ref. 80, p. 79).

Opt. Commun. (1)

O. Willi, P. T. Rumsby, “Filamentation on laser irradiated spherical targets,” Opt. Commun. 37, 45–48 (1981).
[CrossRef]

Phil. Trans. R. Soc. London Ser. A (1)

J. H. Poynting, “Radiation in the solar system: its effect on temperature and its pressure on small bodies,” Phil. Trans. R. Soc. London Ser. A 202, 525–552 (1904); H. P. Robertson, “Dynamical effects on radiation in the solar system,” Mon. Not. R. Astron. Soc. 97, 423–438 (1937).
[CrossRef]

Phys. Fluids (5)

M. D’Evelyn, G. M. Morales, “Properties of large amplitude Langmuir solitons,” Phys. Fluids 21, 1997–2008 (1978).
[CrossRef]

P. Mulser, A. Giulietti, M. Vaselli, “Quantitative explanation of oscillating two-stream and parametric decay instabilities in terms of wave pressure,” Phys. Fluids 27, 2035–2038 (1984).
[CrossRef]

K. Lee, D. W. Forslund, J. M. Kindel, E. L. Lindman, “Theoretical derivation of laser induced plasma profiles,” Phys. Fluids 20, 51–54 (1977); C. Max, C. McKee, “Effects of flow on density profiles in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1336–1339 (1977).
[CrossRef]

H. Takabe, P. Mulser, “Self consistent treatment of resonance absorption in a streaming plasma,” Phys. Fluids 25, 2304–2306 (1982); W. L. Kruer, “Model of resonance absorption with profile modification,” Phys. Fluids 25, 2324–2325 (1982).
[CrossRef]

A. Zeidler, H. Schnabl, P. Mulser, “Light pressure of time-dependent fields in plasmas,” Phys. Fluids 28, 372–376 (1985). The time-dependent expression of π was found in 1982 (see Annual Report 1982, Institute of Applied Physics, Technical University, 6100 Darmstadt, p. 55). For a homogeneous plasma it is also obtained by summing up all terms for B0= 0 in Ref. 44.
[CrossRef]

Phys. Rep. (2)

V. S. Letokhov, V. G. Minogin, “Laser radiation pressure on free atoms,” Phys. Rep. 73, 1–65 (1981).
[CrossRef]

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep. 52, 133–201 (1979).
[CrossRef]

Phys. Rev. A (1)

R. J. Cook, “Theory of resonance-radiation pressure,” Phys. Rev. A 22, 1078–1098 (1980).
[CrossRef]

Phys. Rev. Lett. (11)

R. L. Carmen, D. W. Forslund, J. M. Kindel, “Visible harmonic emission as a way of measuring profile steepening,” Phys. Rev. Lett. 46, 29–32 (1981).
[CrossRef]

R. Fedosejevs, M. D. J. Burgess, G. D. Enright, M. C. Richardson, “Supercritical density profiles of CO2-laser-irradiated microballoons,” Phys. Rev. Lett. 43, 1664–1667 (1979); D. R. Bach, D. E. Casperson, D. W. Forslund, S. J. Gitomer, P. D. Goldstone, A. Hauer, J. F. Kephart, J. M. Kindel, R. Kristal, G. A. Kyrala, K. B. Mitchell, D. B. van Hulsteyn, A. H. Williams, “Intensity dependent absorption in 10.6-μ m laser-illuminated spheres,” Phys. Rev. Lett. 50, 2082–2085 (1983).
[CrossRef]

P. Mulser, C. van Kessel, “Profile modifications and plateau formation due to light pressure in laser irradiated targets,” Phys. Rev. Lett. 38, 902–905 (1977).
[CrossRef]

A. B. Langdon, “Nonlinear inverse bremsstrahlung and heated-electron distributions,” Phys. Rev. Lett. 44, 575–579 (1980).
[CrossRef]

H. H. Chen, Ch. S. Liu, “Soliton generation at resonance and density modification in laser-irradiated plasmas,” Phys. Rev. Lett. 39, 1147–1151 (1977); G. D. Doolen, D. F. DuBois, H. A. Rose, “Nucleation of cavitons in strong Langmuir turbulence,” Phys. Rev. Lett. 54, 804–807 (1985).
[CrossRef] [PubMed]

H. C. Kim, R. L. Stenzel, A. Y. Wong, “Development of cavitons and trapping of rf fields,” Phys. Rev. Lett. 33, 886–889 (1974).
[CrossRef]

J. A. Stamper, E. A. McLean, B. H. Ripin, “Studies of spontaneous magnetic fields in laser-produced plasmas by Faraday rotation,” Phys. Rev. Lett. 40, 1177–1180 (1978); A. Raven, O. Willi, P. T. Rumsby, “Megagauss magnetic field profiles in laser-produced plasmas,” Phys. Rev. Lett. 41, 554–557 (1979).
[CrossRef]

D. G. Colombant, N. K. Winsor, “Thermal-force terms and self-generated magnetic fields in laser-produced plasmas,” Phys. Rev. Lett. 38, 697–701 (1977).
[CrossRef]

J. J. Thomson, C. E. Max, K. Estabrook, “Magnetic fields due to resonance absorption of laser light,” Phys. Rev. Lett. 35, 663–667 (1975); W. Woo, J. S. DeGroot, “Magnetic fields due to laser light absorption,” Phys. Fluids 21, 2072–2075 (1978).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. Toschek, “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev. Lett. 41, 233–236 (1978).
[CrossRef]

D. W. Wineland, R. E. Drullinger, F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,” Phys. Rev. Lett. 40, 1639–1642 (1978).
[CrossRef]

Planet Space Sci. (1)

W. J. Boulton, “The effect of solar radiation pressure on the orbit of a cylindrical satellite,” Planet Space Sci. 32, 287–296 (1984).
[CrossRef]

Plasma Phys. (1)

G. Stratham, D. ter Haar, “Strong turbulence of a magnetized plasma. II. The ponderomotive force,” Plasma Phys. 25, 681–698 (1983).
[CrossRef]

Proc. IEEE (1)

Th. M. Johnson, “Inertial confinement fusion: review and perspective,” Proc. IEEE 72, 548–594 (1984).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

R. Peierls, “The momentum of light in a refracting medium,” Proc. R. Soc. London Ser. A 347, 475–491 (1976). The following paper contains a comment on Peierls result: H. M. Lai, W. M. Suen, K. Young, “Microscopic derivation of a force on a dielectric fluid in an electromagnetic field,” Phys. Rev. A 25, 1755–1763 (1982).
[CrossRef]

Proc. Soc. PhotoOpt. Eng. (1)

B. Guillame, A. Delfour, D. Bize, “10.6 μ m Mie scattering by a single particle in optical levitation,” Proc. Soc. PhotoOpt. Eng. 384, 66–72 (1983).

Rev. Mod. Phys. (2)

N. Bloembergen, “Nonlinear optics and spectroscopy,” Rev. Mod. Phys. 54, 685–695 (1982).
[CrossRef]

A. Reiman, “Space-time evolution of nonlinear three-wave interactions. II. Interaction in an inhomogeneous medium,” Rev. Mod. Phys. 51, 311–330 (1979).
[CrossRef]

Sov. Phys. Usp. (1)

V. S. Starunov, I. L. Fabelinskii, “Stimulated Mandel’shtam–Brillouin scattering and stimulated entropy (temperature) scattering of light,” Sov. Phys. Usp. 12, 463–489 (1969–70) [Usp. Fiz. Nauk 98, 441–491 (1969)].
[CrossRef]

Wied. Ann. (1)

L. Boltzmann, “Ableitung des Stefanschen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der elektromagnetischen Lichttheorie (Derivation of Stefan’s law concerning the temperature dependence of thermal radiation from the electromagnetic theory of light),” Wied. Ann. 22, 291–293 (1884).
[CrossRef]

Z. Naturforsch. (2)

H. Hora, D. Pfirsch, A. Schlüter, “Beschleunigung von inhomogenen Plasmen durch Laserlicht (Acceleration of inhomogeneous plasmas by laser light),” Z. Naturforsch. 22a, 278–280 (1967).

P. Mulser, G. Spindler, “Radiation pressure dominated plasma flow,” Z. Naturforsch. 34a, 1059–1062 (1979).

Z. Phys. (1)

W. Gerlach, A. Golsen, “Untersuchung an Radiometern. II. Eine neue Messung des Strahlungsdruckes (Investigations with radiometers. II. A new measurement of the radiation pressure),” Z. Phys. 15, 1–7 (1923).
[CrossRef]

Other (28)

J. C. Maxwell, A Treatise on Electricity and Magnetism (Oxford U. Press, Oxford, 1871).

L. Spitzer, Diffuse Matter in Space (Wiley/Interscience, New York, 1968), pp. 207–212.

S. Weinberg, The First Three Minutes (Basic, New York, 1977).

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1975), Chap. 11.

H. A. Lorentz, “Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern (Attempt to establish a theory of the electrical and optical phenomena in moving bodies),” (Brill, Leiden, 1895; reprint Teubner, Leipzig, 1906), pp. 21–29; H. A. Lorentz, The Theory of Electrons (1909; republished by Dover, New York, 1952).

P. Penfield, H. A. Haus, Electrodynamics of Moving Media (MIT Press, Cambridge, Mass.1967), Chaps. 1, 7, 8. For additional references see also M. M. Novak, “Interaction of photons with electrons in dielectric media,” Fortschr. Phys. 28, 285–355 (1980).
[CrossRef]

Proceedings of the Workshop on Laser-Cooled and Trapped Atoms, Washington, April 14-15, 1983 [Nat. Bur. Stand. (U.S.) Spec. Publ. 653 (1983); contains 20 papers].

A. E. Roy, Orbital Motion (Adam Hilger, Bristol, England, 1978), Chap. 12.

J. M. Jauch, F. Rohrlich, The Theory of Photons and Electrons (Springer, New York, 1976); J. Schwinger, Quantum Electrodynamics (Dover, New York, 1958) (contains a collection of original papers since 1927); C. Itzykson, J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1950).

F. F. Chen, “Physical mechanisms for laser-plasma parametric instabilities,” in Laser Interaction and Related Plasma Phenomena, H. J. Schwarz, H. Hora, eds. (Plenum, New York, 1974), p. 294; Introduction to Plasma Physics (Plenum, New York, 1976), p. 264.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1978).

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

J. J. Duderstadt, G. A. Moses, Inertial Confinement Fusion (Wiley, New York, 1982), Chaps. 4 and 5.

O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 1–51.
[CrossRef]

See, for example, L. D. Landau, E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1979), Chaps. 1 and 2.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1981), Secs. 15 and 16; R. Becker, F. Sauter, Electromagnetic Fields and Interactions (Dover, New York, 1982), Vol. I, Sec. 35. See also Ref. 21, Chap. 6.

P. Kaw, G. Schmidt, T. Wilcox, “Filamentation and trapping of electromagnetic radiation in plasmas,” Phys. Fluids16, 1522–1525 (1973); R. W. Short, R. Bingham, E. A. Williams, “Filamentation of laser light in flowing plasmas,” Phys. Fluids 25, 2302–2305 (1982); M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 171–265.
[CrossRef]

P. Mulser, “Nonlinear optics and wave pressure in laser plasmas,” in Laser–Plasma Interactions 2, R. A. Cairns, ed. (SUSSP, Edinburgh, U.K., 1983), pp. 29–54.

W. Schneider, “Elektronenbeschleunigung durch inhomogene Langmuirwellen hoher Amplitude (Electron acceleration in inhomogeneous high-amplitude Langmuir waves),” Phys. Fluids (to be published).

For V see M. S. Sodha, A. K. Ghatak, V. K. Tripathi, “Self-focusing of laser beams in plasmas and semiconductors,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), pp. 194–212. For π see Ref. 44.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 122.

G. C. Pomraning, Radiation Hydrodynamics (Pergamon, Oxford, 1973); M. S. Zubairy, “Radiative energy transfer in presence of random source distributions,” in Coherence and Quantum Optics IV, L. Mandel, E. Wolf, eds. (Plenum, New York, 1978), pp. 459–467.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), pp. 247–251; V. A. Kulkarny, B. S. White, “Focusing and waves in turbulent inhomogeneous media,” Phys. Fluids 25, 1770–1784 (1982); M. J. Beran, “Coherence theory and caustic corrections,” Proc. Soc. Photo-Opt. Eng. 358, 176–183 (1982).
[CrossRef]

A. Bers, “Space–time evolution of plasma instabilities—absolute and convective,” in Handbook of Plasma Physics, M. N. Rosenbluth, R. Z. Sagdeev, eds. (North-Holland, Amsterdam, 1983), pp. 451–517.

C. S. Liu, “Parametric instabilities in homogeneous unmagnetized plasmas,” in Advances in Plasma Physics (Wiley, New York, 1976), pp. 83–120.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

R. C. Davidson, Methods in Nonlinear Plasma Theory (Academic, New York, 1972), p. 125.

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Figures (5)

Fig. 1
Fig. 1

In an oscillating longitudinal E field a charged particle experiences a drift in the direction of decreasing wave amplitude. The drift is independent of the sign of charge. x0, starting point; x1, x2, x3, turning points. In a transverse wave the drift is caused by the Lorentz force.

Fig. 2
Fig. 2

In the radiation field the electrons oscillate around the nuclei on their trajectory x(t). Owing to asymmetries in the oscillation amplitude the electrons transmit a secular force to the heavy particles. Solidly outlined circles, volume elements of the nuclei; dashed lines, electronic fluid elements at different times.

Fig. 3
Fig. 3

Steepening of a flat plasma density profile n0 owing to radiation pressure of the standing light wave produced by reflection from the critical density nc. The arrows indicate the direction of the ponderomotive-force density π. The steepened equilibrium density profile is indicated by n.

Fig. 4
Fig. 4

Stimulated Raman backscattering Er of a wave Ei incident upon a plasma: (a) Er is shifted by π/2 with respect to the electron density ne. The arrows indicate the positions of maximum and minimum radiation-force density. (b) Classical reflection of the light wave from the modulations of ne. (c) The k vectors of (b) in the lab frame.

Fig. 5
Fig. 5

Epstein transition layer of width Δ for the square of refractive index. The wave is incident from the left. Parameter P = −3/4 is assumed.

Tables (1)

Tables Icon

Table 1 Normalized Reflection Coefficient r for the Layer of Fig. 5 as a Function of the Transiton Width Δ

Equations (94)

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p r = ( 1 + R ) I c ,
p r = 1 3 ρ = 4 π 3 I c .
κ = ρ el E + j × B ,
t 1 c 2 S + div T ¯ = - κ ,
E = ω ,             p = k .
P = 0 χ ¯ E .
χ = - ω p 2 ω 2 α ,
E ( x , t ) = E ^ ( x , t ) e - i ω t ,             × E ^ = i ω B ^ - t B ^ ,
κ = - 1 c 2 t S - T ¯ ,
κ = t ( ρ e v e + ρ i v i ) + ( ρ e v e v e + ρ i v i v i + p ¯ e + p ¯ i ) .
t ( ρ e v e + ρ i v i + 1 c 2 S ) + ( ρ e v e v e + ρ i v i v i + p ¯ e + p ¯ i + T ¯ ) = 0.
g = ν g ν ,             g ν = g ^ ν ( x , t ) e - i ν ω t ,
E t = E T + E 0 + E ^ ( x , t ) e - i ω t + higher harmonics ,
( f g ) 0 = ν f - ν g ν .
ρ = m e n e + m i n i = ρ e + ρ i ,             ρ el = q ( n i - n e ) , j = q ( n i v i - n e v e ) ,             v = ( ρ e v e + ρ i v i ) / ρ .
t ( ρ v + 1 c 2 S ) + ( ρ vv + p ¯ + T ¯ ) + ρ e ρ i ρ ( v i - v e ) ( v i - v e ) = 0.
t ρ v + ( ρ vv + p ¯ ) + 1 c 2 t S + ( T ¯ + ρ e ρ i ρ ww ) = 0 ,
p ¯ 0 = p ¯ ( n i , T i , T e , E ^ = 0 ) ,
t ρ v + 1 c 2 S T + ( ρ vv + p ¯ 0 + T ¯ T ) = - 1 c 2 t ( S - S T ) + ( T ¯ - T ¯ T + ρ e ρ i ρ ww + p ¯ - p ¯ 0 ) .
π = ρ el ( E t - E T ) + j × ( B - B T ) - ρ e ρ i ρ ww - ( p ¯ - p ¯ 0 ) .
t ρ v + ( ρ vv + p ¯ 0 ) = f T + π
ρ d v d t = - p ¯ 0 + f T + π ,
π = - 1 c 2 t S - T ¯ - ρ e ρ i ρ ww + p ¯ - p ¯ 0 ,
v e 1 = - i q m e ω e - i ω t ( 1 + i 2 ω t ) α ω E ^ ( t ) , δ e 1 = q m e ω 2 e - i ω t ( 1 + i 2 ω t ) α ω 2 E ^ ( t ) .
n e 0 n i 0 = n 0 ( quasi - neutrality ) , v e 0 v i 0 ,             n e 1 n 0 .
j 1 = - q ( n 0 v e 1 + n e 1 v e 0 ) - q n 0 v e 1 = e - i ω t × ( 1 + i 2 ω t ) σ E ^ ( t ) n i 1 m e m i n e 1 ,             ρ el , 1 = - q n e 1 ,             n e 1 + n 0 δ e 1 = 0 ,
i σ 0 ω = n 2 - 1 = χ .
j = t P + × ( P × v i ) ,             ρ el = - P .
0 = q n e 1 + q n 0 δ e = - ( ρ el , 1 + P 1 ) , 0 = q n e 1 t + q n 0 v e 1 = ρ el , 1 t + j 1 .
ρ e ρ i ρ ww = ρ e 0 v e 1 v e 1 = ρ e 0 ( v e 1 ) v e 1 - v e 1 ρ e 1 t , π = j 1 × B 1 - m e n 0 ( v e 1 ) v e 1 - q n e 1 E - m e v e 1 n e 1 t + p ¯ 0 - p ¯ .
B 1 = - i ω × ( E ^ - i ω t E ^ ) e - i ω t , σ = i q 2 n 0 m e ω α = i 0 ω p 2 ω α ,             χ = - ω p 2 ω 2 α ,
m e v e 1 n e 1 t - q n e 1 E = m e t n e 1 v e 1 + q n e 1 Re [ e - i ω t ( 1 + i ω t ) ( α - 1 ) E ^ ( t ) ] .
t v e + ( v e ) v e = - e m ( E ^ + v e × B ^ ) e - i ω t .
π = - 0 4 ω p 2 ω 2 [ E ^ t E ^ * + i ω ( E ^ t E ^ * - c c ) ] + i 0 4 ω t [ E ^ ( ω p 2 ω 2 E ^ * ) - E ^ * ( ω p 2 ω 2 E ^ ) ] .
p e , i j = m e ( u i - v i ) ( u j - v j ) f e ( x , u + v e 1 , t ) d u = p 0 i j e + m e ( u i - v i ) ( u j - v j ) v e 1 u f ( x , u , t ) d u = p 0 i j e ,
π = 0 4 { χ + χ * 2 E ^ E ^ * + [ ( α * - 1 ) χ E ^ * E ^ + c . c . ] } + π t .
[ ( α * - 1 ) χ E ^ * E ^ ) ] i = j ( α * - 1 ) χ E ^ i * E ^ j .
α n c - n 0 α = μ 3 0 = const . ,             n c = 0 m e ω 2 / q 2 .
( p ¯ 0 - p ¯ ) = 0
π = 0 2 [ n 0 χ n 0 E 2 + E 2 ( n 0 χ n 0 - χ ) ] .
E 0 = π q n e 0 π q n 0 ,
t ρ v + ( ρ vv ) = - p ¯ 0 + f T + π .
v 0 = ( ρ e 0 v e 0 + ρ i 0 v i 0 + ρ e 1 v e 1 ) / ρ 0
t ρ v + ρ vv = ρ 0 [ t v 0 + ( v 0 ) v 0 ] .
ρ 0 d d t v 0 = - p ¯ 0 + f T + π .
μ ( d 2 d t 2 δ + γ d d t δ + ω 0 2 δ ) = q Re [ E ^ ( x ) e - i ω t + d δ d t × B ^ ( x ) e - i ω t ] .
δ = δ 0 + 1 2 ν 1 δ ν + δ ν * ,             δ ν = δ ^ ν e - i ω t .
d 2 d t 2 δ 1 + γ d d t δ 1 + ω 0 2 δ 1 = q μ E ^ ( x 0 ) e - i ω t
δ 1 = q μ ω 0 2 - ω 2 + i γ ω ( ω 0 2 - ω 2 ) 2 + ω 2 γ 2 E ^ ( x 0 ) e - i ω t
E ^ ( x 0 + δ ) = E ^ [ x 0 + 1 2 ( δ 1 + δ 1 * ) ] = 1 2 [ ( 2 + δ 1 + δ 1 * ) ] E ^ ( x 0 ) .
d 2 d t 2 δ 0 + γ d d t δ 0 + ω 0 δ 0 = q 4 μ [ ( δ 1 ) E ^ * + d δ 1 d t × B ^ * + c . c . ] x = x 0
d 2 d t 2 δ 0 + ω 0 2 δ 0 = 1 ω 0 2 - ω 2 ( q q μ ) 2 ( E ^ E ^ * )
π 0 = - 1 1 - ω 0 2 ω 2 0 4 ω p 2 ω 2 E 2 = 0 4 χ E 2
d d t ( N m v ) = f
μ d 2 d t 2 δ = q μ ( E eff + δ ˙ × B - μ ω 0 2 q δ ) = q μ ( E 1 + δ × B ) ,
t m e n e 1 v e 1 ,
ρ ( v ) v = - p ¯ 0 + F + π .
n 1 = 0 E max 2 4 s c 2 ( 1 - M 1 2 ) ,             n 2 = n 1 M 1 , M 1 2 - l n M 1 2 - 1 = 0 E max 2 2 m i n c s c 2 .
i u t + 2 x 2 u + u [ 1 + f ( u ) ] = 0
× B ^ = j ^ 0 c 2 - i ω c 2 E ^ + 1 c 2 E ^ t .
ρ e 0 v e 1 t = - p e - n e q E = - m e s e 2 n e 1 - n e q E ,
i c 2 E ^ t + s e 2 ω c 2 2 x 2 E ^ - ω p 2 ω c 2 E ^ = i × B ^ .
n 0 = n ¯ 0 exp [ - β ( E 2 - E ¯ 2 ) ] ,             β = q 2 4 m e m i ω 2 s 2 .
i ω E ^ t + s e 2 2 x 2 E ^ - ω p 0 2 E ^ exp [ - β ( E 2 - E ¯ 2 ) ] = i ω c 2 × B ^
× × E + 1 c 2 2 t 2 E = - 1 0 c 2 t j ,
1 0 P i = χ i j 0 E j + χ i j k 1 E j E k + χ i j k l 2 E j E k E l + .
E = l E ^ l ( x , t ) exp ( i ϕ l ) ,             ϕ l = k l x - ω l t
Re { i exp ( i ϕ m ) [ ( k m ) E ^ m + ω m ( 1 + χ m 0 ) 1 / 2 c c group E ^ m t ] } = - 1 8 c 2 j k l r { χ j k l + r ( ω l + ω r ) 2 E ^ l j E ^ r k exp [ i ( ϕ l + ϕ r ) ] + χ j k l - r ( ω l - ω r ) 2 E l j E r k * exp [ i ( ϕ l - ϕ r ) ] + c . c . 1 } .
ω l = ω m + ω r ,             k l = k m + k r ,
d d x E ^ m = i 8 k m ( 1 + χ m 0 ) - 1 j k χ j k l - r E ^ l j E ^ l j E ^ r k * .
ϕ = kx - ω t = K j X j ,
ω m = ω l ,             k m = k j + k r ,
ω = γ ( ω - kv ) ,             k = k + γ - 1 v 2 ( vk ) v - γ v ω c 2 , γ = ( 1 - v 2 / c 2 ) - 1 / 2 ,
ω 2 = a + b k 2 ,
P r = P ^ r exp ( i k r x ) = - q n e r δ r ,
m eff n e r d v e d t = - p ¯ 0 + π .
π = 0 4 χ [ E ^ l exp ( i k l x l - ω l t ) + E ^ m exp ( i k m x m - ω l t ) ] 2 0 4 χ E ^ 1 E ^ m * exp [ i ( k l - k m ) x ] + c . c .
π = i a j k χ ˜ j k l - m E ^ l j E ^ m k * exp ( i ϕ r )
j M = × M ,
1 2 m v 2 + V = E 0 .
d d s ( n k 0 ) = k 0 n ( x ) .
I Δ A ( s ) = const . ,             I = S = 1 2 c n E ^ E ^ * ,
n 2 ( x ) = 1 + P exp ( k x / s ) 1 + exp ( k x / s ) .
Δ = 4 s P k ,             k = 2 π / λ .
R = sinh 2 [ π s ( 1 - 1 + P ) ] sinh 2 [ π s ( 1 + 1 + P ) ] .
f = - 1 c 2 t V S d τ - Σ T ¯ d Σ .
E = E i + E r = Re E ^ i ( exp i ϕ 1 + r exp i ϕ r ) , B = Re k 0 x E ^ i ( exp i ϕ i - r exp i ϕ r ) / ω ,
p r = - 1 c 2 t 0 x Sd x - 0 x T x x d x = T x x ( 0 ) = 0 2 E 2 + c 2 B 2 = ( 1 + R ) I c ,
p r θ = - 2 R ( θ ) I c n ^ cos 2 θ + [ 1 - R ( θ ) ] I c k 0 k 0 .
p ω = 1 3 ρ ω = 4 π 3 I ω c ,
d ρ ω ρ ω = - 2 d V V ,             d ρ ω ρ ω = - 4 3 d V V ,
f = A Q p r I c ,             A Q p r = σ T , σ R .
j ω = σ ( ω ) E ω .
j = j ω exp ( - i ω t ) d ω = σ ( ω ) E ω exp ( - i ω t ) d ω [ σ ( ω ) + σ ω ( ω - ω ) ] E ω exp ( - i ω t ) d ω = σ ( ω ) E ( x , t ) + σ ω ( ω - ω ) E ω exp ( - i ω t ) d ω = σ ( ω ) E + i σ ω exp ( - i ω t ) t E ω exp [ - i ( ω - ω ) t ] d ω = σ ( ω ) E + i σ ω exp ( - i ω t ) t [ E exp ( i ω t ) ] = σ ( ω ) E + i exp ( - i ω t ) σ ω t E ^ .

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