Advertisement

Astrophysics and Space Science

, Volume 18, Issue 1, pp 104–120 | Cite as

Quantum theory of the dielectric constant of a magnetized plasma and astrophysical applications

I. Theory
  • V. Canuto
  • J. Ventura
Article

Abstract

A quantum mechanical treatment of an electron plasma in a constant and homogeneous magnetic field is considered, with the aim of (a) defining the range of validity of the magnetoionic theory (b) studying the deviations from this theory, in applications involving high densities, and intense magnetic field. While treating the magnetic field exactly, a perturbation approach in the photon field is used to derive general expressions for the dielectric tensor εαβ. The properties of εαβ are explored in the various limits. Numerical estimates on the range of applicability of the magnetoionic theory are given for the case of the ‘one-dimensional’ electron gas, where only the lowest Landau level is occupied.

Keywords

General Expression Magnetic Field Dielectric Constant Quantum Theory Numerical Estimate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Canuto, V. and Chiu, H. Y.: 1971,Space Sci. Rev. 12, 3.Google Scholar
  2. [2]
    Woltjer, L.: 1964,Astrophys. J. 140, 1309.Google Scholar
  3. [3]
    Lee, H. J., Canuto, V., Chiu, H. Y., and Chiuderi, C.: 1969,Phys. Rev. Letters 23, 390;Google Scholar
  4. [3a]
    Canuto, V., Chiu, H. Y., Chiuderi, C. and Lee, H. J.: 1970,Nature 225, 47.Google Scholar
  5. [4]
    Kemp, J. C., Swedlund, J. B., Landstreet, J. D., and Angel, J. R. P.: 1970,Astrophys. J. 161, L77; alsoAstrophys. J. 162, L67 (1970).Google Scholar
  6. [5]
    Canuto, V. and Chiu, H. Y.: 1968,Phys. Rev. 173, 1210;Phys. Rev. 173, 1220;Phys. Rev. 173, 1229.Google Scholar
  7. [6]
    Canuto, V. and Chiu, H. Y.: 1970,Phys. Rev. A2, 518.Google Scholar
  8. [7]
    Ginzburg, V. L.: 1964,The Propagation of Electronmagnetic Waves in Plasmas, Pergamon, New York;Google Scholar
  9. [7a]
    Stix, T. H.: 1962,The Theory of Plasma Waves, McGraw-Hill, New York.Google Scholar
  10. [8]
    Ginzburg, V. L.: 1964,The Propagation of Electronmagnetic Waves in Plasmas, Pergamon, New York, p. 82. See also ref. [1].Google Scholar
  11. [9]
    Kelly, D. C.: 1964,Phys. Rev. 134, A641;Google Scholar
  12. [9a]
    Quinn, J. J. and Rodriguez, S.:Phys. Rev. 128, 2487 (1962). Reference to earlier work can be found in these papers.Google Scholar
  13. [10]
    Landau, L.: 1930,Z. Phys. 64, 629;Google Scholar
  14. [10a]
    Johnson, M. H. and Lippman, B. A.: 1949,Phys. Rev. 76, 828.Google Scholar
  15. [11]
    Mangus, W. and Oberhettinger, F.: 1947,Functions of Mathematical Physics, Chelsea, New York. The hermite polynomial of Equation (2) relates to the one defined in this reference by 120-1.Google Scholar
  16. [12]
    Bekefi, G.: 1966,Radiation Processes in Plasmas, Wiley, New York, p. 5.Google Scholar
  17. [13]
    Mangus, W. and Oberhettinger, F.: 1949,Functions of Mathematical Physics, p. 120.Google Scholar
  18. [14]
    Sokolov, A. A. and Ternov, I. M.: 1968,Synchrotron Radiation, Akademie Verlag, Berlin, p. 67.Google Scholar
  19. [15]
    Canuto, V. and Chiu, H. Y.: 1968,Phys. Rev. 173, 1210;Google Scholar
  20. [15a]
    Huang, K.,Statistical mechanics, Wiley, New York, 1963, Chap. 11, pp. 237–243.Google Scholar
  21. [16]
    Galitskii, V. M. and Migdal, A. B.: 1959,Plasma Phys. Contr. Thermonuclear Reactions 1, 191.Google Scholar
  22. [17]
    Sokolov, A. A. and Ternov, I. M.:Synchrotron Radiation, p. 86. See also Quinn, J. J. and Rodriguez, S.,Phys. Rev. 128, 2487 (1962).Google Scholar
  23. [18]
    Sitenko, A. G.: 1967,Electromagnetic Fluctuations in Plasmas, Academic Press, New York, p. 94. Our result differs from Sitenko's in that thex andy components of the tensor are interchanged. This is consistent with our choice of coordinates so that the propagation vector k is in thez−y plane.Google Scholar
  24. [19]
    Landau, L.: 1957,Sov. Phys. JETP 3, 920; ibid.,5, 101 (1957).Google Scholar
  25. [20]
    Kelly, D. C.: 1964,Phys. Rev. 134, A641.Google Scholar
  26. [21]
    Chiu, H. Y.: 1968,Stellar Physics, Blaisdell, p. 178.Google Scholar
  27. [22]
    Cohen, R., Lodenquai, J., and Ruderman, M.: 1970,Phys. Rev. Letters 25, 467.Google Scholar
  28. [22a]
    Canuto, V. and Kelly, D. C.: 1971, to be published.Google Scholar
  29. [23]
    Horing, N.: 1969,Ann. Phys. 54, 405.Google Scholar

Copyright information

© D. Reidel Publishing Company 1972

Authors and Affiliations

  • V. Canuto
    • 1
  • J. Ventura
    • 2
  1. 1.Institute for Space Studies, Goddard Space Flight CenterNASANew YorkU.S.A.
  2. 2.Physics Dept.City College of the City UniversityNew YorkU.S.A.

Personalised recommendations