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.
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References
Canuto, V. and Chiu, H. Y.: 1971,Space Sci. Rev. 12, 3.
Woltjer, L.: 1964,Astrophys. J. 140, 1309.
Lee, H. J., Canuto, V., Chiu, H. Y., and Chiuderi, C.: 1969,Phys. Rev. Letters 23, 390;
Canuto, V., Chiu, H. Y., Chiuderi, C. and Lee, H. J.: 1970,Nature 225, 47.
Kemp, J. C., Swedlund, J. B., Landstreet, J. D., and Angel, J. R. P.: 1970,Astrophys. J. 161, L77; alsoAstrophys. J. 162, L67 (1970).
Canuto, V. and Chiu, H. Y.: 1968,Phys. Rev. 173, 1210;Phys. Rev. 173, 1220;Phys. Rev. 173, 1229.
Canuto, V. and Chiu, H. Y.: 1970,Phys. Rev. A2, 518.
Ginzburg, V. L.: 1964,The Propagation of Electronmagnetic Waves in Plasmas, Pergamon, New York;
Stix, T. H.: 1962,The Theory of Plasma Waves, McGraw-Hill, New York.
Ginzburg, V. L.: 1964,The Propagation of Electronmagnetic Waves in Plasmas, Pergamon, New York, p. 82. See also ref. [1].
Kelly, D. C.: 1964,Phys. Rev. 134, A641;
Quinn, J. J. and Rodriguez, S.:Phys. Rev. 128, 2487 (1962). Reference to earlier work can be found in these papers.
Landau, L.: 1930,Z. Phys. 64, 629;
Johnson, M. H. and Lippman, B. A.: 1949,Phys. Rev. 76, 828.
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.
Bekefi, G.: 1966,Radiation Processes in Plasmas, Wiley, New York, p. 5.
Mangus, W. and Oberhettinger, F.: 1949,Functions of Mathematical Physics, p. 120.
Sokolov, A. A. and Ternov, I. M.: 1968,Synchrotron Radiation, Akademie Verlag, Berlin, p. 67.
Canuto, V. and Chiu, H. Y.: 1968,Phys. Rev. 173, 1210;
Huang, K.,Statistical mechanics, Wiley, New York, 1963, Chap. 11, pp. 237–243.
Galitskii, V. M. and Migdal, A. B.: 1959,Plasma Phys. Contr. Thermonuclear Reactions 1, 191.
Sokolov, A. A. and Ternov, I. M.:Synchrotron Radiation, p. 86. See also Quinn, J. J. and Rodriguez, S.,Phys. Rev. 128, 2487 (1962).
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.
Landau, L.: 1957,Sov. Phys. JETP 3, 920; ibid.,5, 101 (1957).
Kelly, D. C.: 1964,Phys. Rev. 134, A641.
Chiu, H. Y.: 1968,Stellar Physics, Blaisdell, p. 178.
Cohen, R., Lodenquai, J., and Ruderman, M.: 1970,Phys. Rev. Letters 25, 467.
Canuto, V. and Kelly, D. C.: 1971, to be published.
Horing, N.: 1969,Ann. Phys. 54, 405.
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Canuto, V., Ventura, J. Quantum theory of the dielectric constant of a magnetized plasma and astrophysical applications. Astrophys Space Sci 18, 104–120 (1972). https://doi.org/10.1007/BF00645284
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DOI: https://doi.org/10.1007/BF00645284