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Nonlocal weakly relativistic permittivity tensor of magnetized plasma near electron cyclotron resonances

  • Oscillations and Waves in Plasma
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Abstract

Compact expressions are derived for the nonlocal permittivity tensor of weakly relativistic plasma in a 2D nonuniform magnetic field near the resonances at the second harmonic of the electron cyclotron frequency for an extraordinary wave and at the first harmonic for an ordinary wave. It is shown that the wave equation with allowance for the obtained thermal correction to the permittivity tensor in the form of a differential operator in transverse (with respect to the external magnetic field) coordinates possesses an integral in the form of the energy conservation law.

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References

  1. A. G. Litvak, G. V. Permitin, E. V. Suvorov, and A. A. Frajman, Nucl. Fusion 17, 659 (1977).

    Article  ADS  Google Scholar 

  2. A. D. Piliya and V. I. Fedorov, in Reviews of Plasma Physics, Ed. by B. B. Kadomtsev (Consultants Bureau, New York, 1987), Vol. 13, p. 335.

    Google Scholar 

  3. V. Erckmann and U. Gasparino, Plasma Phys. Controlled Fusion 36, 1869 (1994).

    Article  ADS  Google Scholar 

  4. R. W. Harvey, W. M. Nevins, G. R. Smith, B. Lloyd, M. R. O’Brien, and C. D. Warrick, Nucl. Fusion 37, 97 (1997).

    Article  Google Scholar 

  5. V. V. Alikaev, A. G. Litvak, E. V. Suvorov, and A. A. Fraiman, in High-Frequency Plasma Heating, Ed. by A. G. Litvak (AIP, New York, 1992), p.1.

  6. M. Bornatici, R. Cano, O. De Barbieri, and F. Engelmann, Nucl. Fusion 23, 1153 (1983).

    Article  Google Scholar 

  7. M. Tereshchenko, F. Castejon, and A. Cappa, TRUBA User Manual, Informes Técnicos CIEMAT. 2008, No. 1134. http://www-fusion.ciemat.es/InternalReport/ IR1134.pdf.

  8. E. R. Tracy, A. J. Brizard, A. S. Richardson, and A. N. Kaufman, Ray Tracing and Beyond: Phase Space Methods in Plasma Wave Theory (Cambridge University Press, Cambridge, 2014).

    Book  Google Scholar 

  9. T. M. Antonsen and W. M. Manheimer, Phys. Fluids 21, 2295 (1978).

    Article  ADS  Google Scholar 

  10. A. V. Zvonkov and A. V. Timofeev, Sov. J. Plasma Phys. 6, 668 (1980).

    ADS  Google Scholar 

  11. V. I. Fedorov, Sov. Tech. Phys. Lett. 6, 560 (1980).

    Google Scholar 

  12. A. V. Timofeev, Phys. Usp. 47, 555 (2004).

    Article  ADS  Google Scholar 

  13. G. M. Batanov, V. D. Borzosekov, L. V. Kolik, E.M.Konchekov, D. V. Malakhov, A. E. Petrov, K. A. Sarksyan, A. S. Sakharov, N. N. Skvortsova, V. D. Stepakhin, and N. K. Kharchev, Plasma Phys. Rep. 39, 882 (2013).

    Article  ADS  Google Scholar 

  14. G. M. Batanov, V. D. Borzosekov, D. G. Vasilkov, L.V. Kolik, E. M. Konchekov, D. V. Malakhov, I. Yu. Vafin, A. E. Petrov, K. A. Sarksyan, A. S. Sakharov, V. D. Stepakhin, and N. K. Kharchev, Plasma Phys. Rep. 42, 734 (2016).

    Article  ADS  Google Scholar 

  15. T. H. Stix and D. G. Swanson, in Basic Plasma Physics, Ed. by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983), Vol. 1, p. 335.

    Google Scholar 

  16. A. A. Balakin, E. D. Gospodchikov, and A. G. Shalashov, JETP Lett. 104, 690 (2016).

    Article  ADS  Google Scholar 

  17. A. G. Shalashov, A. A. Balakin, T. A. Khusainov, E. D. Gospodchikov, and A. L. Solomakhin, JETP 124, 324 (2017).

    Article  ADS  Google Scholar 

  18. D. G. Swanson, Phys. Fluids 24, 2035 (1981).

    Article  ADS  Google Scholar 

  19. M. Brambilla, Plasma Phys. Controlled Fusion 31, 723 (1989).

    Article  ADS  Google Scholar 

  20. V. L. Vdovin, in Proceedings of the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, 2006, p. 323.

    Google Scholar 

  21. V. L. Vdovin, Fusion Sci. Technol. 59, 690 (2011).

    Article  Google Scholar 

  22. C. Maroli and V. Petrillo, Plasma Phys. Controlled Fusion 28, 615 (1986).

    Article  ADS  Google Scholar 

  23. R. A. Cairns, C. N. Lashmore-Davies, R. O. Dendy, B. M. Harvey, R. J. Hastie, and H. HoIt, Phys. Fluids B 3, 2953 (1991).

    Article  ADS  Google Scholar 

  24. D. C. McDonald, R. A. Cairns, and C. N. Lashmore- Davies, AIP Conf. Proc. 289, 265 (1994).

    Article  ADS  Google Scholar 

  25. D. C. McDonald, R. A. Cairns, and C. N. Lashmore- Davies, Phys. Plasmas 1, 842 (1994).

    Article  ADS  Google Scholar 

  26. D. C. McDonald, R. A. Cairns, and C. N. Lashmore- Davies, and G. Le Clair, Phys. Plasmas 5, 883 (1998).

    Article  ADS  Google Scholar 

  27. D. C. McDonald, R. A. Cairns, and C. N. Lashmore- Davies, AIP Conf. Proc. 403, 351 (1997).

    Article  ADS  Google Scholar 

  28. S. S. Pavlov, Probl. At. Sci. Technol., Ser. Plasma Phys., No. 1, 53 (2011).

    ADS  Google Scholar 

  29. D. G. Swanson, Plasma Waves (IOP, Bristol, 2003).

    Google Scholar 

  30. B. A. Trubnikov, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Pergamon, New York, 1959), Vol. 3, p. 122.

    ADS  Google Scholar 

  31. P. A. Robinson, J. Math. Phys. 28, 1203 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  32. P. A. Robinson, J. Math. Phys. 27, 1207 (1986).

    Article  ADS  Google Scholar 

  33. I. P. Shkarofsky, Phys. Fluidss 9, 561 (1966).

    Article  ADS  Google Scholar 

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Correspondence to A. S. Sakharov.

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Original Russian Text © A.S. Sakharov, 2017, published in Fizika Plazmy, 2017, Vol. 43, No. 11, pp. 903–909.

The article was translated by the author.

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Sakharov, A.S. Nonlocal weakly relativistic permittivity tensor of magnetized plasma near electron cyclotron resonances. Plasma Phys. Rep. 43, 1065–1071 (2017). https://doi.org/10.1134/S1063780X17110083

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  • DOI: https://doi.org/10.1134/S1063780X17110083

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