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Russian Physics Journal

, Volume 61, Issue 9, pp 1551–1558 | Cite as

Fractional Differential Model of Resonant Transfer of Excitations in Plasma

  • V. V. UchaikinEmail author
  • E. V. Kozhemyakina
PLASMA PHYSICS
  • 10 Downloads

The most crucial feature of excitation transfer in low-temperature plasma forming the physical basis for operation of contemporary lighting devices is participation of resonant photons in the process. The widely used approximation of complete frequency redistribution assumes independence of the emitted photon frequency from frequency of the absorbed one. Averaged over frequency distribution in a resonance line, the natural transfer equation with the exponential kernel becomes the equation with an inverse power kernel, which in case of an infinite homogeneous medium is asymptotically equivalent to the Laplace equation of non-integer (fractional) order, considered in this article.

Keywords

resonance trapping fractional Laplacian 

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References

  1. 1.
    A. M. Kolchuzhkin, V. V. Uchaikin, Introduction to the Theory of Passage of Particles Through Matter [in Russian], Atomizdat, Moscow (1978).Google Scholar
  2. 2.
    L. M. Biberman, JETP [in Russian], 17, Issue 5, 416–426 (1947).Google Scholar
  3. 3.
    T. Holstein, Phys. Rev., 72 (1)2, 1212–1233 (1947).CrossRefGoogle Scholar
  4. 4.
    L. M. Biberman, V. S. Vorobyev, I. G. Yakubov, Kinetics of Non-Equilibrium Low-Temperature Plasma [in Russian], Nauka, Moscow (1982).Google Scholar
  5. 5.
    Yu. Yu. Abramov, A. M. Dykhne, A. P. Napartovich, JETP [in Russian], 56, Issue 2, 654– 661 (1969).Google Scholar
  6. 6.
    L. M. Biberman, I. M. Gurevich, JETP [in Russian], 19, Issue 6, 507 (1949).Google Scholar
  7. 7.
    S. G. Samko, A.A. Kilbas, O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications [in Russian], Nauka I tekhnika, Minsk (1987).Google Scholar
  8. 8.
    V. M. Zolotarev, V. V. Uchaikin, V. V. Saenko, JETP, 88, Issue 4, 780– 787 (1999).Google Scholar
  9. 9.
    V. V. Uchaikin, Method of Fractional Derivatives [in Russian], Artishok, Ulyanovsk (2008).Google Scholar
  10. 10.
    V. V. Uchaikin, in: Encyclopedia of Low-Temperature Plasma, Ser. B, Vol. VII-1, Part 3 [in Russian], Yu. P. Popov, ed., Yanus-K, Moscow, 366–383 (2008).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ulyanovsk State UniversityUlyanovskRussia

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