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Path Integral Method in the Mean-field Model for the Magnetic Vector Potential

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Abstract

The method of path integrals is used to average the magnetic-induction equation written for the vector potential over the velocity field. This approach avoids the assumption that the random field is two-scale, replacing it with the assumption of short time correlations. As a result of averaging, the classical equation of the mean field is obtained, at least for a homogeneous and isotropic medium. Based on the developed approach, the problem of the average field solenoidality is discussed, as well as a possible generalization of the method to the case of a statistically inhomogeneous and anisotropic flow.

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Funding

The work on the averaging of the induction equation with the functional-integration method was supported by the Russian Foundation for Basic Research, project no. 18-02-00085. The statement of the problem and interpretation of the results was carried out within the framework of the grant of the BAZIS Fund for the Development of Theoretical Physics and Mathematics, no. 18-1-1-77-1.

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Authors and Affiliations

  1. Moscow State University, Faculty of Physics, 119234, Moscow, Russia

    E. V. Yushkov, C. R. Kamaletdinov & D. D. Sokoloff

  2. Space Research Institute, Russian Academy of Sciences, 117997, Moscow, Russia

    E. V. Yushkov & C. R. Kamaletdinov

  3. Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, 108840, Troitsk, Russia

    D. D. Sokoloff

  4. Moscow Center of Fundamental and Applied Mathematics, 119234, Moscow, Russia

    E. V. Yushkov & D. D. Sokoloff

Authors
  1. E. V. Yushkov
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  2. C. R. Kamaletdinov
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  3. D. D. Sokoloff
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Correspondence to E. V. Yushkov.

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Yushkov, E.V., Kamaletdinov, C.R. & Sokoloff, D.D. Path Integral Method in the Mean-field Model for the Magnetic Vector Potential. Geomagn. Aeron. 60, 989–992 (2020). https://doi.org/10.1134/S0016793220070300

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  • DOI: https://doi.org/10.1134/S0016793220070300

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