Abstract:
The mean magnetic field equation describes the process of generating a magnetic field on a large scale as a result the EMF arising on a small scale. We consider the case where the large-scale magnetic field is also random and determine the density function of magnetic helicity. This function is invariant under gauge transformations of the magnetic vector potential. We study the equation for the magnetic helicity flux of a large-scale field and introduce a correction term related to the quadratic magnetic helicity invariant.
Keywords:
magnetic helicity, magnetic energy, current helicity, highest moment of magnetic helicity.
Citation:
P. M. Akhmet'ev, “Magnetic helicity flux for mean magnetic field equations”, TMF, 204:1 (2020), 130–141; Theoret. and Math. Phys., 204:1 (2020), 947–956
\Bibitem{Akh20}
\by P.~M.~Akhmet'ev
\paper Magnetic helicity flux for mean magnetic field equations
\jour TMF
\yr 2020
\vol 204
\issue 1
\pages 130--141
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\crossref{https://doi.org/10.4213/tmf9877}
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\transl
\jour Theoret. and Math. Phys.
\yr 2020
\vol 204
\issue 1
\pages 947--956
\crossref{https://doi.org/10.1134/S0040577920070089}
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Linking options:
https://www.mathnet.ru/eng/tmf9877
https://doi.org/10.4213/tmf9877
https://www.mathnet.ru/eng/tmf/v204/i1/p130
This publication is cited in the following 4 articles:
M. S. Dvornikov, P. M. Akhmet'ev, “Evolution of the magnetic field in spatially inhomogeneous axion structures”, Theoret. and Math. Phys., 218:3 (2024), 515–529
P. M. Akhmet'ev, “Topological meaning of the slope of the Kolmogorov spectrum of magnetic turbulence”, Theoret. and Math. Phys., 209:2 (2021), 1620–1632
P. M. Akhmet'ev, “On a higher integral invariant for closed magnetic lines, revisited”, J. Geom. Phys., 170 (2021), 104379
Akhmet'ev P., Cirilo-Lombardo D.J., Smirnov A., “Quadratic Helicity and Cosmological Magnetic Fields”, Int. J. Geom. Methods Mod. Phys., 17:10 (2020), 2050137
Citation in format AMSBIB
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