Magnetic helicity flux for mean magnetic field equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 130-141 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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P. M. Akhmet'ev. Magnetic helicity flux for mean magnetic field equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 130-141. http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a7/

[1] H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids, Cambridge Univ. Press, Cambridge, 1978

[2] K.-H. Rädler, “The generation of cosmic magnetic fields”, From the Sun to the Great Attractor, Lecture Notes in Physics, 556, eds. D. Page, J. G. Hirsch, Springer, Berlin, 1999, 101–172 | DOI

[3] V. B. Semikoz, D. Sokoloff, “Magnetic helicity and cosmological magnetic field”, Astron. Astrophys., 433:3 (2005), L53–L56 | DOI

[4] U. Frish, Turbulentnost. Nasledie A. N. Kolmogorova, FAZIS, M., 1998 | MR | Zbl

[5] P. Frick, D. Sokoloff, “Cascade and dynamo action in a shell model of magnetohydrodynamic turbulence”, Phys. Rev. E, 57:4 (1998), 4155–4164 | DOI | MR

[6] V. I. Arnold, “Asimptoticheskii invariant Khopfa i ego prilozheniya”, Materialy Vsesoyuznoi shkoly po differentsialnym uravneniyam s beskonechnym chislom nezavisimykh peremennykh i po dinamicheskim sistemam s beskonechnym chislom stepenei svobody (Dilizhan, 21\;maya\;–\;3\;iyunya 1973\;g.), AN Arm. SSR, Erevan, 1974, 229–256 | Zbl

[7] P. M. Akhmetev, “Kvadratichnye spiralnosti i energiya magnitnogo polya”, Tr. MIAN, 278 (2012), 16–28 | DOI | MR

[8] D. Sokoloff, P. Akhmetyev, E. Illarionov, “Magnetic helicity and higher helicity invariants as constraints for dynamo action”, Fluid Dyn. Res., 50:1 (2018), 011407, 10 pp. | DOI | MR

[9] V. I. Arnold, B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, 125, Springer, New York, 1998 | MR

[10] P. M. Akhmet'ev, S. Candelaresi, A. Yu. Smirnov, “Calculations for the practical applications of quadratic helicity in MHD”, Phys. Plasmas, 24:10 (2017), 102128, 9 pp., arXiv: 1710.08833 | DOI

[11] K. Subramanian, A. Brandenburg, “Magnetic helicity density and its flux in weakly inhomogeneous turbulence”, Astrophys. J. Lett., 648:1 (2006), L71–L74, arXiv: astro-ph/0509392 | DOI

[12] V. A. Gordin, V. I. Petviashvili, “Ustoichivye po Lyapunovu MGD-ravnovesiya plazmy s nenulevym davleniem”, ZhETF, 95:5 (1989), 1711–1722

[13] A. J. B. Russell, A. R. Yeates, G. Hornig, A. L. Wilmot-Smith, “Evolution of field line helicity during magnetic reconnection”, Phys. Plasmas, 22:3 (2015), 032106, 11 pp., arXiv: 1501.04856 | DOI

[14] P. M. Akhmet'ev, I. V. Vyugin, “Dispersion of the Arnold's asymptotic ergodic Hopf invariant and a formula for its calculation”, Arnold Math. J., 2020, published 18.06.2020, ; arXiv: https://doi.org/10.1007/s40598-020-00144-w1906.12131

[15] U. Frish, A. Pouqet, J. Léorat, A. Mazure, “Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence”, J. Fluid Mech., 68 (1975), 769–778 | DOI

[16] P. M. Akhmetev, O. V. Kunakovskaya, V. A. Kutvitskii, “Zamechanie o dissipatsii integrala magnitnoi spiralnosti”, TMF, 158:1 (2009), 150–160 | DOI | DOI | MR | Zbl

[17] P. R. Halmos, Lectures on Ergodic Theory, Chelsea Publ., New York, 1960 | MR

[18] A. D. Bryuno, I. V. Goryuchkina, “Neformalnye resheniya ODU”, Preprinty IPM im. M. V. Keldysha, 2009, 061, 14 pp.