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Notes on Collapse in Magnetic Hydrodynamics

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Abstract

We consider the magnetic collapse as a possible process of the magnetic field singularity formation in a finite time in the framework of ideal magnetohydrodynamics for incompressible fluids, which is important for various astrophysical applications (in particular, as the mechanism of formation of magnetic filaments in the convective zone of the Sun). The possibility of collapse is associated with the compressibility of the continuously distributed magnetic field lines. The well-known example of magnetic filament formation in the kinematic dynamo approximation with a given velocity field, which was considered for the first time by Parker in 1963, rather indicates that the magnetic field increases with time exponentially. In the case of the kinematic approximation for the induction equation, the filaments are formed in regions with a hyperbolic velocity profile.

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ACKNOWLEDGMENTS

The authors thank V.V. Krasnoselskykh, I.N. Kitiashvili, A.G. Kosovichev, and I.V. Kolokolov for fruitful discussions and a number of valuable remarks.

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    E. A. Kuznetsov

  2. Landau Institute of Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia

    E. A. Kuznetsov

  3. Skolkovo Institute of Science and Technology, 143026, Skolkovo, Moscow oblast, Russia

    E. A. Kuznetsov

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

    E. A. Kuznetsov

  5. Moscow State University, 119991, Moscow, Russia

    E. A. Mikhailov

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  1. E. A. Kuznetsov
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  2. E. A. Mikhailov
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Correspondence to E. A. Kuznetsov.

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Translated by N. Wadhwa

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Kuznetsov, E.A., Mikhailov, E.A. Notes on Collapse in Magnetic Hydrodynamics. J. Exp. Theor. Phys. 131, 496–505 (2020). https://doi.org/10.1134/S106377612009006X

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