We investigate a stochastic model of the galactic dynamo in the planar approximation, assuming that turbulent diffusivity is a renewal process. For linear and nonlinear modifications of this model, numerical methods are applied to construct statistical moments and correlation tensors of the magnetic field.
Similar content being viewed by others
References
N. G. Bochkarev, Magnetic Fields in Space [in Russian], 2nd ed., Librokom Pub. (2011).
Ya. B. Zel’dovich, A. A. Ruzmaikin, and D. D. Sokolov, Magnetic Fields in Astrophysics [in Russian], Scientific-Research Center Regular and Chaotic Dynamics and Institute of Computer Studies, Moscow-Izhevsk (2006).
D. D. Sokolov, “Topics in magnetic dynamo,” UFN, 185, No. 6, 643–648 (2015).
H. Moffat, Magnetic Field Generation in Electrically Conducting Fluids [Russian translation], Mir, Moscow (1980).
E. A. Mikhailov, Magnetohydrodynamics and the Dynamo Theory [in Russian], MGU Phys. Faculty, Moscow (2018).
T. G. Arshakian, R. Beck, M. Krause, and D. Sokoloff, “Evolution of magnetic fields in galaxies and future observational tests with the Square Kilometre Array,” Astronomy & Astrophysics, 494, No. 1, 21–32 (2009).
D. Moss, D. Sokoloff, and V. Suleimanov, “Dynamo generated magnetic configurations in accretion discs and the nature of quasiperiodic oscillations in accreting binary systems,” Astronomy & Astrophysics, 588, A18 (2016).
D. Moss, “On the generation of bisymmetric magnetic field structures in spiral galaxies by tidal interactions,” Monthly Notices of the Royal Astronomical Society, 275, No. 1, 191-194 (1995).
E. A. Mikhailov, “Spectral decomposition of the solution of the problem of galactic magnetic field generation in the planar approximation,” Vestnik MGU, Ser. 3: Fiz., Astron., No. 5, 40–45 (2020).
E. A. Mikhailov and V. V. Pushkarev, “Fluctuations of turbulent diffusivity in galactic dynamo problems,” Vychisl. Metody i Programmirovanie: Novye Vychisl. Tekhnol., 17, 447–454 (2016).
E. A. Mikhailov and V. V. Pushkarev, “The effect of star formation on large-scale galactic magnetic field structures,” Astrofiz. Bull., 73, No. 4, 451–456 (2018).
M. R. E. Proctor, “Effects of fluctuation on αΩ dynamo models,” Monthly Notices of the Royal Astronomical Society: Letters, 382, No. 1, L39–L42 (2007).
A. P. L. Newton and E. Kim, “Determining the temporal dynamics of the solar α effect,” Astronomy & Astrophysics, 551, A66 (2013).
D. Passos, D. Nandy, S. Hazra, and I. Lopes, “A solar dynamo model driven by mean-field alpha and Babcock-Leighton sources: fluctuations, grand-minima-maxima, and hemispheric asymmetry in sunspot cycles,” Astronomy & Astrophysics, 563, A18 (2014).
S. Sur and K. Subramanian, “Galactic dynamo action in presence of stochastic α and shear,” Monthly Notices of the Royal Astronomical Society: Letters, 392, No. 1, L6–L10 (2009).
D. Moss, D. Sokoloff, R. Beck, and M. Krause, “Enhancement of magnetic fields arising from galactic encounters,” Astronomy & Astrophysics, 566, A40 (2014).
D. A. Grachev, S. A. Elistratov, and E. A. Mikhailov, “Statistical moments and multipoint magnetic-field correlators in the galactic dynamo model with stochastic turbulent diffusion,” Vychisl. Metody i Programmirovanie: Novye Vychisl. Tekhnol., 20, 88–96 (2019).
D. A. Grachev and S. A. Elistratov, “Numerical simulation of statistical magnetic-field moments in a galactic dynamo problem with a nonlinearity,” Vychisl. Metody i Programmirovanie: Novye Vychisl. Tekhnol., 21, 172–179 (2020).
D. A. Grachev and E. A. Mikhailov, “Numerical simulation of a two-point correlator for Lagrangian solutions of some evolution equations,” Vychisl. Metody i Programmirovanie: Novye Vychisl. Tekhnol., 18, 277–283 (2017).
F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory [Russian translation], Mir, Moscow (1984).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 65, 2021, pp. 61–69.
Rights and permissions
About this article
Cite this article
Mikhailov, E.A., Elistratov, S.A. & Grachev, D.A. The Magnetic Correlation Tensor in the Dynamo Theory. Comput Math Model 32, 45–51 (2021). https://doi.org/10.1007/s10598-021-09515-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-021-09515-0