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Simulation of a Multifractal Turbulent Electromagnetic Field in Cosmic Plasma

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Abstract

A two-dimensional model of a multifractal turbulent electromagnetic field is proposed that allows flexibly varying the width of the multifractal spectrum and the level of intermittency. The electromagnetic field is modeled using a superposition of wavelets that are distributed uniformly throughout the computational domain. By means of a special distribution of amplitudes, we ensure that the resulting field is multifractal and intermittent. This model was used to study the effect of multifractality and intermittency on the acceleration of charged particles in a turbulent field in the Earth’s magnetotail. It was shown that, in the case of a multifractal field, individual particles are able to achieve higher energy values in comparison with monofractal turbulence.

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REFERENCES

  1. Lui, A., Multifractal and intermittent nature of substorm-associated magnetic turbulence in the magnetotail, J. Atmos. Sol.-Terr. Phys., 2001, vol. 63, no. 13, pp. 1379–1385. https://doi.org/10.1016/S1364-6826(00)00239-X

    Article  ADS  Google Scholar 

  2. Wawrzaszek, A., Echim, M., and Bruno, R., Multifractal analysis of heliospheric magnetic field fluctuations observed by Ulysses, Astrophys. J., 2019, vol. 876, no. 2, pp. 153–166. https://doi.org/10.3847/1538-4357/ab1750

    Article  ADS  Google Scholar 

  3. Chang, T., Self-organized criticality, multi-fractal spectra, sporadic localized reconnections and intermittent turbulence in the magnetotail, Phys. Plasmas, 1999, no. 6, pp. 4137–4145. https://doi.org/10.1063/1.873678

  4. Zelenyi, L.M., Bykov, A.M., Uvarov, Y.A., et al., Intermittency of magnetic field turbulence: astrophysical applications of in-situ observations, J. Plasma Phys., 2015, vol. 81, no. 4, p. 395810401. https://doi.org/10.1017/S0022377815000409

    Article  Google Scholar 

  5. Zelenyi, L.M., Rybalko, S.D., Artemyev, A.V., et al., Charged particle acceleration by intermittent electromagnetic turbulence, Geophys. Res. Lett., 2011, vol. 38, no. 17, p. L17110. https://doi.org/10.1029/2011GL048983

    Article  ADS  Google Scholar 

  6. Levashov, N.N., Popov, V.Yu., Malova, H.V., and Zeleny, L.M., Simulation of Intermediate turbulence in space plasma, Cosmic Res., 2022, vol. 60, no. 1, pp. 9–14. https://doi.org/10.1134/S0010952522010087

    Article  ADS  Google Scholar 

  7. Levashov, N.N., Popov, V.Yu., Malova, Kh.V., and Zelenyi, L.M., Investigation of charged particle acceleration processes in turbulent space plasma with intermittency, Uch. Zap. Fiz. Fak. Mosk. Univ., 2021, no. 4, p. 2140802.

  8. Perri, S., Lepreti, F., Carbone, V., et al., Position and velocity space diffusion of test particles in stochastic electromagnetic fields, Europhys. Lett., 2007, vol. 78, no. 4, p. 40003. https://doi.org/10.1209/0295-5075/78/40003

    Article  ADS  Google Scholar 

  9. Perri, S., Greco, A., and Zimbardo, G., Stochastic and direct acceleration mechanisms in the Earth’s magnetotail, Geophys. Res. Lett., 2009, vol. 36, no. 4, p. L04103. https://doi.org/10.1029/2008GL036619

    Article  ADS  Google Scholar 

  10. Pavlov, A.N. and Anishchenko, V.S., Multifractal signal analysis based on wavelet transform, Izv. Saratov. Univ., 2007, vol. 7, no. 1, pp. 3–25.

    Google Scholar 

  11. Frisch, U., Turbulence: The Legacy of A.N. Kolmogorov, Cambridge: Cambridge Univ. Press, 1995. https://doi.org/10.1017/CBO9781139170666

    Book  MATH  Google Scholar 

  12. Bozhokin, S.V. and Parshin, D.A., Fraktaly i mul’tifraktaly (Fractals and Multifractals), Izhevsk: NITs Regulyarnaya i khaoticheskaya dinamika, 2001.

  13. Korolenko, P.V., Maganova, M.S., and Mesnyankin, A.V., Novatsionnye metody analiza stokhasticheskikh protsessov i struktur v optike (Innovative Methods for the Analysis of Stochastic Processes and Structures in Optics), Moscow: Nauchn.-Issled. Inst. Yad. Fiz. Mosk. Gos. Univ., 2004.

  14. Dudok de Wit, T. and Krasnosel’skikh, V.V., Non-Gaussian statistics in space plasma turbulence: Fractal properties and pitfalls, Nonlin. Process. Geophys., 1996, vol. 3, no. 6, pp. 262–273.

    Article  ADS  Google Scholar 

  15. Keith, D.W., Pettit, C.L., and Vecherin, S.N., Wavelet-based cascade model for intermittent structure in terrestrial environments, Data Analysis, Statistics and Probability, 2013, p. 58. https://doi.org/10.48550/arXiv.1312.5649

    Book  Google Scholar 

  16. Feder, J. Fractals, New York: Springer, 1988.

    Book  MATH  Google Scholar 

  17. Budaev, V.P., Savin, S.P., and Zelenyi, L.M., Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: Towards a quantitative definition of plasma transport features, Phys.-Usp., 2011, vol. 54, no. 9, pp. 875–918. https://doi.org/10.3367/UFNe.0181.201109a.0905

    Article  ADS  Google Scholar 

  18. Kozak, L.V., Petrenko, B.A., and Lui, A., Turbulent processes in the Earth’s magnetotail: Spectral and statistical research, Ann. Geophys., 2018, vol. 36, no. 5, pp. 1303–1318. https://doi.org/10.5194/angeo-36-1303-2018

    Article  ADS  Google Scholar 

  19. Zelenyi, L.M., Artemyev, A.V., Malova, H.V., et al., Particle transport and acceleration in a time-varying electromagnetic field with a multi-scale structure, Phys. Lett., 2008, vol. 372, no. 41, pp. 6284–6287. https://doi.org/10.1016/j.physleta.2008.08.035

    Article  MATH  Google Scholar 

  20. Artemyev, A.V., Zelenyi, L.M., Malova, H.V., et al., Acceleration and transport of ions in turbulent current sheets: formation of non-Maxwelian energy distribution, Nonlin. Process. Geophys., 2009, vol. 16, pp. 631–639. https://doi.org/10.5194/npg-16-631-2009

    Article  ADS  Google Scholar 

  21. Chiaravalloti, F., Milovanov, A.V., and Zimbardo, G., Self-similar transport processes in a two-dimensional realization of multiscale magnetic field turbulence, Phys. Scr., 2006, vol. 122, pp. 79–88. https://doi.org/10.1088/0031-8949/2006/T122/012

    Article  Google Scholar 

  22. Zelenyi, L.M. and Milovanov, A.V., Fractal topology and strange kinetics: From percolation theory to problems in cosmic electrodynamics, Phys.-Usp., 2004, vol. 47, no. 8, pp. 749–788.

    Article  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    N. N. Levashov & V. Yu. Popov

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

    N. N. Levashov, V. Yu. Popov & L. M. Zelenyi

  3. Higher School of Economics University, 101000, Moscow, Russia

    V. Yu. Popov & H. V. Malova

  4. Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991, Moscow, Russia

    H. V. Malova

Authors
  1. N. N. Levashov
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  2. V. Yu. Popov
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  3. H. V. Malova
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  4. L. M. Zelenyi
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Correspondence to N. N. Levashov.

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Translated by M. Chubarova

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Levashov, N.N., Popov, V.Y., Malova, H.V. et al. Simulation of a Multifractal Turbulent Electromagnetic Field in Cosmic Plasma. Cosmic Res 61, 113–119 (2023). https://doi.org/10.1134/S0010952522700149

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  • DOI: https://doi.org/10.1134/S0010952522700149

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