SpringerLink
Log in

Modeling of Proton Acceleration in a Magnetic Island Inside the Ripple of the Heliospheric Current Sheet

  • Published:
Solar System Research Aims and scope Submit manuscript

Abstract

Crossings of the heliospheric current sheet (HCS) at the Earth’s orbit are often associated with observations of anisotropic beams of energetic protons accelerated to energies from hundreds of keV to several MeV and above. A connection between this phenomenon and the occurrence of small-scale magnetic islands (SMIs) near reconnecting current sheets has recently been found. This study shows how pre-accelerated protons can be energized additionally due to oscillations of multiple SMIs inside the ripple of the reconnecting HCS. A model of the electromagnetic field of an oscillating 3D SMI with a characteristic size of ~0.001 AU is developed. A SMI is supposed to be bombarded by protons accelerated by magnetic reconnection at the HCS to energies from ~1keV to tens of keV. Numerical simulations have demonstrated that the resulting longitudinal inductive electric fields can additionally reaccelerate protons injected into a SMI. It is shown that there is a local “acceleration” region within the island in which particles gain energy most effectively. As a result, their average escape energies range from hundreds of keV to 2 MeV and above. There is almost no particle acceleration outside the region. It is shown that energies gained by protons significantly depend on the initial phase and the place of their entry into a SMI but weakly depend on the initial energy. Therefore, low-energy particles can be accelerated more efficiently than high-energy particles, and all particles can reach the total energy limit upon their escape from a SMI. It is also found that the escape velocity possesses a strong directional anisotropy. The results are consistent with observations in the solar wind plasma.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bemporad, A., Spectroscopic detection of turbulence in post-CME current sheets, Astrophys. J., 2008, vol. 689, no. 1, pp. 572–584. doi: https://doi.org/10.1086/592377

    Article  ADS  Google Scholar 

  • Bian, N.H. and Kontar, E.P., Stochastic acceleration by multi-island contraction during turbulent magnetic reconnection, Phys. Rev. Lett., 2013, vol. 110, no. 15, art. ID 151101. doi: https://doi.org/10.1103/PhysRevLett.110.151101

    Google Scholar 

  • Borodachev, L.V., Mingalev, I.V., and Mingalev, O.V., Algorithm for simulating the drift motion of a particle in plasma described by the Darwin model, Comput. Math. Math. Phys., 2003, vol. 43, no. 3, pp. 446–458.

    MathSciNet  MATH  Google Scholar 

  • Cartwright, M.L. and Moldwin, M.B., Comparison of small-scale flux rope magnetic properties to large-scale magnetic clouds: Evidence for reconnection across the HCS? J. Geophys. Res.: Space Phys., 2008, vol. 113, no. 9, art. ID A09105. doi: https://doi.org/10.1029/2008JA013389

    Google Scholar 

  • Dai, L., Wygant, J.R., Cattel, C.A., Thaller, S., Kersten, K., Breneman, A., and Tang, X., Cluster observations of fast magnetosonic waves in the heliospheric current sheet, Geophys. Res. Lett., 2014, vol. 41, pp. 1398–1405. doi: https://doi.org/10.1002/2014GL059223

    Article  ADS  Google Scholar 

  • Drake, J.F., Swisdak, M., Che, H., and Shay, M.A., Electron acceleration from contracting magnetic islands during reconnection, Nature, 2006, vol. 433, no. 7111, pp. 553–556. doi https://doi.org/10.1038/nature05116

    Article  ADS  Google Scholar 

  • Eastwood, J.P., Balogh, A., Dunlop, M.W., and Smith, C.W., Cluster observations of the heliospheric current sheet and an associated magnetic flux rope and comparisons with ACE, J. Geophys. Res.: Space Phys., 2002, vol. 107, no. 11, pp. SSH 9–1–SSH 9–9. doi: https://doi.org/10.1029/2001JA009158

    Google Scholar 

  • Greco, A., Perri, S., Servidio, S., Yordanova, E., and Veltri, P., The complex structure of magnetic field discontinuities in the turbulent solar wind, Astrophys. J. Lett., 2016, vol. 823, no. 2, art. ID L39. doi https://doi.org/10.3847/2041-8205/823/2/L39

    Google Scholar 

  • Khabarova, O., Zank, G.P., Li, G., le Roux, J.A., Webb, G.M., Dosch, A. and Malandraki, O.E., Small-scale magnetic islands in the solar wind and their role in particle acceleration. I. Dynamics of magnetic islands near the heliospheric current sheet, Astrophys. J., 2015a, vol. 808, no. 2, art. ID 181. doi https://doi.org/10.1088/0004-637X/808/2/181

    Google Scholar 

  • Khabarova, O., Zank, G.P., Li, G., le Roux, J.A., Webb, G.M., Malandraki, O.E. and Zharkova, V.V., Dynamical small-scale magnetic islands as a source of local acceleration of particles in the solar wind, J. Phys.: Conf. Ser., 2015b, vol. 642, art. ID 012033. doi https://doi.org/10.1088/1742-6596/642/1/012033

  • Khabarova, O., Zank, G.P., Li, G., Malandraki, O.E., le Roux, J.A., Webb, G.M., and Dosch, A., Small-scale magnetic islands in the solar wind and their role in particle acceleration. II. Particle energization inside magnetically confined cavities, Astrophys. J., 2016, vol. 827, no. 2, art. ID 122. doi https://doi.org/10.3847/0004-637X/827/2/122

    Google Scholar 

  • Khabarova, O.V., Zank, G.P., Malandraki, O.E., Li, G., le Roux, J.A., and Webb, G.M., Observational evidence for local particle acceleration associated with magnetically confined magnetic islands in the heliosphere—a review, Sun Geosphere, 2017, vol. 12, no. 1, pp. 23–30.

    ADS  Google Scholar 

  • Landau, L.D. and Lifshitz, E.M., A Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields, New York: Pergamon, 1971.

    Google Scholar 

  • le Roux, J.A., Zank, G.P., Webb, G.M., and Khabarova, O.A., Energetic ion acceleration by small-scale solar wind flux ropes, Astrophys. J., 2015, vol. 801, no. 2, art. ID 112. doi https://doi.org/10.1088/0004-637X/801/2/112

    Google Scholar 

  • le Roux, J.A., Zank, G.P., Webb, G.M., and Khabarova, O.V., Kinetic transport theory for particle acceleration and transport in regions of multiple contracting and reconnecting inertial-scale flux ropes, Astrophys. J., 2016, vol. 827, no. 1, art. ID 47. doi https://doi.org/10.3847/0004-637X/827/1/47

    Google Scholar 

  • Lifshitz, E.M. and Pitaevskii, L.P., Course of Theoretical Physics, Vol. 10: Physical Kinetics, Amsterdam: Elsevier, 1981.

    Google Scholar 

  • Malova, H.V., Mingalev, O.V., Grigorenko, E.E., Mingalev, I.V., Melnik, M.N., Popov, V.Yu., Delcourt, D.C., Petrukovich, A.A., Shen, C., Rong, D., and Zelenyi, L.M., Formation of self-organized shear structures in thin current sheets, J. Geophys. Res.: Space Phys., 2015, vol. 120. doi: https://doi.org/10.1002/2014JA020974

  • Markidis, S., Henri, P., Lapenta, G., Divin, A., Goldman, M., Newman, D., and Laure, E., Kinetic simulations of plasmoid chain dynamics, Phys. Plasmas, 2013, vol. 20, no. 8, art. ID 082105. http://dx.doi.org/10.1063/L4817286

    Google Scholar 

  • Matthaeus, W.H., Ambrosiano, J.J., and Goldstein, M.L., Particle acceleration by turbulent magnetohydrodynamic reconnection, Phys. Rev. Lett., 1984, vol. 53, pp. 1449–1452. doi: https://doi.org/10.1103/PhysRevLett.53.1449

    Article  ADS  Google Scholar 

  • Merkin, VG., Lyon, J.G., McGregor, S.L., and Pahud, D.M., Disruption of a heliospheric current sheet fold, Geophys. Res. Lett., 2011, vol. 38, art. ID L14107. doi: https://doi.org/10.1029/2011GL047822

  • Mingalev, O.V., Mingalev, I.V., and Mingalev, V.S., Two-dimensional numerical simulation of dynamics of small-scale irregularities in the near-Earth plasma, Cosmic Res., 2006, vol. 44, no. 5, pp. 398–408.

    Article  ADS  MATH  Google Scholar 

  • Mingalev, O.V., Mingalev, I.V., Malova, Kh.V., and Zelenyi, L.M., Numerical simulations of plasma equilibrium in a one-dimensional current sheet with a nonzero normal magnetic field component, Plasma Phys. Rep., 2007, vol. 33, no. 11, pp. 942–955.

    Article  ADS  Google Scholar 

  • Mingalev, O.V., Mingalev, I.V., Malova, Kh.V., Zelenyi, L.M., and Artem’ev, A.V., Asymmetric configurations of a thin current sheet with a constant normal magnetic field component, Plasma Phys. Rep., 2009, vol. 35, no. 1, pp. 76–83.

    Article  ADS  Google Scholar 

  • Mingalev, O.V., Mingalev, I.V., Mel’nik, M.N., Artemyev, A.V., Malova, H.V., Popov, V.Y., Chao, S., and Zelenyi, L.M., Kinetic models of current sheets with a sheared magnetic field, Plasma Phys. Rep., 2012, vol. 38, no. 4, pp. 300–314.

    Article  ADS  Google Scholar 

  • Musielak, Z.E. and Suess, S.T., Magnetohydrodynamic bending waves in a current sheet, Sol. Phys., 1988, vol. 330, pp. 456–465. doi: https://doi.org/10.1086/166483

    Google Scholar 

  • Oka, M., Phan, T.-D., Krucker, S., Fujimoto, M., and Shinohara, I., Electron acceleration by multi-island coalescence, Astrophys. J., 2010, vol. 714, no. 1, pp. 915–926. doi https://doi.org/10.1088/0004-637X/714/1/915

    Article  ADS  Google Scholar 

  • Ruderman, M.S., Nonlinear surface wave propagation on heliospheric current sheet, Proc. 1st COSPAR Colloquium “Physics of the Outer Heliosphere,” Warsaw, Poland, Oxford: Pergamon, 1990, vol. 1, pp. 249–252. doi https://doi.org/10.1016/B978-0-08-040780-7.50046-410.1016/B978-0-08-040780-7.50046-4

    Google Scholar 

  • Ruderman, M.S., On the analogy between a system of harmonic oscillators and resonant Alfven waves in plasmas, Phys. Plasmas, 1998, vol. 5, no. 6, pp. 2463–2465. doi: https://doi.org/10.1063/1.872927

    Article  ADS  MathSciNet  Google Scholar 

  • Wang, S., Lee, L.C., Wei, C.Q., and Akasofu, S.-I., A mechanism for the formation of plasmoids and kink waves in the heliospheric current sheet, Sol. Phys., 1988, vol. 117, pp. 157–169.

    Article  ADS  Google Scholar 

  • Yamauchi, M. and Lui, A.T.Y., Modified magnetohydrodynamic waves in a current sheet in space, Phys. Plasmas, 1997, vol. 4, no. 12, pp. 4382–4387. doi: https://doi.org/10.1063/1.872600

    Article  ADS  Google Scholar 

  • Zank, G.P., le Roux, J.A., Webb, G.M., Dosch, A., and Khabarova, O., Particle acceleration via reconnection processes in the supersonic solar wind, Astrophys. J., 2014, vol. 797, no. 1. doi https://doi.org/10.1088/0004-637X/797/1/28

    Google Scholar 

  • Zank, G.P., Hunana, P., Mostafavi, P., le Roux, J.A., Li, G., Webb, G.M., and Khabarova, O.V., Particle acceleration by combined diffusive shock acceleration and downstream multiple magnetic island acceleration, J. Phys.: Conf. Ser., 2015a, vol. 642, no. 1, art. ID 012031. doi. http://iopscience.iop.org/1742-6596/642/1/012031.10.1088/1742-6596/642/1/012031

    Google Scholar 

  • Zank, G.P., Hunana, P., Mostafavi, P., le Roux, J.A., Li, G., Webb, G.M., Khabarova, O., Cummings, A., Stone, E., and Decker, R., Diffusive shock acceleration and reconnection acceleration processes, Astrophys. J., 2015b, vol. 814, no. 2, art. ID 137. doi https://doi.org/10.1088/0004-637X/814/2/137

    Google Scholar 

  • Zharkova, V. and Khabarova, O., Particle acceleration in the reconnecting heliospheric current sheet: solar wind data versus 3D PIC simulations, Astrophys. J., 2012, vol. 752, no. 1, art. ID 35. doi https://doi.org/10.1088/0004-637X/752/1/35

    Google Scholar 

  • Zharkova, V. and Khabarova, O., Additional acceleration of solar-wind particles in current sheets of the heliosphere, Ann. Geophys., 2015, vol. 33, no. 457, pp. 457–470. doi: https://doi.org/10.5194/angeo-33-457-2015

    Article  ADS  Google Scholar 

  • Zheng, J. and Hu, Q., Observational evidence for self-generation of small-scale magnetic flux ropes from intermittent solar wind turbulence, Astrophys. J. Lett., 2018, vol. 852, no. 2, art. ID L23. doi https://doi.org/10.3847/2041-8213/aaa3d7

    Google Scholar 

  • Zhou, X., Büchner, J., Bárta, M., Gan, W., and Liu, S., Electron acceleration by cascading reconnection in the solar corona. I. Magnetic gradient and curvature drift effects, Astrophys. J., 2015, vol. 815, no. 1, art. ID 6. doi https://doi.org/10.1088/0004-637X/815/1/6

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polar Geophysical Institute, Apatity, 184209, Russia

    O. V. Mingalev, I. V. Mingalev, M. N. Mel’nik & P. V. Setsko

  2. Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Moscow, 108840, Russia

    O. V. Khabarova & R. A. Kislov

  3. Institute of Nuclear Physics, Moscow State University, Moscow, 119234, Russia

    Kh. V. Malova, R. A. Kislov & L. M. Zelenyi

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

    Kh. V. Malova

  5. Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama, Huntsville, 35899, USA

    G. P. Zank

  6. Department of Space Science, University of Alabama, Huntsville, 35899, USA

    G. P. Zank

Authors
  1. O. V. Mingalev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. V. Khabarova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kh. V. Malova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. I. V. Mingalev
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. A. Kislov
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. N. Mel’nik
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. P. V. Setsko
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. L. M. Zelenyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. G. P. Zank
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to O. V. Mingalev or O. V. Khabarova.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mingalev, O.V., Khabarova, O.V., Malova, K.V. et al. Modeling of Proton Acceleration in a Magnetic Island Inside the Ripple of the Heliospheric Current Sheet. Sol Syst Res 53, 30–55 (2019). https://doi.org/10.1134/S0038094619010064

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0038094619010064

Keywords

Search

Navigation