Skip to main content Accesibility Help
×
×
Home

Resistive evolution of toroidal field distributions and their relation to magnetic clouds

  • C. B. Smiet (a1) (a2), H. J. de Blank (a3), T. A. de Jong (a2), D. N. L. Kok (a2) and D. Bouwmeester (a2) (a4)...
Abstract

We study the resistive evolution of a localized self-organizing magnetohydrodynamic equilibrium. In this configuration the magnetic forces are balanced by a pressure force caused by a toroidal depression in the pressure. Equilibrium is attained when this low-pressure region prevents further expansion into the higher-pressure external plasma. We find that, for the parameters investigated, the resistive evolution of the structures follows a universal pattern when rescaled to resistive time. The finite resistivity causes both a decrease in the magnetic field strength and a finite slip of the plasma fluid against the static equilibrium. This slip is caused by a Pfirsch–Schlüter-type diffusion, similar to what is seen in tokamak equilibria. The net effect is that the configuration remains in magnetostatic equilibrium whilst it slowly grows in size. The rotational transform of the structure becomes nearly constant throughout the entire structure, and decreases according to a power law. In simulations this equilibrium is observed when highly tangled field lines relax in a high-pressure (relative to the magnetic field strength) environment, a situation that occurs when the twisted field of a coronal loop is ejected into the interplanetary solar wind. In this paper we relate this localized magnetohydrodynamic equilibrium to magnetic clouds in the solar wind.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Resistive evolution of toroidal field distributions and their relation to magnetic clouds
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Resistive evolution of toroidal field distributions and their relation to magnetic clouds
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Resistive evolution of toroidal field distributions and their relation to magnetic clouds
      Available formats
      ×
Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email address for correspondence: csmiet@pppl.gov
References
Hide All
Alfvén, H. 1943 On the existence of electromagnetic-hydrodynamic waves. Ark. Astron. 29, 17.
Arnol’d, V. I. 1986 The asymptotic hopf invariant and its applications. Sel. Math. Sov. 5 (4), 327.
Arrayás, M. & Trueba, J. L. 2014 A class of non-null toroidal electromagnetic fields and its relation to the model of electromagnetic knots. J. Phys. A 48 (2), 025203.
Batchelor, G. K. 1950 On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. R. Soc. Lond. A 201 (1066), 405416.
Bellan, P. M. 2000 Spheromaks: A Practical Application of Magnetohydrodynamic Dynamos and Plasma Self-Organization. World Scientific.
Berger, M. A. & Field, G. B. 1984 The topological properties of magnetic helicity. J. Fluid Mech. 147, 133148.
Braithwaite, J. 2010 Magnetohydrodynamic relaxation of agn ejecta: radio bubbles in the intracluster medium. Mon. Not. R. Astron. Soc. 406 (2), 705719.
Brandenburg, A. & Dobler, W. 2002 Hydromagnetic turbulence in computer simulations. Comput. Phys. Commun. 147 (1–2), 471475.
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417 (1–4), 1209.
Burlaga, L. F. 1991 Magnetic clouds. In Physics of the Inner Heliosphere II, pp. 122. Springer.
Candelaresi, S. & Brandenburg, A. 2011 Decay of helical and nonhelical magnetic knots. Phys. Rev. E 84 (1), 016406.
Chandrasekhar, S. & Kendall, P. 1957 On force-free magnetic fields. Astrophys. J. 126, 457.
Del Sordo, F., Candelaresi, S. & Brandenburg, A. 2010 Magnetic-field decay of three interlocked flux rings with zero linking number. Phys. Rev. E 81 (3), 036401.
Finkelstein, D. & Weil, D. 1978 Magnetohydrodynamic kinks in astrophysics. Intl J. Theoret. Phys. 17 (3), 201217.
Garren, D. A. & Chen, J. 1994 Lorentz self-forces on curved current loops. Phys. Plasmas 1 (10), 34253436.
Goedbloed, J. P., Keppens, R. & Poedts, S. 2010 Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas. Cambridge University Press.
Goedbloed, J. P. & Poedts, S. 2004 Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas. Cambridge University Press.
Haugen, N. E. L., Brandenburg, A. & Dobler, W. 2004 Simulations of nonhelical hydromagnetic turbulence. Phys. Rev. E 70 (1), 016308.
Hopf, H. 1931 Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche. Math. Ann. 104 (1), 637665.
Ivanov, K. & Harshiladze, A. 1985 Interplanetary hydromagnetic clouds as flare-generated spheromaks. Solar Phys. 98 (2), 379386.
Johansen, A., Oishi, J. S., Mac Low, M.-M., Klahr, H., Henning, T. & Youdin, A. 2007 Rapid planetesimal formation in turbulent circumstellar disks. Nature 448 (7157), 1022.
de Jong, T. A., Kok, D. N. L. & Smiet, C. B.2018 TAdeJong/plasma-analysis: reference release for citation (Version v0.1). Zenodo. http://doi.org/10.5281/zenodo.2069945.
Kulsrud, R. M. 2011 Intuitive approach to magnetic reconnection. Phys. Plasmas 18 (11), 111201.
Kumar, A. & Rust, D. 1996 Interplanetary magnetic clouds, helicity conservation, and current-core flux-ropes. J. Geophys. Res. 101 (A7), 1566715684.
Lundquist, S. 1950 Magneto-hydrostatic fields. Ark. fys. 2 (4), 361365.
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35 (1), 117129.
Priest, E. R. & Forbes, T. G. 2000 Magnetic Reconnection: MHD Theory and Applications. Cambridge University Press.
Raghav, A. N. & Kule, A. 2018 The first in situ observation of torsional Alfvén waves during the interaction of large-scale magnetic clouds. Mon. Not. R. Astron. Soc. 476 (1), L6L9.
Shafranov, V. 1966 Plasma equilibrium in a magnetic field. Rev. Plasma Phys. 2, 103.
Smiet, C., Candelaresi, S., Thompson, A., Swearngin, J., Dalhuisen, J. & Bouwmeester, D. 2015 Self-organizing knotted magnetic structures in plasma. Phys. Rev. Lett. 115 (9), 095001.
Smiet, C. B., Candelaresi, S. & Bouwmeester, D. 2017 Ideal relaxation of the hopf fibration. Phys. Plasmas 24 (7), 072110.
Taylor, J. 1974 Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33 (19), 11391141.
Taylor, J. 1986 Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 58 (3), 741.
Vandas, M., Fischer, S., Pelant, P. & Geranios, A. 1992 Magnetic clouds: comparison between spacecraft measurements and theoretical magnetic force-free solutions. In Solar Wind Seven, pp. 671674. Elsevier.
Wesson, J. & Campbell, D. J. 2011 Tokamaks, vol. 149. Oxford University Press.
Woltjer, L. 1958 A theorem on force-free magnetic fields. Proc. Natl Acad. Sci. USA 44 (6), 489491.
Zurbuchen, T. H. & Richardson, I. G. 2006 In-situ solar wind and magnetic field signatures of interplanetary coronal mass ejections. In Coronal Mass Ejections, pp. 3143. Springer.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

Type Description Title
UNKNOWN
Supplementary materials

Smiet et al. supplementary material
Smiet et al. supplementary material 1

 Unknown (346 KB)
346 KB

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed