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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year

IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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Volume 70, Issue 8


Dynamics of Line Preserving Field Line Motions

Przemysław Figura / Wiesław M. Macek
  • Space Research Centre, Polish Academy of Sciences, Warsaw, Poland
  • Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, Warsaw, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-06-05 | DOI: https://doi.org/10.1515/zna-2015-0123


We develop the theory of line preserving flows and the magnetic reconnection using the Euler potentials formalism. In addition to our recently proposed model, we formulate new equations describing the time evolution of the Euler potentials in the line preserving regime. We also look at a special case of the flows represented by the ideal plasma flows. We consider the magnetic reconnection as a breakage of the line preservation regime. Because general solutions of the obtained dynamics equations do not have their closed-form expressions, we provide two different approaches to the possible solutions, in particular, a linear approximation and a solution by finding a Lagrangian and a Hamiltonian that generate the dynamics equations. We also provide some simple examples of the physical interpretation of the solutions obtained.

Keywords: Euler Potentials; Field Line Flows; Magnetic Reconnection; Magnetohydrodynamics; Plasma Physics

PACS numbers:: 52.30.Cv; 52.35.Vd


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About the article

Corresponding author: Przemysław Figura, Space Research Centre, Polish Academy of Sciences, Warsaw, Poland, E-mail:

Received: 2015-03-12

Accepted: 2015-05-11

Published Online: 2015-06-05

Published in Print: 2015-08-01

Citation Information: Zeitschrift für Naturforschung A, Volume 70, Issue 8, Pages 643–651, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2015-0123.

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