Abstract
A special Lagrangian coordinate system is introduced, in which the magnetic flux tube is the main object of investigation. The flux tube is shown to behave as a nonlinear relativistic string in relation to tangential force. General and particular variational principles are also discussed. With the introduction of a Lagrangian coordinate system the relativistic magnetohydrodynamic equation of motion reduces to a set of nonlinear string equations. From these results it follows that a highly conductive plasma with a ‘frozen-in’ magnetic field can be considered as a gas of nonlinear strings interacting through pressure forces. A method is developed which allows the multi-dimensional nonlinear problems of RMHD (relativistic MHD) with boundary layers to be reduced to a set of two-dimensional problems for flux tubes, i.e., nonlinear strings.
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Semenov, V.S., Bernikov, L.V. Magnetic flux tubes — nonlinear strings in relativistic magnetohydrodynamics. Astrophys Space Sci 184, 157–166 (1991). https://doi.org/10.1007/BF00644873
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DOI: https://doi.org/10.1007/BF00644873