The Evolution and Deformation of Magnetic Flux Tube Along Neutral Points


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Parlak E., ÖZDEMİR Z.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.18, sa.2, ss.277-292, 2025 (ESCI, Scopus)

Özet

This study aims to characterize magnetic flux tubes (MFTs) associated with null (neutral) curves in the three-dimensional Lorentzian space. To this end, a system of differential equations is first obtained for the flux surfaces associated with a null curve, using the magnetic vector field components and the Frenet frame at each point. The solution of this system of equations allows us to determine the magnetic field lines and kinematic equations of the magnetic tube surfaces. Furthermore, characteristic values of the Jacobian matrix generated by the magnetic field components are utilized to describe the deformation of the MFTs near null points. A new geometric perspective is then presented through split-quaternion algebra, demonstrating that an MFT can be fully characterized by a split-quaternion product or a homothetic motion. Finally, analytical solutions of the kinematic equations are obtained and illustrated with some theoretical examples.