Opened Access Magnetic vortex filament flows

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Author: Barros Díaz, Manuel
Cabrerizo Jaraíz, José Luis
Fernández Andrés, Manuel
Romero Sarabia, Alfonso
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2007-08
Published in: Journal of Mathematical Physics, 48 (8), 082904-1-082904-27.
Document type: Article
Abstract: We exhibit a variational approach to study the magnetic flow associated with a Killing magnetic field in dimension 3. In this context, the solutions of the Lorentz force equation are viewed as Kirchhoff elastic rods and conversely. This provides an amazing connection between two apparently unrelated physical models and, in particular, it ties the classical elastic theory with the Hall effect. Then, these magnetic flows can be regarded as vortex filament flows within the localized induction approximation. The Hasimoto transformation can be used to see the magnetic trajectories as solutions of the cubic nonlinear Schrödinger equation showing the solitonic nature of those.
Cite: Barros Díaz, M., Cabrerizo Jaraíz, J.L. y Fernández Andrés, M. (2007). Magnetic vortex filament flows. Journal of Mathematical Physics, 48 (8), 082904-1-082904-27.
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DOI: 10.1063/1.2767535

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