Magnetic vortex filament flows

Manuel Barros, José L. Cabrerizo, Manuel Fernández, Alfonso Romero

doi:10.1063/1.2767535

Magnetic vortex filament flows

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Manuel Barros

Universidad de Granada Departamento de Geometría y Topología, Facultad de Ciencias, , 18071-Granada, Spain
José L. Cabrerizo

Universidad de Sevilla Departamento de Geometría y Topología, Facultad de Matematicas, , 41012-Sevilla, Spain
Manuel Fernández

Universidad de Sevilla Departamento de Geometría y Topología, Facultad de Matematicas, , 41012-Sevilla, Spain
Alfonso Romero

Universidad de Granada Departamento de Geometría y Topología, Facultad de Ciencias, , 18071-Granada, Spain

書誌事項

公開日: 2007-08-01

DOI

10.1063/1.2767535

公開者: AIP Publishing

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説明

<jats:p>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.</jats:p>