Dixon Model for Magnetic Field of a Neutron Star

This Demonstration shows a model of the magnetic field of a neutron star. It consists of two concentric spherical bodies with opposite charges and differing angular velocities. Assume there is viscous damping between them, as well as a uniform charge distribution on the outer body, such that its rotation yields a uniform magnetic field.


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These are the reduced equations of motion:
where and are the Cartesian components of the magnetization of the inner sphere, and is related to damping parameters. The reduced 2D system evidently violates the Poincaré–Bendixson theorem.
[1] F. W. Cummings, D. D. Dixon, and P. E. Kaus, "Dynamical Model of the Magnetic Field of Neutron Stars," Astrophysical Journal, 386(1), 1992 pp. 215–221. adsabs.harvard.edu/full/1992ApJ...386..215C.
[2] D. D. Dixon, F. W. Cummings, and P. E. Kaus, "Continuous 'Chaotic' Dynamics in Two Dimensions," Physica D 65(1–2), 1993 pp. 109–116. doi:10.1016/0167-2789(93)90008-O.
[3] Wikipedia. "Poincaré–Bendixson Theorem." (May 1, 2013). en.wikipedia.org/wiki/Poincar% C3 % A9 % E2 %80 %93 Bendixson_theorem.
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