Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines

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Here we briefly report on results of self-consistent numerical modeling of a differentially rotating force-free magnetosphere of an aligned rotator. We show that differential rotation of the open field line zone is significant for adjusting of the global structure of the magnetosphere to the current density flowing through the polar cap cascades. We argue that for most pulsars stationary cascades in the polar cap can not support stationary force-free configurations of the magnetosphere.
5 pages, 4 figures. Presented at the conference "Isolated Neutron Stars: from the Interior to the Surface", London, April 24-28, 2006; to appear in Astrophysics and Space Science. Significantly revised version, a mistake found by ourselfs in the numerical code was corrected, all presented results are obtained with the correct version of the code

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