  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.
