  We find a class of twisted and differentially rotating neutron star
magnetospheres that do not have a light cylinder, generate no wind and thus do
not spin-down. The magnetosphere is composed of embedded differentially
rotating flux surfaces, with the angular velocity decreasing as $\Omega \propto
1/r$ (equivalently, becoming smaller at the foot-points closer to the axis of
rotation). For each given North-South self-similar twist profile there is a set
of self-similar angular velocity profiles (limited from above) with a "smooth",
dipolar-like magnetic field structure extending to infinity. For spin
parameters larger than some critical value, the light cylinder appears,
magnetosphere opens up, and the wind is generated.
