Force-free pulsar magnetosphere: instability and generation of magnetohydrodynamic waves

Context. Magnetohydrodynamic (MHD) instabilities can play an important role in the structure and dynamics of the pulsar magnetosphere. Aims. We consider the instability caused by differential rotation that is suggested by many theoretical models. Methods. Stability is considered by means of a linear analysis within the frame of the force-free MHD. Results. We argue that differentially rotating magnetospheres are unstable for any particular geometry of the magnetic field and rotation law. The characteristic growth time of instability is of the order of the rotation period. The instability can lead to fluctuations of the emission and enhancement of diffusion in the magnetosphere.