Propagation and Transmission of Alfven Waves in Rotating Magnetars

We study the propagation and transmission of Alfven waves in the context of cylindrical geometry. This approximates the polar cap region of aligned pulsar with strong magnetic fields. Non-propagating region appears in the presence of rotation. The displacement current further prevents the low frequency modes from propagating near the stellar surface. The transmission rates to the exterior through the surface are calculated. The rates increase with the frequency and the magnetic field strength. The transmission also depends on the helicity states of the waves, but the difference becomes small in the high frequency regime. We also point out the possibility of the spin-up by outgoing wave emission in the low frequency regime, if a certain condition holds.