The electromagnetic field produced by oscillations of a magnetized incompressible infinitely long cylinder

The oscillations of a magnetized incompressible cylinder with a uniform magnetic field along its axis and the resulting electromagnetic field are studied. Two types of characteristic oscillations, torsional and Alfvén, are found to exist in the linear approximation. In the case of an infinite cylinder with torsional oscillations, no electromagnetic field is generated. In the case of Alfvén oscillations, an electromagnetic field develops around the cylinder with a local flux density that falls off exponentially with radial distance from the axis of the cylinder and has a time average of zero. The results are interpreted physically.