Velocity and profile of the boundary between circular domains in cylindrical ferromagnetic samples

The velocity of the boundary between circular domains driven by DC current in a ferromagnetic cylindrical sample (wire) and its profile were calculated up to the first order approximation. The formula for critical current above which the curvature of the CDW can no longer compensate field variations was derived in this approximation. Its value is not more than a few milliamperes for typical stress annealed amorphous wires. Taking into account wall distortion the velocity versus current (circular field) dependence deviates from the linear one and for higher currents (i.e. for higher degree of wall distortion) velocity is higher than for planar CDW.