It is shown, that the bamboo domain structure in outer shell of the wire may exist due to small disturbances in the axial symmetry of the wire. The inner core magnetization of amorphous wire with small enough value of the an isotropy constant maybe twisted near the wire ends due to influence of the demagnetizing field of the surface magnetic charges. As a result, the longitudinal component of the wire magnetization reduces slowly near the wire ends. The critical length of the magnetizationreduction is several orders larger than the wire radius. For a wire with length lower than the critical one the remenent wire magnetization is the increasing function of the wire length.
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