  We analyze the bosonic current densities induced by a magnetic flux running
along an idealized cosmic string considering that the coordinate along its axis
is compactified. We also consider the presence of a magnetic flux enclosed by
the compactificatified axis. To develop this analysis, we calculate the
complete set of normalized bosonic wave functions obeying a quasiperiodicity
condition along the compactified dimension. We show that in this context only
the azimuthal and axial currents take place.
