  The relativistic charged spinor matter field is quantized in the background
of a straight cosmic string with nonvanishing transverse size. The most general
boundary conditions ensuring the impossibility for matter to penetrate through
the edge of the string core are considered. The role of discrete symmetries is
elucidated, and analytic expressions for the temporal and spatial components of
the induced vacuum current are derived in the case of either P or CT invariant
boundary condition with two parameters varying arbitrarily from point to point
of the edge. The requirement of physical plausibility for the global induced
vacuum characteristics is shown to remove completely an arbitrariness in
boundary conditions. We find out that a magnetic field is induced in the vacuum
and that a sheath in the form of a tube of the magnetic flux lines encloses a
cosmic string. The dependence of the induced vacuum magnetic field strength on
the string flux and tension, as well as on the transverse size of the string
and on the distance from the string, is unambiguously determined.
