  We calculate the vacuum averages of the energy-momentum tensor associated
with a massless left-handed spinor fields due to magnetic fluxes on idealized
cosmic string spacetime. In this analysis three distinct configurations of
magnetic fields are considered: {\it{i)}} a homogeneous field inside the tube,
{\it{ii)}} a magnetic field proportional to $1/r$ and {\it{iii)}} a cylindrical
shell with $\delta$-function. In these three cases the axis of the infinitely
long tubes of radius $R$ coincides with the cosmic string. In order to proceed
with these calculations we explicitly obtain the Euclidean Feynman propagators
associated with these physical systems. As we shall see, these propagators
possess two distinct parts. The first are the standard ones, i.e.,
corresponding to the spinor Green functions associated with the massless
fermionic fields on the idealized cosmic string spacetime with a magnetic flux
running through the line singularity. The second parts are new, they are due to
the finite thickness of the radius of the tubes. As we shall see these extra
parts provide relevant contributions to the vacuum averages of the
energy-momentum tensor.
