  Applying the London theory we study curved vortices produced by an external
current near and parallel to the surface of a type II superconductor. By
minimizing the energy functional we find the contour describing the hard core
of the flux line, and predict the threshold current for entrance of the first
vortex. We assume that the vortex entrance is allowed due to surface defects,
despite the Bean-Livingston barrier. Compared to the usual situation with a
homogeneous magnetic field, the main effect of the present geometry is that
larger magnetic fields can be applied locally before vortices enter the
superconducting sample. It is argued that this effect can be further enhanced
in anisotropic superconductors.
