  Vortex-line equilibrium configurations and critical currents for type-II
superconducting films at zero-temperature are studied theoretically. The films
are assumed to be of thickness less than or equal to the penetration depth,
free of pinning by imperfections, and to be subjected to a magnetic field
parallel to the film surfaces and to a transport current perpendicular to the
field. By numerical minimization of the exact London theory energy expression,
using simulated annealing techniques, the equilibrium configurations are
determined with great accuracy over a wide range of fields and currents. These
consist of chains of straight vortex-lines whose number depends both on the
field and on the current. Transitions involving a change by one in the chain
number are found to take place either if the field is increased at zero
transport current or if the transport current is increased at constant field.
At the transitions, there is a considerable rearrangement in the vortex-line
positions and a small, discontinuous, change in their number. The equilibrium
configurations with chain numbers that are not too small form a nearly perfect
triangular lattice, centered with respect to the film surfaces. However, small
deviations from this arrangement are found to be important in determining the
behavior near the transition and when the transport current approaches the
critical current. It is found that the critical current has a a non-monotonic
dependence on the field. The zero-temperature equilibrium phase diagram in the
field-transport current plane is reported.
