  We design magnetic traps for atoms based on the average magnetic field of
vortices induced in a type-II superconducting thin film. This magnetic field is
the critical ingredient of the demonstrated vortex-based atom traps, which
operate without transport current. We use Bean's critical-state method to model
the vortex field through mesoscopic supercurrents induced in the thin strip.
The resulting inhomogeneous magnetic fields are studied in detail and compared
to those generated by multiple normally-conducting wires with transport
currents. Various vortex patterns can be obtained by programming different
loading-field and transport current sequences. These variable magnetic fields
are employed to make versatile trapping potentials.
