  We have investigated vortex states in two-dimensional superconductors under a
oscillating magnetic field from a chiral helimagnet. We have solved the
two-dimensional Ginzburg-Landau equations with finite element method. We have
found that when the magnetic field from the chiral helimagnet increases,
vortices appear all at once in all periodic regions. This transition is
different from that under the uniform magnetic field. Under the composite
magnetic field with the oscillating and uniform fields (down-vortices),
vortices antiparallel to the uniform magnetic field disappear. Then, the small
uniform magnetic field easily remove down-vortices.
