  We study the dynamics of vortices in an asymmetric ring channel driven by an
external current I in a Corbino setup. The asymmetric potential can rectify the
motion of vortices and cause a net flow without any unbiased external drive,
which is called ratchet effect. With an applied ac current, the potential can
rectify the motion of vortices in the channel and induce a dc net flow. We show
that the net flow of vortices strongly depends on vortex density and frequency
of the driving current. Depending on the density, we distinguish a
"single-vortex" rectification regime (low density) determined by the
potential-energy landscape inside each cell of the channel (i.e., "hard" and
"easy" directions of motion) and "multi-vortex", or "collective", rectification
(high density) when the interaction between vortices becomes important. The
frequency of the driving ac current determines a possible distance that a
vortex could move during one period. For high frequency current, vortices only
oscillate in the triangular cell. For low frequency, the vortex angular
velocity $\omega$ increases nearly linearly until the driving force reaches the
maximum friction force in the hard direction. Furthermore, the commensurability
between the number of vortices and the number of cells results in a stepwise
$\omega-I$ curve. Besides the integer steps, i.e., the large steps found in the
single vortex case, we also found fractional steps corresponding to fractional
ratio between the numbers of vortices and triangular cells. The principal and
fractional frequencies for different currents are found, when the net flow of
vortices reaches the maximum that is proportional to the frequency when the
density of vortices is low. We have performed preliminary measurements on a
device containing a single weak-pinning circular ratchet channel in a Corbino
geometry and observed a substantial asymmetric vortex response.
