  We analyze the dynamics of a magnetic flux quantum (current vortex) trapped
in a current-biased long planar elliptic annular Josephson tunnel junction. The
system is modeled by a perturbed sine-Gordon equation that determines the
spatial and temporal behavior of the phase difference across the tunnel barrier
separating the two superconducting electrodes. In the absence of an external
magnetic field the fluxon dynamics in an elliptic annulus does not differ from
that of a circular annulus where the stationary fluxon speed merely is
determined by the system losses. The interaction between the vortex magnetic
moment and a spatially homogeneous in-plane magnetic field gives rise to a
tunable periodic non-sinusoidal potential which is strongly dependent on the
annulus aspect ratio. We study the escape of the vortex from a well in the
tilted potential when the bias current exceeds the depinning current. The
smallest depinning current as well as the lowest sensitivity of the annulus to
the external field is achieved when the eccentricity is equal to -1. The
presented extensive numerical results are in good agreement with the findings
of the perturbative approach. We also probe the rectifying properties of an
asymmetric potential implemented with an egg-shaped annulus formed by two
semi-elliptic arcs.
