  We have investigated the static properties of one-dimensional planar
Josephson tunnel junctions in the most general case of elliptic annuli. We have
analyzed the dependence of the critical current in the presence of an external
magnetic field applied either in the junction plane or in the perpendicular
direction. We report a detailed study of both short and long elliptic annular
junctions having different eccentricities. For junctions having a normalized
perimeter less than one the threshold curves are derived and computed even in
the case with one trapped Josephson vortex. For longer junctions a numerical
analysis is carried out after the derivation of the appropriate Perturbed
sine-Gordon Equation. For a given applied field we find that a number of
different phase profiles exist which differ according to the number of
fluxon-antifluxon pairs. We demonstrate that in samples made by specularly
symmetric electrodes a transverse magnetic field is equivalent to an in-plane
field applied in the direction of the current flow. Varying the ellipse
eccentricity we reproduce all known results for linear and ring-shaped
Josephson tunnel junctions. Experimental data on high-quality Nb/Al-AlOx/Nb
elliptic annular junctions support the theoretical analysis provided self-field
effects are taken into account.
