  The physics of Josephson tunnel junctions drastically depends on their
geometrical configurations and here we show that also tiny geometrical details
play a determinant role. More specifically, we develop the theory of short and
long confocal annular Josephson tunnel junctions in the presence of an in-plane
magnetic field of arbitrary orientations. The behavior of a circular annular
Josephson tunnel junction is then seen to be simply a special case of the above
result. For junctions having a normalized perimeter less than one the threshold
curves are derived and computed even in the case with trapped Josephson
vortices. For longer junctions a numerical analysis is carried out after the
derivation of the appropriate motion equation for the Josephson phase. We found
that the system is modeled by a modified and perturbed sine-Gordon equation
with a space dependent effective Josephson penetration length inversely
proportional to the local junction width. Both the fluxon statics and dynamics
are deeply affected by the non-uniform annulus width. Static zero-field
multiple-fluxon solutions exist even in presence of a large bias current. The
tangential velocity of a traveling fluxon is not determined by the balance
between the driving and drag forces due to the dissipative losses. Furthermore,
the fluxon motion is characterized by a strong radial inward acceleration which
causes electromagnetic radiation concentrated at the ellipse equatorial points.
