Causal model of launching an X wave by a superluminal rectilinear current pulse

A model describing steady-state localized X-shaped field generation by a superluminal pointlike charge (tachyon) infinitely moving along a straight line is extended to the case of a source current pulse of an arbitrary shape launched at time zero and propagating rectilinearly at constant superluminal speed. In the case of infinitely short (delta) pulse, the extended model yields an analytical solution, corresponding to the propagation-invariant X-shaped wave clipped by a droplet-shape support, infinitely expanding along both propagation and transversal directions, thus tending the droplet-shaped wave to the X-shaped one.