  Propagation of a particle accelerated by an external field through a
scattering medium is studied within the generalized Lorentz model allowing
inelastic collisions. Energy losses at collisions are proportional to
$(1-\alpha^{2})$, where $0\le\alpha\le 1$ is the restitution coefficient. For
$\alpha =1$ (elastic collisions) there is no stationary state. It is proved in
one dimension that when $\alpha <1$ the stationary state exists . The
corresponding velocity distribution changes from a highly asymmetric
half-gaussian ($\alpha =0$) to an asymptotically symmetric distribution $\sim
{\rm exp}[-(1-\alpha)v^{4}/2]$, for $\alpha\to 1$. The identical scaling
behavior in the limit of weak inelasticity is derived in three dimensions by a
self-consistent perturbation analysis, in accordance with the behavior of
rigorously evaluated moments. The dependence on the external field scales out
in any dimension, predicting in particular the stationary current to be
proportional to the square root of the external acceleration.
