We report the near-steady state propagation over long distance of a 25
psec, tightly focused relativistic electron beam which creates, by ra
dial ejection of plasma electrons, a focusing ion channel in a plasma
of electron density smaller than the beam. A dense beam core, close in
radius to the injected beam, which was nearly matched to the ion focu
sing strength, is observed at the plasma exit. Time-resolved imaging c
onfirms that this core is situated in the trailing half of the beam, a
s predicted by analytical and computer models. We discuss the impact o
f these results on plasma wake field acceleration schemes.