Dynamic focusing of an electron beam through a long plasma

The focusing effects of a 1.4 m long, (0-2) x 10{sup 14} cm{sup -3} plasma on a single 28.5 GeV electron bunch are studied experimentally in the underdense or blowout regime, where the beam density is much greater than the plasma density. As the beam propagates through the plasma, the density of plasma electrons along the incoming bunch drops from the ambient density to zero leaving a pure ion channel for the bulk of the beam. Thus, from the head of the beam up to the point where all plasma electrons are blown out, each successive longitudinal slice of the bunch experiences a different focusing force due to the plasma ions. The time-changing focusing force results in a different number of betatron oscillations for each slice depending upon its location within the bunch. By using an electron beam that has a correlated energy spread, this time-dependent focusing of the electron bunch has been observed by measuring the beam spot size in the image plane of a magnetic energy-spectrometer placed at the plasma exit.