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The transverse dynamics of a 28.5 GeV electron beam propagating in a 1.4 m long, 0-2 x 1014cm-3 plasma are studied experimentally in the underdense or blow-out regime. The transverse component of the wake field excited by the short electron bunch focuses the bunch, which experiences multiple betatron oscillations as the plasma density is increased. The spot size variations are observed using optical transition radiation and Cherenkov radiation. In this regime, the behavior of the spot size as adoi:10.1103/physrevlett.88.154801 pmid:11955201 fatcat:xf6v3pml6zggflm4dvaprs7ubq