A major concern for the DARHT second axis (2 kA, 18.6 MeV, 2000 ns) is that ions or ionized neutrals released from solid surfaces (e.g., apertures, septums, dumps, and targets) by beam impact can be accelerated and trapped by the beam potential. This positive charge could disrupt the beam. To study this, experiments were performed on the DARHT first axis. The beam, focused to a range of diameters, is transmitted through thin foils made of various materials. The time-dependent beam radial profile is measured downstream of the target. For low current density, the downstream-beam profile is time invariant as expected. At higher current density, the downstream-beam radius changes during the pulse followed by transverse instability.