  In plasma wakefield accelerators, the wave excited in the plasma eventually
breaks and leaves behind slowly changing fields and currents that perturb the
ion density background. We study this process numerically using the example of
a FACET experiment where the wave is excited by an electron bunch in the bubble
regime in a radially bounded plasma. Four physical effects underlie the
dynamics of ions: (1) attraction of ions toward the axis by the fields of the
driver and the wave, resulting in formation of a density peak, (2) generation
of ion-acoustic solitons following the decay of the density peak, (3) positive
plasma charging after wave breaking, leading to acceleration of some ions in
the radial direction, and (4) plasma pinching by the current generated during
the wavebreaking. Interplay of these effects result in formation of various
radial density profiles, which are difficult to produce in any other way
