  A future plasma based linear collider has the potential to reach
unprecedented energies and transform our understanding of high energy physics.
The extremely dense beams in such a device would cause the plasma ions to fall
toward the axis. For more mild ion motion, this introduces a nonlinear
perturbation to the focusing fields inside of the bubble. However, for extreme
ion motion, the ion distribution collapses to a quasi-equilibrium characterized
by a thin filament of extreme density on the axis which generates strong,
nonlinear focusing fields. These fields can provoke unacceptable emittance
growth that can be reduced through careful beam matching. In this paper, we
discuss the rich physics of ion motion, give a brief overview of plans for the
E-314 experiment at FACET-II which will experimentally demonstrate ion motion
in plasma accelerators, and present results of particle-in-cell simulations of
ion motion relevant to the E-314 experiment.
