We explore the role of the background plasma ion motion in self-modulated plasma wakefield accelerators. We employ J. Dawsons plasma sheet model to derive expressions for the transverse plasma electric field and ponderomotive force in the narrow bunc
h limit. We use these results to determine the on-set of the ion dynamics, and demonstrate that the ion motion could occur in self-modulated plasma wakefield accelerators. Simulations show the motion of the plasma ions can lead to the early suppression of the self-modulation instability and of the accelerating fields. The background plasma ion motion can nevertheless be fully mitigated by using plasmas with heavier plasmas.
