  In this paper, after reviewing the concept of an adiabatic focuser we
numerically study the effect of ion motion. Our work has been motivated by a
recent suggestion that ion motion in an adiabatic focuser might be significant
and even preclude operation of the focuser as previously envisioned. It is
shown that for parameters associated with cases in which the adiabatic lens
would be used, despite ion motion, the adiabatic focuser should work as well as
originally envisioned. We then extend the study by considering a very long
electron pulse (which accentuates the effect of ion motion).
