When a cylindrical pure electron plasma is dispalced from the center o
f the trap, it performs a bulk circular orbital motion known as the l
= 1 diocotron mode. The slow application of a perturbing potential to
a patch on the trap wall distorts the orbit into a noncircular closed
path. Experiments and a simple theoretical model indicate that the are
a enclosed by the loop is an adiabatic invariant. Detailed studies are
made of the breaking of the invariant when perturbations are rapidly
applied. When the perturbation is applied with discontinuous time deri
vatives, the invariant breaking greatly exceeds the predictions of the
standard theory for smooth perturbations.