A trapped pure electron plasma column can be unstable if the plasma co
lumn is contaminated by a small number of oppositely charged ions. Thi
s instability was analyzed by Levy, Daugherty, and Buneman [Phys. Flui
ds, 12, 2616 (1969)] for the case of trapped ions. The instability is
analyzed here for the case of untrapped ions. The analysis is inherent
ly nonlinear, and growth results from averaging over the ion initial c
onditions. Several significant differences exist between the two cases
, including, for the latter, growth over a much broader parameter regi
on and linear (secular) rather than exponential growth. The prediction
s of the analysis are compared to the results from a recent experiment
on the instability.