  One dimensional analysis is presented of solitary positive potential plasma
structures whose velocity lies within the range of ion distribution velocities
that are strongly populated: so called "slow" electron holes. It is shown that
to avoid the self-acceleration of the hole velocity away from ion velocities it
must lie within a local minimum in the ion velocity distribution. Quantitative
criteria for the existence of stable equilibria are obtained. The background
ion distributions required are generally stable to ion-ion modes unless the
electron temperature is much higher than the ion temperature. Since slow
positive potential solitons are shown not to be possible without a significant
contribution from trapped electrons, it seems highly likely that such observed
slow potential structures are indeed electron holes.
