General Bohm and Langmuir conditions for a strong double layer in space plasmas

The appropriate Bohm and Langmuir conditions when there are three beam-type particles passing through the double layer in addition to the usual two species of trapped particles are derived. It is shown that the Langmuir conditions, which normally imply a net current through the double layer, are consistent with zero net current when the class of accreting ions is included. It is also found that the Bohm criterion is quite different from its usual form, and that it has nothing to do with instabilities of the plasma at some critical level, as is believed to be true.