The existing model of a "co l l is ionless" alkali plasma diode is extended including the case of two incandescent plane electrodes emitting electrons as well as ions with a half-Maxwellian velocity distribution. The potential distributions within the diode space derived from this theory are examined in detail. Physically necessary conditions reduce the well-known ambiguity of solutions to a single one (with uniform plasma potential) at a given set of parameters. Further solutions, corresponding to spatially oscillatory potential shapes which are consistent with the collisionless theory, disappear if the ion-ion collision probability within the diode plasma exceeds 0.1 per emitter distance. In the experiment the potential distributions are scanned using a new electron beam probing technique. The results agree with the theory.