The linearized Vlasov equation is employed to investigate the stability of the various equilibrium solutions determined from the following model: an infinite slab of width 2Lcontains a uniform densityNof infinitely massive, singly charged, positive ions. The bounding planes (cathodes) emit fixed Maxwellian electron distributions and absorb all impinging electrons, so that the total number of electrons in the system, and their energy, need not remain constant. This model permits three types of time‐independent, equilibrium solutions for the electron distribution. One of these solutions shows a Maxwellian electron velocity distribution everywhere in the slab and is stable. The other two types of solution have regions where the electron velocity distribution is not Maxwellian. These latter solutions are shown to be unstable for a range of system parameters to a longitudinal electron collective mode with a growth rate on the order of&ohgr;p≡(4&pgr;e2N/m)12.