The method of expulsion of hydrogen negative ions in the axial direction by a negative space charge formed in the plasma of Penning discharge with metal hydride cathodes is discussed. The plasma is produced on hydrogen, which is stored in metal hydride cathodes and injected locally into the discharge cell without any external gas supply due to ion current impact from plasma. The process of nonequilibrium desorption resulted in high vibrational excitation of H2 molecules, which greatly increases the efficiency of H− ion production. The method of efficient expulsion of H− ions depends on the external magnetic field. At a high magnetic field, it is performed by the supply of negative electric bias of the opposite cathode, but at a low one, H− ions are pushed out by the negative space charge of the anode layer, which expands toward the axis. The impact of both methods is considered in the case of DC discharge and in pulsating regime implementation.