The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths

Effect of positive ions generated at a plane anode upon the space charge limitation of electron currents from a parallel cathode.---Mathematical analysis shows that single ions emitted with negligible velocity permit 0.378 ${(\frac{{m}_{p}}{{m}_{e}})}^{\frac{1}{2}}$ additional electrons to pass; but with an unlimited supply of ions the electron current approaches a limiting value 1.860 times that which flows when no ions are present, and the electron current is then ${(\frac{{m}_{p}}{{m}_{e}})}^{\frac{1}{2}}$ times the ion current, both currents thus being limited by space charge and the electric field being symmetrically distributed between the electrodes. Single ions introduced into a pure electron discharge at a point $\frac{4}{9}\mathrm{ths}$ of the distance from cathode to anode produce a maximum effect, 0.582 ${(\frac{{m}_{p}}{{m}_{e}})}^{\frac{1}{2}}$, in increasing the electron current. These conditions apply to a cathode emitting a surplus of electrons surrounded by ionized gas. The cathode sheath is then a double layer with an inner negative space charge and an equal outer positive charge, the field being zero at the cathode and at the sheath edge. The electron current is thus limited to ${(\frac{{m}_{p}}{{m}_{e}})}^{\frac{1}{2}}$ times the rate at which ions reach the sheath edge. If ions are generated without initial velocities uniformly throughout the space between two plane electrodes, a parabolic potential distribution results. If the total ion generation exceeds 2.86 times the ion current that could flow from the more positive to the more negative electrode, a potential maximum develops in the space. Electrons produced by ionization are trapped within this region and their accumulation modifies the potential distribution yielding a region (named plasma) in which only weak fields exist and where the space charge is nearly zero. The potential distribution in the plasma, given by the Boltzmann equation from the electron temperature and the electron concentrations, determines the motions of the ions and thus fixes the rate at which the ions arrive at the cathode sheath. The anode sheath is usually also a positive ion sheath, but with anodes of small size a detached double-sheath may exist at the boundary of the anode glow. In discharges from hot cathodes in gases where the current is limited by resistance in series with the anode, the electron current is space-charge-limited, being fixed by the rate of arrival of ions at the cathode sheath. Thus the cathode drop is fixed by the necessity of supplying the requisite number of ions to the cathode. The effect of the initial velocities of the ions and electrons that enter a double-sheath from the gas is to decrease the electron current by an amount that varies with the voltage drop in the sheath. A nearly complete theory of this effect is worked out for plane electrodes. A detailed study is made of the potential distribution in the plasma and near the sheath edge for a particular case and the conclusion is drawn that the velocities of the ions that enter the sheath can be calculated from the electron temperature if the geometry of the source of ionization is given.Experiments with double sheaths.---With large cathodes coated with barium oxide in low pressure mercury vapor, simultaneous measurements showed that the electron current density was independent of the cathode temperature and was from 140 to 200 times the ion current density, this ratio being independent of the intensity of ionization and of the gas pressure but varying slowly with the voltage drop in the cathode sheath, in good accord with the theory. The observed ratio, however, was about 40 percent of that calculated, this discrepancy being probably due to nonuniformity in the cathode coating. Similar results were obtained with double sheaths on wire type cathodes, the ratio of the electron current to the ion current through the sheath ranging from 450:1 at high current densities to 2000:1 and more at very low currents, this variation being in agreement with the approximate theory developed for cylindrical sheaths. In these experiments two cathodes were used; one at rather large negative voltage to produce any desired intensity of ionization, while from the volt-ampere characteristics of the other cathode the space-charge-limited electron currents were measured. The ion currents were measured either by cooling the test cathode so that it emitted no electrons, or by the use of an auxiliary ion collector.