Cylindrical Sheath Research Articles

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.

The Drop of Potential at the Cathode in Flames

The theory as given by J. J. Thomson for the drop of potential at plane electrodes has been modified by allowing for recombination in the layer and a similar theory for cylindrical electrodes has been worked out. The equation for plane cathodes is ${V}_{2}={\left(\frac{32\ensuremath{\pi}i}{75{k}_{1}}\right)}^{\frac{1}{2}}{{x}_{2}}^{\frac{3}{2}},$ and for cylindrical cathodes is ${V}_{2}={\left(\frac{2i}{3{k}_{1}{({{r}_{2}}^{2}\ensuremath{-}{{r}_{0}}^{2})}^{2}}\right)}^{\frac{1}{2}}\left[{{r}_{2}}^{3}log\left(\frac{{r}_{2}+{({{r}_{2}}^{2}\ensuremath{-}{{r}_{0}}^{2})}^{\frac{1}{2}}}{{r}_{0}}\right)\ensuremath{-}{{r}_{2}}^{2}{({{r}_{2}}^{2}\ensuremath{-}{{r}_{0}}^{2})}^{\frac{1}{2}}\ensuremath{-}\frac{{({{r}_{2}}^{2}\ensuremath{-}{{r}_{0}}^{2})}^{\frac{3}{2}}}{3}\right],$ where ${V}_{2}$ is the potential drop across the sheath, $i$ the current density, ${x}_{2}$ the sheath thickness at the plane cathode, ${r}_{0}$ the radius of the cylindrical cathode, ${r}_{2}$ the radius of the cylindrical sheath about the cathode, and ${k}_{1}$ the velocity of the positive ions for a gradient of one volt per cm. The experimental results for platinum electrodes immersed in pure and NaCl flames agree well with the theoretical equations given. It is found that the drop in potential at the cathode occurs in a sheath of uniform thickness, which completely surrounds the electrode. By plotting the gas potential at various points in the flame against distance from the cathode it is possible to estimate the thickness of the sheath. Over 95% of the potential drop takes place across the sheath at the cathode provided it is of clean platinum. If the cathode is not clean electrons are emitted which partially neutralize the accumulation of positive ions and thus reduce the sheath thickness. By measuring ${V}_{2}$, $i$, ${x}_{2}$ or ${r}_{0}$ and ${r}_{2}$, and making the proper substitutions in the above equations, the mobility ${k}_{1}$ of the positive ions is found to average 12.4 for a pure flame and 8.1 cms per sec. for one volt per cm for a NaCl flame.A study of the characteristic current-voltage curve for a wire probe in a flame makes it possible to measure the voltage correction to be applied to the measured probe potential in order to obtain the true gas potential adjacent to the test probe. The correction is of the order of +1. volts.It is found that the current density at the surface of the cylindrical sheath is constant for any given flame conditions, and size of cathode. Thus one can measure the current density existing in the small uniform gradient just outside the sheath. The current density at the sheath surface in a pure flame varies from 1. to 2.5 microamperes and for the NaCl flame from 5. to 11. microamperes.

STM imaging of the complete bacterial cell sheath of Methanospirillum hungatei

Using a large range scanning tunnelling microscope (STM) we have obtained images of the complete outer cell wall of the archaebacterium Methanospirillum hungatei, deposited on a graphite substrate and over-coated with an Au or Pt evaporated film. The width of the collapsed cylindrical sheath structure was found to be 5000 Å ± ***10%, which agrees closely with the value from previously published electron microscope (EM) studies. The double thickness of the collapsed sheath was found to be 160 Å ± 10%, which is about 20% smaller than that from the EM results. Higher resolution STM images taken on top of the collapsed sheaths show corrugations running perpendicular to the cylinder axis and having widths which are multiples of ∼ 30 Å, the minimum period expected from EM studies. The height of the corrugations have a minimum value of about 4 Å. The expected 2-D crystalline structure was not seen in the STM images.