Near-cathode Space-charge Sheath Research Articles

Simulating changes in shape of thermionic cathodes during operation of high-pressure arc discharges

A numerical model of current transfer to thermionic cathodes of high-pressure arc discharges is developed with account of deviations from local thermodynamic equilibrium occurring near the cathode surface, in particular, of the near-cathode space-charge sheath, melting of the cathode, and motion of the molten metal under the effect of the plasma pressure, the Lorentz force, gravity, and surface tension. Modelling results are reported for a tungsten cathode of an atmospheric-pressure argon arc and the computed changes in the shape of the cathode closely resemble those observed in the experiment. The modelling has shown that the time scale of change of the cathode shape during arc operation is very sensitive to the temperature attained by the cathode. The fact that the computed time scales conform to those observed in the experiment indicate that the model of non-equilibrium near-cathode layers in high-pressure arc discharges, employed in this work, predicts the cathode temperature for a given arc current with adequate accuracy. In contrast, modelling based on the assumption of local thermodynamic equilibrium in the whole arc plasma computation domain up to the cathode surface could hardly produce a similar agreement.

Revisiting Theoretical Description of the Retrograde Motion of Cathode Spots of Vacuum Arcs

A fresh attempt to develop a self-consistent description of the retrograde motion of cathode spots on volatile cathodes is undertaken. Three potential mechanisms of effect of transversal magnetic field on the distribution of parameters in the spot are studied: the effect of magnetic field on hydrodynamics processes in the spot, in particular, on the formation of liquid-metal jet and the droplet detachment, and the effect of transversal magnetic field over the motion of ions and emitted electrons in the near-cathode space-charge sheath. It is found that for typical conditions of cathode spots in vacuum arcs the effect of magnetic field over the formation of liquid-metal jet and the droplet detachment is negligible; the motion of the ions in the near-cathode space-charge sheath is not disturbed; and the motion of the emitted electrons is disturbed only marginally. Thus, the above-mentioned potential mechanisms are hardly relevant and the first-principle understanding is still missing. A phenomenological description of the retrograde motion is developed as an alternative. The description employs general considerations without relying on specific assumptions and the (only) unknown parameter can be determined from comparison with the experiment.

Pre-Explosion Phenomena Beneath the Plasma of a Vacuum Arc Cathode Spot

A 2-D hydrodynamic model has been developed that describes the pre-explosion processes in a microprotrusion of a vacuum arc cathode based on a self-consistent calculation of the electric potential drop in the near-cathode region. The model includes a calculation of the cathode temperature in view of the surface heat fluxes carried by electrons and ions during the interaction of the cathode surface with the cathode spot plasma and the Joule heating of the cathode. The near-cathode space charge sheath is considered in the 1-D local Bohm approximation. It has been shown that the heat flux from a cathode plasma having parameters characteristic of low-current vacuum arcs can induce thermal instability (thermal runaway) in a cathode microprotrusion and heat it to a critical temperature within some tens of nanoseconds. Comparative analysis of the volumetric Joule mechanism and the surface electron-plasma mechanism underlying the development of thermal instabilities in a cathode has been performed in one numerical experiment. It has been shown that the instability induced by the surface mechanism can arise at lower densities of the cathode spot plasma and its growth rate is lower compared with the instability induced by the Joule mechanism.

Physics of Spotless Mode of Current Transfer to Cathodes of Metal Vapor Arcs

A fresh attempt is made to clarify the physics of the diffuse, or spotless, mode of current transfer that may occur on cathodes of vacuum arcs if the average cathode surface temperature is high enough, about $2000 \operatorname {K}$ . It is shown that in the case of chromium cathode the usual mechanism of current transfer to arc cathodes cannot sustain current densities of the order of $10^{5}$ – $10^{6}~\operatorname {A}{\cdot }\operatorname {m}^{-2}$ observed in the experiment, the reason being that the electrical power deposited into electron gas in the near-cathode space-charge sheath is insufficient. It is hypothesized that the electrical power is supplied to the electron gas primarily in the bulk plasma, rather than in the sheath, and a high level of electron energy in the vicinity of the sheath edge is sustained by electron heat conduction from the bulk plasma. Estimates of the current of ions diffusing to the sheath edge from the quasi-neutral plasma gave values comparable with the experimental current density, which supports the above hypothesis. On the contrary, the spotless attachment of vacuum arcs to gadolinium cathodes may be interpreted as a manifestation of the usual mechanism of current transfer to arc cathodes. Results given for gadolinium cathodes by a model of near-cathode layers in vacuum arcs conform to available experimental information.

Near-Cathode Plasma Layer on CuCr Contacts of Vacuum Arcs

A model of near-cathode layers in vacuum arcs is developed. The model relies on a numerical solution of the problem of near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface, and allows the self-consistent determination of all parameters of the near-cathode layer, including the ion backflow coefficient. The dependence of the density of energy flux from the plasma to the cathode surface on the local surface temperature is nonmonotonic with a maximum, a feature that plays an important role in the physics of plasma–cathode interaction. The developed model may be used for a variety of purposes, including as a module of complex nonstationary multidimensional numerical models of plasma–cathode interaction in vacuum arcs. As a simple example, an analytical evaluation of parameters of stationary spots on copper and chromium is given. In the case of composite CuCr contacts with large grains, spots with current of several tens of amperes burning on the copper matrix coexist with spots with currents of the order of 1 A burning on the chromium grains.

Sheath and arc-column voltages in high-pressure arc discharges

Electrical characteristics of a 1 cm-long free-burning atmospheric-pressure argon arc are calculated by means of a model taking into account the existence of a near-cathode space-charge sheath and the discrepancy between the electron and heavy-particle temperatures in the arc column. The computed arc voltage exhibits a variation with the arc current I similar to the one revealed by the experiment and exceeds experimental values by no more than approximately 2 V in the current range 20–175 A. The sheath contributes about two-thirds or more of the arc voltage. The LTE model predicts a different variation of the arc voltage with I and underestimates the experimental values appreciably for low currents but by no more than approximately 2 V for I ≳ 120 A. However, the latter can hardly be considered as a proof of unimportance of the space-charge sheath at high currents: the LTE model overestimates both the resistance of the bulk of the arc column and the resistance of the part of the column that is adjacent to the cathode, and this overestimation to a certain extent compensates for the neglect of the voltage drop in the sheath. Furthermore, if the latter resistance were evaluated in the framework of the LTE model in an accurate way, then the overestimation would be still much stronger and the obtained voltage would significantly exceed those observed in the experiment.

The double sheath on cathodes of discharges burning in cathode vapour

The model of a collisionless near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface is considered. Numerical calculations showed that the mathematical problem is solvable and its solution is unique. In the framework of this model, the sheath represents a double layer with a potential maximum, with the ions which are produced before the maximum returning to the cathode surface and those produced after the maximum escaping into the plasma. Numerical results are given in a form to be readily applicable in analysis of discharges burning in cathode vapour, such as vacuum arcs. In particular, the results indicate that the ion backflow coefficient in such discharges exceeds 0.5, in agreement with values extracted from the experiment.

Space-charge sheath with ions accelerated into the plasma

The conventional model of near-cathode space-charge sheath with ions entering the sheath from the quasi-neutral plasma may not be applicable to discharges burning in cathode vapour, e.g. vacuum arcs, where ionization of emitted atoms may occur inside the sheath with some of the produced ions returning to the cathode and others moving into the plasma. In this connection, a simple model is considered of a sheath formed by electrons and positive ions injected into the sheath with a very low velocity and moving from the sheath into the plasma. It is shown that such a sheath is possible provided that the sheath voltage is equal to or exceeds approximately 1.256kTe/e. This limitation is due to the space charge in the sheath and is in this sense analogous to the limitation of ion current in a vacuum diode expressed by the Child–Langmuir law. The ions leave the sheath and enter the plasma with a velocity equal to or exceeding approximately 1.585uB.

Unified modelling of near-cathode plasma layers in high-pressure arc discharges

A model of a near-cathode region in high-pressure arc discharges is developed in the framework of the hydrodynamic (diffusion) approximation. Governing equations are solved numerically in 1D without any further simplifications, in particular, without explicitly dividing the near-cathode region into a space-charge sheath and a quasi-neutral plasma. Results of numerical simulation are reported for a very high-pressure mercury arc and an atmospheric-pressure argon arc. Physical mechanisms dominating different sections of the near-cathode region are identified. It is shown that the near-cathode space-charge sheath is of primary importance under conditions of practical interest. Physical bases of simplified models of the near-cathode region in high-pressure arc discharges are analysed. A comparison of results given by the present model with those given by a simplified model has revealed qualitative agreement; the agreement is not only qualitative but also quantitative in the case of an atmospheric-pressure argon plasma at moderate values of the near-cathode voltage drop. The modelling data are compared with results of spectroscopic measurements of the electron temperature and density in the near-cathode region.

Bifurcations of current transfer through a collisional sheath with ionization and self-organization on glow cathodes

A bifurcation analysis is performed of a dc glow discharge between parallel electrodes and of a dc near-cathode space-charge sheath bordering a uniform plasma column. A model of plasma is considered with a single ion species and motion of the charged particles dominated by drift. Bifurcation points are found at which steady-state modes with spots on the cathode branch off from the abnormal mode or from the mode corresponding to the falling section of the current-density-voltage characteristic. In both discharge configurations, bifurcations in the abnormal mode have been detected; an unexpected result given that loss of stability and pattern appearance in dc gas discharges are usually associated with a negative differential resistance of the discharge. The conclusion is drawn that the two most important mechanisms governing appearance of patterns on glow cathodes, which are electrostatic mechanism and diffusion, produce competing effects: the former favors appearance of modes with multiple spots, while the latter favors appearance of a mode with one spot. This may explain the appearance in experiments of a normal spot or, alternatively, of patterns with multiple spots.

Kinetics of plasma particles and electron transport in the current-carrying plasma adjacent to an evaporating and electron emitting wall

The paper reviews the vaporization phenomena at a target heated by heat flux from an adjacent plasma in vacuum and in low-pressure discharges. The kinetics of a nonequilibrium layer and the direct and returned mass fluxes formed in the vicinity of the target are described. The mechanism of cathode vaporization taking into account cathode electron emission in vacuum arcs is considered. It is shown that in vacuum arcs, the cathode electron beam relaxation region is an energetic zone which supports the generation of charged particles by atom ionization, balancing losses from ion motion towards the cathode and electron current. The mechanism of electron transport from the cathode to the plasma for cathode materials with strongly different thermal properties is considered. It is shown that the cathode electron current is controlled by a near-cathode space charge sheath whose structure depends on the thermo-physical properties of the cathode material. The potential structures has a large electric field at the cathode surface (like Cu), or a virtual cathode (W), or double plasma sheath (Hg), depending on the ratio of the electron emission flux to the vaporized atom flux, which in turn depends on the cathode material

Asymptotic calculation of escape factor in atomic plasmas

Simple analytical expressions are obtained for the escape factor for low-energy electrons in an atomic plasma at intermediate and high values of the reduced electric field in the near-cathode region, when the dominating electron energy losses are due to inelastic collisions of electrons with atoms. An approximate account of the reflection of electrons by the cathode surface is introduced. Calculated escape factors are in reasonable agreement with the results of the Monte Carlo simulations available in the literature. When applied to cathodes of high-pressure arc discharges, the obtained results indicate that the escape factor is close to unity in cases where the near-cathode space-charge sheath is collision-free or moderately collisional. If the sheath is collision-dominated, the escape factor may be different from unity; for example, this is the case under conditions of a 100 bar mercury plasma of a mercury arc lamp.

Collision-dominated to collisionless electron-free space-charge sheath in a plasma with variable ion temperature

A theory of the near-cathode space-charge sheath in the case when the near-cathode voltage is high enough and the presence of electrons in the sheath is unessential is developed on the basis of a fluid description of the ion motion with account of ion-atom collisions and of variable ion temperature. The model spans the range of conditions from a collision-free to collision-dominated space-charge sheath. Detailed analytical and numerical results are presented for two models of ion-atom interaction, the model of rigid spheres (constant mean free path) and the model of Maxwell molecules (constant frequency of momentum transfer). It is found, in particular, that the assumption of cold ions provides a good accuracy in the problem considered. An analytical solution has been obtained under this assumption for the model of Maxwell molecules.

A model of the cathode region of atmospheric pressure arcs

The paper deals with calculation of parameters in the near-cathode plasma layer, on the cathode surface and in the body of a cathode in high-pressure arc discharges. These parameters can be calculated independently of the arc column if the heat flux coming from the column to the edge of the near-cathode layer does not play a decisive role in the energy balance of the layer, which, according to the estimates presented, is a likely case. The physics of the near-cathode layer is reconsidered in view of major contradictions that have appeared in the literature recently, in particular with regard to the role of the near-cathode space charge sheath. A model of a near-cathode layer is developed that is based on a multifluid description of the plasma and takes into account multiply charged ions. The model is employed to calculate parameters of the layer as functions of the voltage drop in the layer and of the local value of the surface temperature. By means of these data, an approximate asymptotic theory of arc spots is extended to cathode spots in high-pressure plasmas. Calculated spot parameters are presented for the following combinations cathode/plasma: tungsten/argon, thoriated-tungsten/argon, thoriated-tungsten/nitrogen, and zirconium/nitrogen. The obtained results agree with the recent measurements of the spot temperature.