Field to thermo-field to thermionic electron emission: a practical guide to evaluation and electron emission from arc cathodes

This work is concerned with devising a method of evaluation of electron emission in the framework of the Murphy-Good theory, which would be as simple and computationally efficient as possible while being accurate in the full range of conditions of validity of the theory. The method relies on Pad e approximants. A comparative study of electron emission from cathodes of arcs in ambient gas and vacuum arcs is performed with the use of this method. Electron emission from cathodes of arcs in ambient gas is of thermionic nature even for extremely high gas pressures characteristic of projection and automotive arc lamps and is adequately described by the Richardson-Schottky formula. The electron emission from vaporizing (hot) cathodes of vacuum arcs is of thermo-field nature and is adequately described by the Hantzsche fit formula. Since no analytical formulas are uniformly valid for field to thermo-field to thermionic emission, a numerical evaluation of the Murphy-Good formalism is inevitable in cases where a unified description of the full range of conditions is needed, as is the general case of plasma-cathode interaction in vacuum arcs, and the technique proposed in this work may be the method of choice to this end.info:eu-repo/semantics/publishedVersio

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.info:eu-repo/semantics/publishedVersio

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.info:eu-repo/semantics/publishedVersio

Numerical investigation of AC arc ignition on cold electrodes in atmospheric-pressure argon

Since experiments cannot clarify the mechanism of current transfer to non-thermionic arc cathodes, this can only be done by means of numerical modelling based on first principles and not relying on a priori assumptions. In this work, the first quarter-period after the ignition of an AC arc on cold electrodes in atmospheric-pressure argon is investigated by means of unified one-dimensional modelling, where the conservation and transport equations for all plasma species, the electron and heavy-particle energy equations, and the Poisson equation are solved in the whole interelectrode gap up to the electrode surfaces. Results are compared with those for DC discharges and analysed with the aim to clarify the role of different mechanisms of current transfer to non-thermionic arc cathodes. It is found that the glow-to-arc transition in the AC case occurs in a way substantially different from the quasi-stationary glow-to-arc transition. The dominant mechanisms of current transfer to the cathode during the AC arc ignition on cold electrodes are, subsequently, the displacement current, the ion current, and thermionic emission current. No indications of explosive emission are found. Electron emission from the impact of excited atoms can hardly be a dominant mechanism either. The introduction of the so-called field enhancement factor, which is used for description of field electron emission from cold cathodes in a vacuum, leads to computed cathode surface temperature values that are appreciably lower than the melting temperature of tungsten even in the quasi-stationary case. This means that pure tungsten cathodes of atmospheric-pressure argon arcs can operate without melting, in contradiction with experiments.info:eu-repo/semantics/publishedVersio

The double sheath on cathodes of discharges burning in cathode vapour The double sheath on cathodes of discharges burning in cathode vapour

Abstract 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

Analyzing spotless mode of current transfer to cathodes of metal-vapor arcs

The diffuse, or spotless, mode of current transfer has been observed on cathodes of vacuum arcs under conditions where the average cathode temperature was high enough, about 2000 K. It has been known for many years that none of the known mechanisms of current transfer to cathodes of vacuum arcs and, in particular, of the electron emission is capable of producing the current densities of the order of 105 - 106 Am-2 deduced from the experiment. A fresh attempt to clarify this question is made in this work. Cathodes made of chromium are considered, on which the most of the experiments have been performed. It is shown that an account of the difference between values of thermionic and photoelectric work functions given in the reference literature allows one to significantly reduce the deviation between the theory and the experiment. Unfortunately, data on thermionic work function available in the literature refer to the cathode surface temperatures below 1400 K, which is significantly smaller than measured temperatures of the chromium cathodes of vacuum arcs operating in the spotless mode. Therefore, further experimental data are needed in order to clarify this effect.info:eu-repo/semantics/publishedVersio

Theory of Space-Charge Sheaths on Cathodes of Vacuum Arcs

Abstract- The model of a collisionless near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface is considered. It was found that such 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. Distributions across the sheath have been calculated of ion, electron, and atomic densities, electrostatic potential and electric field. Also calculated have been integral parameters of the sheath. The results may be readily incorporated into models of near-cathode layers of discharges burning in cathode vapor. Besides, these results may be employed for qualitative analysis. In particular, the results indicate that the ion backflow coefficient in such discharges is at least 53%. As an example of application of the theory, calculation results on spots on copper cathodes of vacuum arcs are given and a favorable agreement with available experimental data is found

Modeling cathode spots in vacuum arcs burning on multi-component contacts

A self-consistent space-resolved numerical model of cathode spots in vacuum arcs is developed on the basis of the COMSOL Multiphysics software. The model is applied to cathode spots on copper-chromium (CuCr) contacts of vacuum interrupters. In the limiting case of large grains, the main effect of change in cathode material from Cu to Cr is the reduction of thermal conductivity of the cathode material, which causes a reduction of spot radius and spot current. Hence, the model indicates that spots with currents of the order of tens of amperes on Cu coexist with spots on Cr with currents between one and two amperes. The parameters of spots on small Cr grains of the order of 10 µm size are rather close to those of spots on pure Cu, whereas the parameters for spots on medium-size Cr grains of around 20 µm are quite different from those of spots on both pure Cu and pure Cr. The power flux is directed from the cathode into the plasma, i.e., it is the cathode that heats the plasma – and not the other way round. What maintains the spot is a substantial Joule heating inside the cathode bulk. About 70 percent of the heat is generated in the grain and 30 percent in the surrounding copper. One may hypothesize that such grains are highly unstable, leading to explosive-like behavior with a consequent additional loss of cathode material, and a severe limitation in spot lifetime.info:eu-repo/semantics/publishedVersio

Account of near-cathode sheath in numerical models of high-pressure arc discharges

Three approaches to describing the separation of charges in near-cathode regions of highpressure arc discharges are compared. The first approach employs a single set of equations, including the Poisson equation, in the whole interelectrode gap. The second approach employs a fully non-equilibrium description of the quasi-neutral bulk plasma, complemented with a newly developed description of the space-charge sheaths. The third, and the simplest, approach exploits the fact that significant power is deposited by the arc power supply into the near-cathode plasma layer, which allows one to simulate the plasma–cathode interaction to the first approximation independently of processes in the bulk plasma. It is found that results given by the different models are generally in good agreement, and in some cases the agreement is even surprisingly good. It follows that the predicted integral characteristics of the plasma–cathode interaction are not strongly affected by details of the model provided that the basic physics is right.info:eu-repo/semantics/publishedVersio