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Analysis of deviations from the similarity law, observed at high and very high pressures in experiments on discharge ignition and breakdown in corona-like configurations, can serve as a useful, albeit inevitably indirect, source of information about microprotrusions on the surface of electrodes.
Current-voltage characteristics of field electron emission from cold cathodes in vacuum follow approximately the Fowler-Nordheim formula with the applied electric field being multiplied by the so-called field enhancement factor β, which is of the order of 100 or higher. Various mechanisms for the enhancement have been postulated, among them an enhancement of the applied (average) electric field by microprotrusions present on the cathode surface, a local reduction of the work function of the cathode material caused by, e.g., lattice defects or adsorbed atoms, `nonmetallic' electron emission mechanism, and enhancement of field emission by waves confined to the metal surface (plasmons). There is still no widely accepted understanding, despite several decades of active research.
The effect of enhanced field emission from the cathode surface was considered also in gas discharge physics in connection with deviations of measured breakdown voltage of plane-parallel gaps from Paschen's law. Deviations occurring at atmospheric pressure in microgaps, conventionally described by introducing a field enhancement factor into the Fowler-Nordheim field emission equation, are important for operation of microelectromechanical and nanoelectromechanical systems and are under intensive investigation; e.g., [1] and references therein. Deviations from the Paschen law occurring at very high pressures, starting from pressures of the order of 10 atm, have been known for several decades and a recent surge of interest in this topic is motivated by the possibility to use high-pressure air as a replacement for SF₆ for high-voltage insulation. It was hypothesized that the reason of these deviations is the field emission from the negative electrode enhanced by micrononuniformities as in the case of microgaps. Another hypothesis is that the deviations are not due to field emission (or at least not only), but rather due to enhanced ionization of neutral gas molecules in regions of increased electric field near the protrusions on the surface of the electrodes [2, 3].
In this work, analysis of deviations from the similarity law observed at very high pressures in experiments on corona inception and breakdown for discharges on positive cylindrical electrodes of small radii [2, 4] was performed by means of 2D numerical modelling. Cathodic phenomena are irrelevant and enhanced ionization of neutral gas in regions near protrusions on the anode surface appears to be the only possible explanation. The modelling has shown that the deviations from the similarity law, observed in the experiment, may indeed be attributed to enhanced ionization of air molecules in regions of enhanced electric field near the microprotrusions. A qualitative agreement with the experiments is achieved for protrusion heights of the order of 50μm. Such values appear rather high, however there is no other explanation in sight at present. The enhancement of the field electron emission from the surface of the negative electrode was estimated and found insignificant in the range of values of the protrusion aspect ratio where the enhanced ionization of air molecules in the gas phase comes into play.
[1] Y. Fu, P. Zhang, J. P. Verboncoeur, and X. Wang, Plasma Res. Express 2, 013001 (2020).
[2] A. H. Howell, Electrical Engineering 58, 193 (1939).
[3] M. Seeger, P. Stoller, and A. Garyfallos, IEEE Trans. Dielectr. Electr. Insul. 24, 1582 (2017).
[4] M. Robinson, J. Appl. Phys. 40, 5107 (1969).
Acknowledgments
This work was supported by FCT of Portugal under project UIDP/50010/2020 and by European Regional Development Fund through the program Madeira 2014-2020 under project PlasMa-M1420-01-0145-FEDER-000016 (UMa), and by the RFBR grant No. 20-02-00320 (JIHT). The authors are grateful to Thomas Hammer and Svetlana Gossmann of Siemens Erlangen for stimulating discussions that initiated this work, Martin Seeger of ABB Switzerland for additional information on the experiment [3], and Walter Wuensch of CERN for stimulating discussions.
