A simple model for cathodic electronic emission enhanced by low-energy ions in high-pressure arcs

Abstract

The influence of slow ions on the electronic emission of a cathode in a high-pressure electric arc is investigated. As a first approach, a simple model is introduced, where solving the stationary Schrödinger equation is reduced to integrating a one-dimensional second-order differential equation. We have found that the electronic current may be enhanced through two mechanisms: a non-resonant process related to the lowering of the potential barrier and a resonant mechanism involving bound states of the ions. The non-resonant process is found to be dominant. The influence of various parameters such as ionic density, cathode temperature and charge states of the ions on amplification coefficients is analysed.

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

“…Note that the WKB approximation used in the Murphy-Good formalism [28] will become poor for extremely high electric field strengths of the order of 10 10 V m −1 or higher [40][41][42]. However, values that high have not been encountered in the calculations; the enhanced electric field for β = 100 remained below 4 × 10 9 V m −1 .…”

A comparison of electron-emission equations used in arc - cathode interaction calculations

“…Indeed, the presence of a high density of ions not only induces an important macroscopic electric field outside the metal surface which favours T-F emission but also is responsible for a modification of the potential 'experienced' by the electrons outside the metal surface, thus affecting the emission conditions. Results reported for a Cu cathode exposed to a macroscopic electric field strength E s = 10 9 V m −1 suggest that the enhancement of the T-F emission current (the Murphy and Good equation) sets in for cathode surface temperatures below 4000 K and ion densities above 10 24 m −3 [10]. These conditions of temperature and ion density are encountered within the cathode region of metal vapour arcs (vacuum arcs [5,11] and high-pressure arcs on non-refractory cathodes [6]) and also for high-pressure arcs on refractory cathodes ( 1 atm) [12,13].…”

“…The three different equations used to calculate the cathodic electron-emission current density j T-F are, respectively, the field-enhanced thermionic emission equation, the Murphy and Good equation for T-F emission [8] and the Murphy and Good equation for T-F emission corrected for the ionenhancement effect [10].…”

“…(3) where β is the cathodic electron-emission amplification factor developed by Gayet et al [10]. As discussed by those authors, this cathodic electronic-emission enhancement is due to the significant alteration of the potential 'experienced' by the electrons outside the metal surface induced by the presence of slowly moving ions.…”

“…Gayet et al [10] showed recently that the presence of a high density of slowly moving ions in the cathode region is responsible for an enhancement of the thermofield emission current density above that predicted by the equation of Murphy and Good. Indeed, the presence of a high density of ions not only induces an important macroscopic electric field outside the metal surface which favours T-F emission but also is responsible for a modification of the potential 'experienced' by the electrons outside the metal surface, thus affecting the emission conditions.…”