Analysis of application range of simplified models for field to thermo-field to thermionic emission processes from the cathode

Abstract

Electrons can escape from the cathode surface by acquiring enough energy greater than the work function or weakening the potential barrier at the cathode surface through tunneling effects in gas discharges, which plays a dominant role in the plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications. It is necessary to illustrate the various electron emission mechanisms and corresponding applicable description models to evaluate the impacts on discharge properties, especially for numerical simulation studies. However, most current researches usually rely on previous experience to select the appropriate simplified formula to calculate the electron emission current density, and there is little work that can explicitly give the application range of the simplified formulas for describing electron emission. In this work, the detailed expressions of the simplified formulas valid for field emission to thermo-field emission to thermionic emission typically used in the numerical simulation are proposed, and corresponding application ranges are determined in the framework of the Murphy-Good theory, which is commonly regarded as the general model and to be accurate in the full range of conditions of validity of the theory. The dimensionless parametrization is used to evaluate the emission current density of the Murphy-Good formula and a deviation factor is defined to obtain the application ranges for different work functions (2.5~5 eV), different cathode temperatures (300~6000 K), and different emitted electric field (105 ~1010 V‧m-1). The deviation factor is shown to be a non-monotonic function of the three parameters. A comparative study of particle number densities in atmospheric gas discharge with tungsten cathode is performed based on the one-dimensional implicit particle-in-cell with the Monte Carlo Collision (PIC-MCC) method according to the above application ranges. It is found that small differences in emission current density can lead to variation in the distributions of particle number density due to the change of collisional environment. This present work can provide a theoretical basis to select emission models for the subsequent numerical simulation.