Full-fluid Moment Modeling and Theory of DC Breakdown*

Plasma breakdown in DC gas discharges is primarily described by Paschen theory. The breakdown voltage required to sustain a plasma is considered a function of the gas pressure (P), the electrode gap distance (d), and the secondary electron emission (SEE) coefficient at the cathode (γ). While Paschen theory accounts for the flux balance correctly, the relation between the reduced electric field and the ionization coefficient is given empirically. In this study, DC breakdown is investigated using the full-fluid moment (FFM) model, in which the electron inertial effects are accounted for, and the electron energy is self-consistently modeled [1,2]. The results show a multivalued behavior for small values of Pd, i.e., the left branch of the Paschen curve. Additionally, the results show that the first Townsend coefficient α, often used as a constant modeling parameter in other DC breakdown studies, exhibits spatial variations and generally varies for different values of Pd. The contribution of Joule heating, reactive energy losses, and convective energy losses is also investigated, showing a gradual change between regimes where convective losses dominate reactive losses. The breakdown theory is revisited, including the electron energy equation without any empirical parameters.  

[1] R. Sahu, A. R. Mansour, and K. Hara, "Full fluid moment model for low-temperature magnetized plasmas", Physics of Plasmas 27, 113505 (2020)

[2] A. R. Mansour and K. Hara, “Full Fluid Moment Modeling of Rotating Spokes in Penning-type Configuration”, Plasma Sources Science and Technology 31, 055012 (2022)