A Global Model of Direct Current (DC) Breakdown

Direct current (dc) breakdown conditions are investigated using a 0-D global model based on conservation of mass, momentum, and local mean energy, which is proposed as an alternative to Paschen’s law. Breakdown voltage and the product of the gas pressure and anode–cathode gap distance are obtained as functions of the reduced electric field, <inline-formula> <tex-math notation="LaTeX">$E/N$ </tex-math></inline-formula>. The 0-D results, including the breakdown voltage, electron bulk velocities, and electron temperatures, show good agreement with the results obtained from a 1-D fluid moment model (Mansour et al., 2024). Furthermore, the 0-D global model is used to estimate the effective ion-induced electron emission coefficient, <inline-formula> <tex-math notation="LaTeX">$\gamma _{i}$ </tex-math></inline-formula>, by fitting the 0-D results to experimental results of argon dc breakdown, illustrating that <inline-formula> <tex-math notation="LaTeX">$\gamma _{i} =10^{-3}{\,}-{\,}10^{-2}$ </tex-math></inline-formula> for intermediate <inline-formula> <tex-math notation="LaTeX">$E/N$ </tex-math></inline-formula> (e.g., <inline-formula> <tex-math notation="LaTeX">$E/N=50 - 500$ </tex-math></inline-formula> Td) while <inline-formula> <tex-math notation="LaTeX">$\gamma _{i}$ </tex-math></inline-formula> exponentially increases with decreased <inline-formula> <tex-math notation="LaTeX">$E/N$ </tex-math></inline-formula> at <inline-formula> <tex-math notation="LaTeX">$E/N\lt 50$ </tex-math></inline-formula> Td and with increased <inline-formula> <tex-math notation="LaTeX">$E/N$ </tex-math></inline-formula> at <inline-formula> <tex-math notation="LaTeX">$E/N \gt 500$ </tex-math></inline-formula> Td. The trend of these estimates is consistent with previous work by Phelps and Petrovic (1999), particularly the effective yield obtained from data corresponding to dirty electrodes.