Numerical and theoretical calculation of breakdown voltage in the electrical discharge for rare gases

This work has been devoted to a numerical and analytical calculus of the voltage breakdown in electrical discharge for several rare gases such as argon, krypton, neon, xenon and helium. It was performed using a fluid model 2D, which is based on the numerical solution of the two Boltzmann equations (equation of continuity and momentum), coupled to Poisson's equation to measure the breakdown voltage according to the product of the electrode spacing and the pressure. This study allowed a better comprehension of the physical phenomena occurring in the discharges. We, thus, developed a calculation, based on the empirically Paschen's law, allowing the determination of the breakdown voltage, which describes the transition from insulating gas to the conductive state. Paschen's curves of the different gases are plotted and a comparison between numerical and experimental as well as analytical results is also presented and analyzed.