Revisiting Paschen Theory for DC Breakdown

Paschen theory is primarily used to describe the breakdown mechanism in gas discharge. The breakdown voltage required to sustain a plasma (V_b) is considered to be a function of the gas pressure and the electrode gap distance (Pd). The theory neglects the effect of electron energy on the breakdown behavior, assuming a constant ionization rate and not accounting for the energy balance. The theory behind direct current (DC) breakdown is revisited, accounting for electron energy and including the weak dependence of reaction rates on the electron temperature. The modified theory predicts a multivalued curve in the left branch, primarily due to the temperature dependence of the ionization rate. DC breakdown is studied using the full-fluid moment (FFM) model, where electron inertial effects are accounted for and the electron energy is self-consistently modeled. The results show a multivalued behavior for low values of Pd, i.e., the left branch of the Paschen curve, in agreement with the new theory. Breakdown voltage as a function of the reduced electric field, however, is not multivalued. The contribution of Joule heating, reactive energy losses, and convective energy losses is studied as well. These results provide evidence that the inclusion of the electron energy equation in the formulation of the theory is necessary to appropriately capture the breakdown physics.