Mechanisms and Mathematical Modeling of Electrical Breakdown of Noble Gases in the Paschen Minimum Region

In the Paschen minimum region, the mechanisms of avalanche vacuum breakdown, the anomalous Paschen breakdown mechanism, and the Townsend breakdown mechanism alternate. The boundaries between these mechanisms are not sharply defined, instead, they intermingle and influence each other. Since these electrical breakdown mechanisms are based on gas discharge, this study critically examines the mathematical model of electrical discharge mechanisms based on ionization expressions and coefficients according to Townsend and Takeishi. Based on this analysis, new expressions for the ionization coefficient are proposed, assuming a Maxwellian spectrum of free electron gas. Experimental verification has confirmed that such an ionization coefficient provides the best results in the Paschen effect region. By applying the derived algorithm for calculating breakdown voltage values and comparing them with corresponding experimental values, an explanation of the electrical breakdown mechanism of noble gases in the Paschen region is provided. Experiments were conducted under well-controlled laboratory conditions with minimal measurement uncertainty.