Approximate Analytical Method of Streamer Discharge: Ignition and Its Field Threshold

Because the physical process during the discharge igniting stage is only a part of the physical process during the discharge development stage, the existing criteria for self-sustaining discharge or breakdown are not equivalent to those for the igniting stage. Although the quantity and distribution of seed electrons may influence the igniting electric field, existing theories can only provide explanations from a statistical perspective and lack deterministic analytical explanations. Using the simplified mathematical model of discharge proposed earlier by us, the basic processes and state during ignition are rigorously defined. Based on the calculation and analysis of three reorganized coefficients during the igniting stage, the sufficient conditions for discharge igniting and the necessary conditions for the lowest applied field threshold igniting are mathematically established. The sufficient condition is jointly determined by the seed electron number density and the applied field strengths; the higher the seed electron number density, the lower the applied field threshold, but there is a lowest field threshold. The necessary condition for the lowest applied field threshold igniting is that the discharge coefficient is zero, and for every two electrons added by the collisional ionization process, one electron is lost each by recombination and diffusion processes. The existence of a polarity effect of the lowest field threshold is also demonstrated. The above conclusion can provide more physical understanding and unified analytical expression than existing criteria.