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The gas discharge characteristics are seriously influenced by the effective secondary electron-emission coefficient (γeff) originally defined by Townsend. A theoretical approach has been proposed for the determination of variation of this coefficient as a function of the geometrical parameter d/R (the ratio of inter-electrode distance to electrode radius) in the most practical range of 0.08≤d/R≤1.90. Two geometrical factors gi and gp, which are attributed to ion-induced and photon-induced terms, respectively, were introduced to the effective gamma in parallel-plane arrangement. The factors were theoretically derived and hence the effective gamma and the breakdown voltage for a specified geometrical parameter, such as d/R=0.16, were obtained. Then, the effective gamma and the Paschen curves for various geometrical parameters such as d/R=0.32, 0.63, 1.27, and 1.90 were theoretically reproduced. The obtained results showed quite a good agreement with those reported by other researchers and verified that the proposed gi and gp have properly been introduced and derived.

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The secondary emission coefficient is a valuable parameter for numerical modeling of the discharge process in gaseous insulation. A theoretical model has been developed to consider the effects of the radial electric field, non-uniformity of the axial electric field, and radial diffusion of charged particles on the secondary emission coefficient. In the model, a modified breakdown criterion is employed to determine the effective secondary electron emission, γeff. Using the geometry factor gi which is introduced based on the effect of radial diffusion of charged particles on the fraction of ions which arrive at the cathode, the geometry-independent term of γeff (Δi) was obtained as a function of the energy of the incident ions on the cathode. The results show that Δi is approximately a unique function of the ion energy for the ratios of d/R = 39, 50, 77, 115, and 200. It means that the considered mechanisms in the model are responsible for the deviation from Paschen's law.

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