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By Jeremy A. Riousset, Joshua S. Méndez Harper, Josef Dufek, Jared P. Nelson, Annelisa B. Esparza.

Primary research paper; classical planar Townsend criterion, empirical ionization coefficient and limits of its geometric assumptions. Full byline verified on the primary publisher page.

Publisher: agupubs.onlinelibrary.wiley.com/doi/10.1029/2022JD038427 . The published five-author byline above differs from the earlier arXiv version, which also lists Jacob A. Engle; author contributions are reported in the published article.

Jeremy A. Riousset led the generalized gas-discharge study cited here; the paper credits him with methodology, software and formal analysis. It extends breakdown calculations beyond parallel electrodes.^[ref]

The geometric issue can be seen directly from Gauss's law. In a charge-free gap, a planar field is constant, a radial cylindrical field varies as $1/r$, and a spherical field varies as $1/r^2$. Thus an electron crossing a curved gap encounters a changing electric field, even when the applied electric potential difference is fixed. A breakdown criterion based only on a uniform field can miss that variation. This example motivates the paper's use of electrode geometry as part of the model, rather than treating every gap as two flat plates.