Which local field quantity determines the breakdown-limited gradient
In plain words
Engineers judge whether a new structure will spark using rules of thumb based on surface field, surface heating or energy flow; it is unknown whether one quantity works for all designs.
Precise statement
Candidate criteria include the peak surface electric field, the pulsed surface temperature rise $\Delta T$, and the modified Poynting vector $S_{c} = \operatorname{Re}(S) + \operatorname{Im}(S)/6$ proposed in 2009. Determine whether a single local quantity predicts the breakdown-limited gradient across structure geometries, frequencies $1\text{-}30\,\mathrm{GHz}$ and DC spark systems to within 20 percent at fixed breakdown rate and pulse length, or whether the limit is irreducibly geometry dependent.
What would settle it
A blind comparison of predicted and measured limits for a set of structures differing in geometry and frequency.