On Minimum Static Breakdown Voltage for a Gasfilled Gap

Relying on the condition of the discharge self-sustainment, a theoretical analysis is performed aimed at identifying the lowest possible discharge voltage. It is shown that weak electric field nonuniformity in the discharge gap gives rise to an increase in the static breakdown voltage compared to the Paschen's law case. Strong electric field nonuniformity in the diodes of coaxial and spherical geometry too cannot ensure a decrease in the minimum breakdown voltage compared to the case of a plane parallel gap. It is proven that out of all symmetrical geometries of a gas-filled diode, the planar geometry has the lowest breakdown voltage.