Gap size dependence of the dielectric strength in nano vacuum gaps

We study the dielectric strength of vacuum gaps of under 100 nm. We find their dielectric strengths to have a power law dependence on the gap size. We apply this power law to find that the dielectric strength of a vacuum gap of 10 nm between two tungsten electrodes is 6.5 V/nm. The dielectric strength can be used to compute the maximum energy density, charge density, and power density. For tungsten, the maximum volumetric energy density is 190 MJ/m³. Nano vacuum gaps can discharge in 10 nanoseconds, giving a maximum gravitometric power density of 10¹² W/kg. While the external discharge time is a few nanoseconds, the self-discharge time can be hours or days. The specific capacitance of a vacuum gap of size d is C = ε₀/ d². If d = 10nm then C = 8.85×10⁴ F/m³.