Influence of residual gas on electrical strength of planar vacuum gap with field electron emission on the cathode

A theoretical estimate of the threshold voltage for electrical breakdown in a planar gap filled with rarefied gas with field electron emission at the cathode has been carried out. A quantitative breakdown criterion was obtained reflecting the accumulation of space ion charge within the gap volume and the significant influence of this charge on the field emission current. Various models of the cathode surface relief were analyzed. It has been shown that the breakdown field strength of a diode whose cathode is made of graphite with nanotubes can be lower than 6 kV/cm if the product of the gas pressure (P) and the gap length (D) exceeds 10⁻¹ Pa·cm.