Decrease in the static electric gas breakdown voltage in the presence of free electrons in a discharge gap

The dependence of the gas breakdown voltage UB on the anode-cathode spacing d, pressure p, and other gas characteristics in the presence of a steady external ionizer in the discharge gap was determined within the avalanche discharge theory. The case was considered where the spatial charge created by the external ionizer did not distort the electric field in the discharge gap. In the absence of external ionizer the obtained dependence comes down to the well-known expression for the gas breakdown voltage (the Paschen law).