Departure from Paschen's Law of Breakdown in Gases

The failure of Paschen's law of electrical breakdown in gases at both high pressures and extremely small electrode separations is explained by a single breakdown mechanism. The breakdown field in each of these cases is sufficiently great to draw measurable field-emission current from the cathode, which produces a relatively small number of ions. The space-charge field of these ions is great enough to increase the field-emission current appreciably even when the ratio of ion current to electron current is less than one percent. As more ionic space charge is produced, each ion becomes more effective in enhancing the electron current until the breakdown condition is attained. An expression is derived for the yield of electrons per positive ion as a function of the applied field. This expression is shown to be in quantitative agreement with values of $\gamma$ derived from published data on breakdown voltages at high pressures. It is shown also that the same process explains breakdown at extremely small separations below the "minimum sparking potential."