Ionization layer with collision-free atoms at the edge of partially to fully ionized plasmas

When a hot arc spot has just formed on the cathode surface, e.g., in the course of arc ignition on a cold cathode, a significant part of the current still flows in the glow-discharge mode to the cold surface outside the spot. The near-cathode voltage continues to be high at all points of the cathode surface. The mean free path for collisions between the atoms and the ions within the plasma ball near the spot is comparable to, or exceeds, the thickness of the ionization layer, which is a part of the near-cathode non-equilibrium layer where the ion current to the cathode is generated. The evaluation of the ion current to the cathode surface under such conditions is revisited. A fluid description of the ion motion in the ionization layer is combined with a kinetic description of the atom motion. The resulting problem admits a simple analytical solution. Formulas for the evaluation of the ion current to the cathode for a wide range of conditions are derived and the possibilities of using these formulas to improve the accuracy of existing methods for modeling high-pressure arc discharges in relation to glow-to-arc transitions are discussed.