Determination of the residual charge after current extinction-an integral approach

The paper deals with the post arc period of a vacuum interrupter (VI). An integral model has been developed to simulate numerically the residual charge left in the switching gap at current extinction. The corresponding rate equations of the arc plasma were solved in combination with the development of the anode surface temperature during the preceding arcing phase and vapor emission respectively. The modeling required some adequate simplifications. The arc plasma is assumed to consist of two classes of ion components: "fast ions" and "slow ions". The jets of the cathode spots are the source of "fast ions". The "slow ions" are the result of charge exchange between "fast ions" and metal vapor atoms with thermal velocities. Loss of ions occurs by diffusion out off the switching gap and to the electrodes. At low arcing loads "fast ions" prevail and the "residual charge" depends only on the current decay rate at current zero. The component of "slow ions" increases drastically with melting of the contacts and metal vapor emission when the arcing load exceeds a certain limiting value. High residual charges result because "slow ions" slow down the decay of plasma. Now the "residual charge" depends of the total arcing load (peak current). The numerical results, i.e. the residual charge in dependence of arcing load and the time-behavior of the free recovery are in considerable agreement with measurements of Dullni et al.