Expanding sheath in a bounded plasma in the context of the post-arc phase of a vacuum arc

A numerical model of sheath expansion and plasma decay in a bounded plasma subjected to a linearly increasing voltage has been developed. Numerical results obtained with a hybrid-MB model (Maxwell-Boltzmann electrons, particle ions and Poisson's equations) are compared with analytical theory and results from particle-in-cell (PIC) simulations. The hybrid-MB model is similar to models used for plasma immersion ion implantation except that plasma decay due to particle losses to the electrodes is taken into account. The comparisons with more accurate and much more time consuming PIC models show that the hybrid-MB model provides a very satisfactory description of the sheath expansion and plasma decay even for conditions where the grid spacing is much larger than the Debye length. The model is used for high plasma density conditions, corresponding to the post-arc phase of a vacuum arc circuit breaker where a vacuum gap is subject to a transient recovery voltage (TRV) after it has ceased to sustain a vacuum arc. The results show that the plasma sheath expansion is subsonic under these conditions, and that the plasma starts to decay exponentially after two rarefaction waves from the cathode and anode merge in the centre of the gap. A parametric study also shows the strong influence of the TRV rise rate and initial plasma density on the plasma decay time and on the ion current collected by each electrode. The effect of collisions between charged particles and metal atoms resulting for the electrode evaporation is also discussed.