Electrical network-based time-dependent model of electrical breakdown in water

Abstract

A time-dependent, two-dimensional, percolative approach to model dielectric breakdown based on a network of parallel resistor–capacitor elements having random values, has been developed. The breakdown criteria rely on a threshold electric field and on energy dissipation exceeding the heat of vaporization. By carrying out this time-dependent analysis, the development and propagation of streamers and prebreakdown dynamical evolution have been obtained directly. These model simulations also provide the streamer shape, characteristics such as streamer velocity, the prebreakdown delay time, time-dependent current, and relationship between breakdown times, and applied electric fields for a given geometry. The results agree well with experimental data and reports in literature. The time to breakdown (tbr) for a 100 μm water gap has been shown to be strong function of the applied bias, with a 15–185 ns range. It is also shown that the current is fashioned not only by dynamic changes in local resistance, but that capacitive modifications arising from vaporization and streamer development also affect the transient behavior.