Determination of the Pre-breakdown Electric Field near a Cathode Streamer in Water

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The electrical strength of liquids under the influence of an impulse voltage is determined by the streamer initiation and propagation processes. For a streamer to grow and develop, a strong field must be present near its head. The field strength near a cathode streamer developing in water is estimated. Computer simulation of electro-optical studies of the pre-breakdown stage in water in the submicrosecond range that have already been carried out is performed, and the relevant processes are analyzed. During the simulation, all geometric, optical, and electrophysical conditions of the experiment were fully reproduced. A cathode streamer developing in a system of spherical electrodes in water is considered. The mathematical simulation was carried out using the finite element method inside the measuring cell volume. The experimental kerrogram intensity distribution field was numerically reproduced using the proposed model. The obtained 2D matrix was visualized, and the calculated kerrogram was compared with the experimental one. Calculations with a step of 2.5–5 µm allowed the fragments of interest to be analyzed in detail. Two streamer model versions were considered: a simplified one and a modified one, with the latter being closer to the real streamer kind. Computer simulation of the field near the streamer has shown the following. If the permittivity is assumed to be independent of the field strength, its value at the cathode streamer head does not exceed 1.9 MV/cm. At the same time, if the permittivity non-linearity is taken into account, the field strength estimated using both the streamer model was found to be around 2.4–3.1 MV/cm. It is shown that, despite the fact that the field strength somewhat exceeds the threshold value equal to 3 MV/cm, at which the dipole saturation state is possible, this does not lead to a noticeable change in the result. Thus, it has been confirmed that the field strength near the cathode streamer is essentially lower compared with that near the anode streamer.