Data-driven modeling of an electrical corona discharge

In this work, we explore the potential of data assimilation technique in computational plasma physics. Data assimilation, i.e., optimal combination of simulation results and measurement data in real time, has been essential to numerical weather forecast and not yet been widely applied to modeling plasma processes, with an exception of some astrophysical plasmas in the so-called space weather forecast. The main reason is that most of the plasma processes are too fast and the measurement data is insufficient. Therefore, we study the electrical corona discharge in air between a needle tip (high voltage) and a planar electrode (ground), which, during the 1 ms simulation time, can be considered quasi-steady. The currents at the two electrodes are monitored. The model of the corona discharge is based on the drift-diffusion equations coupled with Poisson's equation. Only three species are considered, namely, electrons, positive ions, and negative ions. During the first 0.5 ms, at each preset time interval, the simulation results are assimilated to the measurements using ensemble Kalman filtering. It is found that, after data assimilation, the model prediction of currents for the second 0.5 ms agrees better with the experimental results. In general, assimilating averaged quantities over the time interval produces better results than assimilating instantaneous values, while the effect of the time interval is still inconclusive, which might be due to the lack of spatially-resolved measurement data.