Data-driven discovery of a model equation describing self-oscillations of direct current discharge

Data-driven techniques developed in recent years for the discovery of equations describing complex physical phenomena open unique opportunities for plasma physics. These methods allow getting insights into the processes difficult for analytical description. Since gas discharges can be represented as complex electrical circuits consisting of impedances and capacitances, it looks natural to use the data-driven techniques to study their complex dynamics. In the present paper, the sparse identification of nonlinear dynamics (SINDy) method is applied to analyze the self-oscillations of direct current discharge in argon. It is obtained that the third order polynomials describe best the oscillations of the discharge voltage and current. They allow an accurate capturing of the oscillations amplitudes as well as the harmonics of these oscillations. To understand the physical meaning of each term, an analytical model is presented which describes the discharge self-oscillations.