Data driven discovery of a model equation for anode-glow oscillations in a low pressure plasma discharge

A plasma glow discharge tube, a versatile device widely employed in several scientific and industrial applications, is also a useful tool for many basic plasma studies in the laboratory. Anode glow oscillations are well-known phenomena in such devices that arise from an instability of the plasma glow around a small positively charged electrode. Depending upon the gas pressure, the applied DC voltage, and the distance between the electrodes, these oscillations can display a rich dynamical behavior. Over a certain parametric regime, these nonlinear oscillations exhibit a stable limit cycle behavior that has been modeled in the past by a Van der Pol like equation. While such a model equation provides a qualitative description of the observations, it lacks quantitative agreement and does not have any predictive capability. We employ the sparse identification of nonlinear dynamics (SINDy) method to obtain a model equation directly from a time series of the experimental data. Our model captures well the main features of the experimental data in a quantitative manner. It also shows a significant deviation from the Van der Pol model due to additional contributions that are akin to nonlinear damping in a Rayleigh oscillator. Such a hybrid Van der Pol–Rayleigh oscillator model could provide a useful paradigm for future explorations of the nonlinear dynamics of this system.