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. Published under an exclusive license by AIP Publishing.

Automated summary

A plasma glow discharge tube is a versatile device widely used in scientific and industrial applications, as well as in basic plasma studies. Anode glow oscillations, a well-known phenomena in these devices, exhibit rich dynamical behavior depending on various parameters. Researchers have used the sparse identification of nonlinear dynamics (SINDy) method to obtain a quantitative model equation directly from experimental data, which captures the main features of the data and deviates significantly from the existing Van der Pol model. This hybrid model could guide future explorations of the nonlinear dynamics of this system.