Data-driven discovery of electron continuity equation and its application to measurement of electron transport coefficients in argon

We develop a novel method for determining electron transport coefficients from measured spatiotemporal distribution of electrons n(t, z). In the hydrodynamic equilibrium regime, n(t, z) satisfies the electron continuity equation, and we discover the continuity equation from measured n(t, z). Electron transport coefficients can be acquired as a series of coefficients in the discovered equation. Our method allows us to determine the ionization rate coefficient, Townsend first ionization coefficient, center-of-mass drift velocity, mean-arrival-time drift velocity, longitudinal diffusion coefficient, and high order transport coefficients. These electron transport coefficients in Ar are determined from n(t, z) measured by the scanning drift tube experiment recently developed by Korolov et al. [Rev. Sci. Instrum. 87, 063102 (2016)]. It is found that considering high order transport coefficients, which are often ignored in the traditional drift-tube experiments, is important to determine longitudinal diffusion coefficient properly at middle and high reduced electric fields.