Physics-informed neural networks for calculation and measurement of fundamental data on electron transport in plasmas*

Electron velocity distribution functions (EVDFs) and electron transport coefficients are fundamental data on electron transport in plasmas. These data provide valuable information to optimize plasmas for various applications. Furthermore, electron transport coefficients are required for simulating plasmas. Accurate fundamental data are inevitable for accurate plasma simulation and proper discussion on plasma applications; therefore, methods for calculating and measuring fundamental data accurately are highly required. Physics-informed neural networks (PINNs) provide a novel way to deal with partial differential equations (PDEs) and combine PDEs and measured data. We have developed two methods for calculating and measuring EVDFs and electron transport coefficients accurately using PINNs. The first is a method for solving the electron Boltzmann equation using PINNs. This method requires no expansion of EVDFs using orthogonal functions; therefore, accurate EVDFs can be calculated. Furthermore, EVDFs in a periodic steady state under uniform AC electric fields can be directly calculated without solving from an initial time. The second is a method for measuring electron transport coefficients by combining PINNs and electron swarm experiments. The electron continuity equation is discovered from electron swarm maps measured by drift tube experiments. This method requires no analytical form of the swarm map, allowing us to consider high-order terms in the continuity equation, which are traditionally truncated. By discovering two kinds of electron continuity equations, we can measure many kinds of electron transport coefficients from a single electron swarm map: effective ionization collision frequency, effective ionization coefficient, center-of-mass electron drift velocity, mean-arrival-time drift velocity, longitudinal-diffusion coefficient, longitudinal third-order transport coefficient, and so forth.