A Deep Learning Treatment of the Plasma Sheath

The plasma sheath strongly impacts the particle and heat transport out of a plasma, yet the rich physics in this area inhibit the development of a generally applicable model. Kinetic modelling of the sheath captures the rich physics, but is computationally prohibitive and limited to a few parameters at a time. More efficient models rely on fluid descriptions of the plasma but require making assumptions that exclude physics from the model. Even the most celebrated closures, like Bohm and Braginskii, are known to breakdown for a wide variety of plasma parameters. We introduce a novel physics-driven machine learning approach that solves fluid equations for a broad range of plasma parameters by leveraging the architecture of physic-informed neural networks (PINN). This approach solves a system of PDEs by converting the system into an optimization problem, which negates any potential singularities, and uses the PINN to perform the optimization. The PINN accurately solves a simplified sheath model and finds the plasma profiles even when departing from conditions where the Bohm criterion is valid. This approach can serve as a rapid surrogate for a wide variety of sheath models.