A runaway electron avalanche surrogate for partially ionized plasmas

A physics-constrained deep learning surrogate that predicts the exponential ‘avalanche’ growth rate of runaway electrons (REs) for a plasma containing partially ionized impurities is developed. Specifically, a physics-informed neural network (PINN) that learns the adjoint of the relativistic Fokker–Planck equation in steady-state is derived, enabling a rapid surrogate of the RE avalanche for a broad range of plasma parameters, motivating a path towards an machine learning-accelerated integrated description of a tokamak disruption. A steady-state power balance equation together with atomic physics data is embedded directly into the PINN, thus limiting the PINN to train across physically consistent temperatures and charge state distributions. This restricted training domain enables accurate predictions of the PINN while drastically reducing the computational cost of training the model. In addition, a novel closure for the relativistic electron population used when evaluating the secondary source of REs is developed that enables improved accuracy compared to a Rosenbluth–Putvinski source. The avalanche surrogate is verified against Monte Carlo simulations, where it is shown to accurately predict the RE avalanche growth rate across a broad range of plasma parameters encompassing distinct tokamak disruption scenarios.