Acceleration of Kinetic Plasma Simulations Using Data-Driven Methods

Abstract

Magnetic confinement fusion (MCF) is a promising candidate for a low-carbon electricity solution. MCF uses strong magnetic fields to confine hot, highly ionized plasmas for long enough times that nuclear fusion reactions can occur. Currently, the two most prominent MCF concepts are the tokamak and the stellarator, which confine plasmas in toroidal vessels. Due to strong temperature gradients, plasmas in both tokamaks and stellarators can exhibit kinetic small-scale turbulence, which drives unwanted macroscopic transport of heat and particles. The gyrokinetic simulations used to model this turbulence can be computationally intensive, so a valuable objective is to accelerate these simulations. A complementary goal is to ensure that simulation results are reliable for a given domain and resolution configuration. In this thesis, we make two contributions in support of these initiatives. First, we explore the use of machine learning to reduce resolution requirements for kinetic plasma simulations, which would make them faster. We achieve this by developing a machine learning (ML) closure model for velocity space in the one-dimensional Vlasov-Poisson system in a Fourier-Hermite spectral basis. The ML closure uses reservoir computing, a framework for training recurrent neural networks. We exploit the locality of interactions in the Hermite representation of velocity space to integrate large-scale dynamics with a kinetic solver, while using the ML closure model of the small-scale dynamics. In the linear limit, when the kinetic Fourier–Hermite solver is augmented with the reservoir closure, the closure permits a reduction of the velocity resolution, with a relative error within 2% for the Hermite moment where the reservoir closes the coupled hierarchy. In the strongly nonlinear regime of the Vlasov-Poisson system, the ML closure model more accurately resolves the low-order Fourier and Hermite spectra when compared with a naive closure by truncation and reduces the required velocity resolution by a factor of 16. Second, we use correlation functions, heat flux and free energy spectra, and nonlinear energy transfer diagnostics to assess the convergence in heat flux for a set of electrostatic gyrokinetic turbulence simulations. We perform a parameter scan of temperature gradients, temperature ratios, domain extents, and resolutions in the plane perpendicular to the magnetic field lines simulated. Though no universal convergence threshold was found in correlation length or resolution, trends in energy and heat flux spectra point toward the potential to use spectra for the automatic identification of under-resolution during the execution of a simulation.