On Constructing Numerical Schemes for a Hierarchy of Fusion Plasma Problems
Ammar Hakim
Princeton Plasma Physics Lab
The description of plasmas, in particular in fusion, is naturally hierarchical. One can start from fully kinetic Vlasov-Maxwell equations and derive various approximations, including gyrokinetics, forms of drift-kinetics, multifluid, multi-moment models, to MHD. All these approximations are useful in different regimes, and, in fact, form a multi-fidelity hierarchy that can be used in conjunction with each other to design future fusion power plants. In this talk I will show that one can construct unified schemes for these models that exploit their underlying mathematical structure, and also run efficiently on modern GPU architectures. For the kinetic equations the Hamiltonian formulation is particularly useful, and I will show a novel class of discontinuous Galerkin schemes for such equations that conserve total energy and other properties. I will conclude with a prospective for further development of both new numerical methods as well as new plasma models, including the use of machine-learned solvers, with an eye towards eventually constructing a simulation-driven Foundation Model for fusion plasmas.