Modeling Multiscale Phenomena in Magnetized Plasmas

Capturing multiscale phenomena in magnetized plasmas is complicated by interactions that connect across the various spatiotemporal scales. For example, the magnetized Kelvin-Helmholtz instability (KHI) is known to develop macroscale plasma structures whose details depend on microscale physics [Vogman et al PoP 27 (2020)]. Kinetic models accurately describe the microscale, but solving kinetic models is often impractical for capturing macroscale dynamics. Hybridizing kinetic and moment models across spatial domains [Datta & Shumlak JCP 483 (2023)] offers an approach to strategically combine computationally efficient reduced models with higher fidelity models, which is facilitated using the finite-element continuum WARPXM framework [Shumlak et al CPC 182 (2011)]. Applications of the domain-decomposed hybrid method include the magnetized KHI and plasma photonic crystals [Thomas & Shumlak PoP 30 (2023)]. Developments in the dynamical low-rank approximation (DLRA) of high-dimensional PDEs suggest an additional promising avenue for the efficient solution of the kinetic plasma model. In particular, the Vlasov equation and the Dougherty-Fokker-Planck collision operator have the structure necessary for DLRA. The applicability of DLRA to this kinetic plasma model is demonstrated on several benchmark problems. The suitability of DLRA to the nonlinear evolution of magnetized plasma instabilities such as the KHI is investigated, with a focus on how collisions impact the rank of the solution manifold.