An Implicit, Moment-Conserving Low-Rank Tensor Method for the Hybrid Kinetic-Ion Fluid-Electron Plasma Model

Abstract

Quasi-neutral hybrid models for simulating plasmas, with kinetic ions and fluid electrons, have shown great promise for approaching the multi-scale nature of plasmas. In this paper we present a novel hybrid scheme for electromagnetic settings that conserves mass, momentum, and energy, employing a low-rank tensor method utilizing the Tensor Train decomposition to avoid the \enquote{curse of dimensionality.} Electrons are simulated as a continuous fluid, while the kinetic ions are modeled as a distribution function governed by the Vlasov equation. The Vlasov equation is updated with the implicit midpoint method. We use a modified version of a conservative truncation method to guarantee conservation of mass, momentum, and energy throughout the method, which corrects the truncated distribution function without needing to advance a separate set of fluid-moment equations. A series of electrostatic and electromagnetic test problems is used to demonstrate the correctness of the method and its conservation properties.