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.
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BibTeX
@misc{white2026implicit,
title = {{An Implicit, Moment-Conserving Low-Rank Tensor Method for the Hybrid Kinetic-Ion Fluid-Electron Plasma Model}},
author = {Stephen R. White and Adam J. Stanier and Luis Chacón and Will T. Taitano and Isaac A. Castro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07215},
eprint = {2610.07215},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07215},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Implicit, Moment-Conserving Low-Rank Tensor Method for the Hybrid Kinetic-Ion Fluid-Electron Plasma Model
AU - Stephen R. White
AU - Adam J. Stanier
AU - Luis Chacón
AU - Will T. Taitano
AU - Isaac A. Castro
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07215
UR - https://arxiv.org/abs/2610.07215
AB - 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.
ER -