A θ-implicit hybrid particle-in-cell algorithm for kinetic simulations of magnetized plasmas
Abstract
Hybrid particle-in-cell (PIC) models with kinetic ions and an inertialess electron fluid are widely used to simulate magnetized plasmas at ion scales, but explicit time advances are constrained by the whistler-wave CFL condition dt ∝ Δx2, and the sub-cycling and artificial dissipation used to mitigate it carry accumulating costs. We present a θ-implicit hybrid PIC algorithm, implemented in the open-source GPU-capable code WarpX, in which fields and particles are advanced as a single nonlinear system solved by a particle-suppressed Jacobian-free Newton--Krylov method: the particles are nonlinearly eliminated, the electric field of the generalized Ohm's law is the sole unknown, and mass matrices remove all particle operations from the linear iterations. The electron pressure is advanced inside the nonlinear solve, and the scheme satisfies a discrete energy law whose single dissipation term vanishes at θ= 1/2 and damps only temporally under-resolved modes for θ> 1/2. The advance reproduces parallel and perpendicular wave dispersion including the ion Bernstein modes, conserves total energy to machine roundoff where the explicit advance heats secularly, does not develop the cold-beam finite-grid instability, and reproduces the m=0 instability of a Bennett pinch in RZ geometry. We conclude with 3D simulations of a field-reversed configuration initialized from a Grad--Shafranov equilibrium, comparing the explicit and implicit advances on the growth of the tilt instability and the preservation of trapped magnetic flux.
Related
- An implicit multiscale solver for steady kinetic equations based on wave-particle decomposition
- A semi-implicit unified gas-kinetic wave-particle method with energy-conserving electromagnetic coupling for multiscale plasmas
- A physics-based-preconditioned quasi-Newton solver for energy- and momentum-conserving implicit hybrid particle-in-cell simulations
- KEMPIC-3D: A transparent and extensible electromagnetic Particle-in-Cell framework for kinetic plasma simulations
- NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations
BibTeX
@misc{kumar2026θimplicit,
title = {{A $θ$-implicit hybrid particle-in-cell algorithm for kinetic simulations of magnetized plasmas}},
author = {Prabhat Kumar and William J. White and Stephen E. Clark},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00127},
eprint = {2611.00127},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00127},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A θ-implicit hybrid particle-in-cell algorithm for kinetic simulations of magnetized plasmas
AU - Prabhat Kumar
AU - William J. White
AU - Stephen E. Clark
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00127
UR - https://arxiv.org/abs/2611.00127
AB - Hybrid particle-in-cell (PIC) models with kinetic ions and an inertialess electron fluid are widely used to simulate magnetized plasmas at ion scales, but explicit time advances are constrained by the whistler-wave CFL condition dt ∝ Δx^2, and the sub-cycling and artificial dissipation used to mitigate it carry accumulating costs. We present a θ-implicit hybrid PIC algorithm, implemented in the open-source GPU-capable code WarpX, in which fields and particles are advanced as a single nonlinear system solved by a particle-suppressed Jacobian-free Newton--Krylov method: the particles are nonlinearly eliminated, the electric field of the generalized Ohm's law is the sole unknown, and mass matrices remove all particle operations from the linear iterations. The electron pressure is advanced inside the nonlinear solve, and the scheme satisfies a discrete energy law whose single dissipation term vanishes at θ= 1/2 and damps only temporally under-resolved modes for θ> 1/2. The advance reproduces parallel and perpendicular wave dispersion including the ion Bernstein modes, conserves total energy to machine roundoff where the explicit advance heats secularly, does not develop the cold-beam finite-grid instability, and reproduces the m=0 instability of a Bennett pinch in RZ geometry. We conclude with 3D simulations of a field-reversed configuration initialized from a Grad--Shafranov equilibrium, comparing the explicit and implicit advances on the growth of the tilt instability and the preservation of trapped magnetic flux.
ER -