A Reduced-Order Particle-in-Cell Method with Azimuthal Fourier-Decomposed Fields for Nominally Axisymmetric Plasmas
Abstract
A reduced-order Particle-in-Cell method is introduced for kinetic simulation of otherwise axisymmetric cylindrical plasmas that exhibit azimuthal instabilities. The method spatially decomposes all field quantities into a small number of azimuthal Fourier modes m=0,...,Nm, Nm ≪ Nθ, reducing the costly three-dimensional field solve 𝒪(NzNrNθ) to a family of decoupled independent two-dimensional problems 𝒪((Nm+1)NzNr) on the meridional plane - one per mode - while particles continue to move in full three-dimensional space. Fields are reconstructed at particle positions by coherent superposition of these modal contributions, preserving complete azimuthal variation at a fraction of the cost of a conventional three-dimensional simulation. For initial validation, the method is tested against two benchmark problems with restricted axial dimension: The diocotron instability of a hollow electron annulus across three geometrically distinct configurations, recovering linear growth rates and eigenpotential structures within 7% of closed-form analytic predictions, and reproducing the non-linear vortex dynamics characteristic of the instability saturation; and a further benchmark against the community-standard Landmark Penning discharge problem recovers the rotating-spoke frequency, radial plasma profiles, and modal energy hierarchy in quantitative agreement with long-time reference simulations, at approximately 640 CPU-hours - a factor of 46 speed-up compared to the median benchmark cost. The approach represents a step toward addressing the important gap between computationally prohibitive full three-dimensional kinetic simulation and the physically limited reduced-dimensionality models on which predictive modelling of anomalous transport in magnetised plasma devices currently relies.
Versions
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BibTeX
@misc{andrews2026reducedorder,
title = {{A Reduced-Order Particle-in-Cell Method with Azimuthal Fourier-Decomposed Fields for Nominally Axisymmetric Plasmas}},
author = {Shaun Andrews},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.04887},
eprint = {2606.04887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04887},
}
RIS
TY - UNPB
TI - A Reduced-Order Particle-in-Cell Method with Azimuthal Fourier-Decomposed Fields for Nominally Axisymmetric Plasmas
AU - Shaun Andrews
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2606.04887
UR - https://arxiv.org/abs/2606.04887
AB - A reduced-order Particle-in-Cell method is introduced for kinetic simulation of otherwise axisymmetric cylindrical plasmas that exhibit azimuthal instabilities. The method spatially decomposes all field quantities into a small number of azimuthal Fourier modes m=0,...,N_m, N_m ≪ N_θ, reducing the costly three-dimensional field solve 𝒪(N_zN_rN_θ) to a family of decoupled independent two-dimensional problems 𝒪((N_m+1)N_zN_r) on the meridional plane - one per mode - while particles continue to move in full three-dimensional space. Fields are reconstructed at particle positions by coherent superposition of these modal contributions, preserving complete azimuthal variation at a fraction of the cost of a conventional three-dimensional simulation. For initial validation, the method is tested against two benchmark problems with restricted axial dimension: The diocotron instability of a hollow electron annulus across three geometrically distinct configurations, recovering linear growth rates and eigenpotential structures within 7% of closed-form analytic predictions, and reproducing the non-linear vortex dynamics characteristic of the instability saturation; and a further benchmark against the community-standard Landmark Penning discharge problem recovers the rotating-spoke frequency, radial plasma profiles, and modal energy hierarchy in quantitative agreement with long-time reference simulations, at approximately 640 CPU-hours - a factor of 46 speed-up compared to the median benchmark cost. The approach represents a step toward addressing the important gap between computationally prohibitive full three-dimensional kinetic simulation and the physically limited reduced-dimensionality models on which predictive modelling of anomalous transport in magnetised plasma devices currently relies.
ER -