Azimuthal mode decomposition Particle in Cell algorithm for cylindrical plasma sources
Abstract
An efficient Particle-in-Cell numerical approach to perform full-dimensional kinetic simulations of low temperature plasmas is presented. Taking advantage of the cylindrical geometry of most plasma sources, a Fourier mode decomposition of the fields is carried out in the azimuthal (θ) direction up to a chosen maximum number of modes Nm. Macroparticles are pushed in all D dimensions and weighed, for each mode m, onto a (D−1) dimensional grid. The computation of the electric field for each mode is independent and reduces to solving (Nm+1) (D−1) dimensional Poisson problems. The approach brings spectral accuracy in the azimuthal direction, while the computational cost is comparable to that of a simulation with (D−1) dimensions. We verify this approach against a planar test case based on a Penning discharge, widely used for benchmarking and validation purposes in the low-temperature plasma community. Our approach allows us to reduce the 2D problem into a collection of coupled 1D problems and to naturally perform spectral analysis of the different azimuthal modes, recovering the contribution of each mode to radial transport, with a computational time saving of one order of magnitude with respect to state of the art 2D particle-in-cell codes.
Related
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BibTeX
@misc{ripoli2026azimuthal,
title = {{Azimuthal mode decomposition Particle in Cell algorithm for cylindrical plasma sources}},
author = {Matteo Ripoli and Eduardo Ahedo and Mario Merino},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21951},
eprint = {2609.21951},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21951},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Azimuthal mode decomposition Particle in Cell algorithm for cylindrical plasma sources
AU - Matteo Ripoli
AU - Eduardo Ahedo
AU - Mario Merino
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21951
UR - https://arxiv.org/abs/2609.21951
AB - An efficient Particle-in-Cell numerical approach to perform full-dimensional kinetic simulations of low temperature plasmas is presented. Taking advantage of the cylindrical geometry of most plasma sources, a Fourier mode decomposition of the fields is carried out in the azimuthal (θ) direction up to a chosen maximum number of modes N_m. Macroparticles are pushed in all D dimensions and weighed, for each mode m, onto a (D−1) dimensional grid. The computation of the electric field for each mode is independent and reduces to solving (N_m+1) (D−1) dimensional Poisson problems. The approach brings spectral accuracy in the azimuthal direction, while the computational cost is comparable to that of a simulation with (D−1) dimensions. We verify this approach against a planar test case based on a Penning discharge, widely used for benchmarking and validation purposes in the low-temperature plasma community. Our approach allows us to reduce the 2D problem into a collection of coupled 1D problems and to naturally perform spectral analysis of the different azimuthal modes, recovering the contribution of each mode to radial transport, with a computational time saving of one order of magnitude with respect to state of the art 2D particle-in-cell codes.
ER -