Dynamics-aware bandwidth selection for smoothed charge deposition in 2D electrostatic particle-in-cell
Abstract
Charge deposition in the particle-in-cell (PIC) method can be viewed as kernel density estimation on a spatial mesh. This allows the smoothing bandwidth to be selected through statistical criteria such as mean integrated squared error or cross-validation, but it also changes the electric field acting on the particles. Therefore, a selected bandwidth can alter the growth or damping of physical modes. We develop a dynamics-aware bandwidth-selection procedure that combines a density-error objective with constraints on specified linear modes. These constraints follow from the plasma equilibrium and the combined transfer of deposition, filtering and field gathering within the model rate-tolerance boundary. We demonstrate the need for equilibrium information through a controlled two-stream experiment. The controlled two-stream scan varies the beam drift while holding the initial spatial density, thermal samples, wavevector and fixed-filter transfer unchanged. Across four resolved equilibria approaching marginal stability, this filter reduces the measured growth rate by 0.7% to 9.1%. Equilibrium-dependent interior settings satisfy the prescribed 10% rate tolerance. We then apply the constrained selection rule to 85 Gaussian candidates, that reduces density and grid-field mean-square errors by 7.40% and 3.70% on independently evaluated snapshots. A separate projected-linear calculation at that exact width gives a ratio of mean individual growth rates of $0.9556$, with paired 95% interval $[0.9453,0.9640]$, consistent with the prediction $0.9513$. Analysis of finite-marker loading and ensemble averaging explains how the measured rates relate to the response model. Together, these results demonstrate a filter-design procedure that combines statistical error reduction with subsequent validation of the selected linear dynamics.
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BibTeX
@misc{agrawal2026dynamicsaware,
title = {{Dynamics-aware bandwidth selection for smoothed charge deposition in 2D electrostatic particle-in-cell}},
author = {Ayushi Agrawal and Shan-Chang Lin and Ezhilmathi Krishnasamy and Pascal Bouvry},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03230},
eprint = {2610.03230},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03230},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Dynamics-aware bandwidth selection for smoothed charge deposition in 2D electrostatic particle-in-cell
AU - Ayushi Agrawal
AU - Shan-Chang Lin
AU - Ezhilmathi Krishnasamy
AU - Pascal Bouvry
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.03230
UR - https://arxiv.org/abs/2610.03230
AB - Charge deposition in the particle-in-cell (PIC) method can be viewed as kernel density estimation on a spatial mesh. This allows the smoothing bandwidth to be selected through statistical criteria such as mean integrated squared error or cross-validation, but it also changes the electric field acting on the particles. Therefore, a selected bandwidth can alter the growth or damping of physical modes. We develop a dynamics-aware bandwidth-selection procedure that combines a density-error objective with constraints on specified linear modes. These constraints follow from the plasma equilibrium and the combined transfer of deposition, filtering and field gathering within the model rate-tolerance boundary. We demonstrate the need for equilibrium information through a controlled two-stream experiment. The controlled two-stream scan varies the beam drift while holding the initial spatial density, thermal samples, wavevector and fixed-filter transfer unchanged. Across four resolved equilibria approaching marginal stability, this filter reduces the measured growth rate by 0.7% to 9.1%. Equilibrium-dependent interior settings satisfy the prescribed 10% rate tolerance. We then apply the constrained selection rule to 85 Gaussian candidates, that reduces density and grid-field mean-square errors by 7.40% and 3.70% on independently evaluated snapshots. A separate projected-linear calculation at that exact width gives a ratio of mean individual growth rates of $0.9556$, with paired 95% interval $[0.9453,0.9640]$, consistent with the prediction $0.9513$. Analysis of finite-marker loading and ensemble averaging explains how the measured rates relate to the response model. Together, these results demonstrate a filter-design procedure that combines statistical error reduction with subsequent validation of the selected linear dynamics.
ER -