Phasor-particle-in-cell algorithm for bidirectional external-circuit coupling of inductively coupled plasma
Abstract
We develop a self-consistent phasor-particle-in-cell algorithm to capture bidirectional inductive and capacitive feedback between an inductively coupled plasma and a distributed radio-frequency coil circuit. The method couples a two-dimensional axisymmetric particle-in-cell model with Monte Carlo collisions to a network that resolves the current and potential of each coil turn. Precomputed unit-current Helmholtz solutions provide the vacuum impedance matrix, while projection of the plasma-only field supplies the series back electromotive force. An established charge-based electrostatic coupling is extended to individual turns: surface charges obtained from a discrete Gauss law consistent with the Poisson solver yield shunt displacement currents through their fundamental harmonics. Both responses are accumulated over a complete radio-frequency period to update the relaxed circuit state once per period. Vacuum tests showed differences of -1.58 percent in single-solenoid inductance and -4.38 percent in mutual inductance relative to analytical references. A particle-free five-node manufactured benchmark with both coupling channels active yielded a scaled complex-state error of 1.90 x 10^-5 against the continuous reference and approximately second-order spatial convergence. Application to an unshielded argon reference cell reached statistically stationary states at coil-port powers of 60 and 100 W. Net capacitive heating accounted for 29.35 percent and 20.07 percent, respectively, of the combined inductive and capacitive plasma power. Independently accumulated field-side and circuit-side powers, including conductor loss, agreed within approximately 0.5 percent. These results support turn-resolved bidirectional field-circuit coupling for axisymmetric plasma simulations using a fundamental-frequency circuit representation.
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BibTeX
@misc{chen2026phasorparticleincell,
title = {{Phasor-particle-in-cell algorithm for bidirectional external-circuit coupling of inductively coupled plasma}},
author = {Zhaoyu Chen and Zili Chen and Jingwen Xu and Yonghua Ding and Wei Jiang and Donghui Xia and Ya Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15043},
eprint = {2609.15043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15043},
}
RIS
TY - UNPB
TI - Phasor-particle-in-cell algorithm for bidirectional external-circuit coupling of inductively coupled plasma
AU - Zhaoyu Chen
AU - Zili Chen
AU - Jingwen Xu
AU - Yonghua Ding
AU - Wei Jiang
AU - Donghui Xia
AU - Ya Zhang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.15043
UR - https://arxiv.org/abs/2609.15043
AB - We develop a self-consistent phasor-particle-in-cell algorithm to capture bidirectional inductive and capacitive feedback between an inductively coupled plasma and a distributed radio-frequency coil circuit. The method couples a two-dimensional axisymmetric particle-in-cell model with Monte Carlo collisions to a network that resolves the current and potential of each coil turn. Precomputed unit-current Helmholtz solutions provide the vacuum impedance matrix, while projection of the plasma-only field supplies the series back electromotive force. An established charge-based electrostatic coupling is extended to individual turns: surface charges obtained from a discrete Gauss law consistent with the Poisson solver yield shunt displacement currents through their fundamental harmonics. Both responses are accumulated over a complete radio-frequency period to update the relaxed circuit state once per period. Vacuum tests showed differences of -1.58 percent in single-solenoid inductance and -4.38 percent in mutual inductance relative to analytical references. A particle-free five-node manufactured benchmark with both coupling channels active yielded a scaled complex-state error of 1.90 x 10^-5 against the continuous reference and approximately second-order spatial convergence. Application to an unshielded argon reference cell reached statistically stationary states at coil-port powers of 60 and 100 W. Net capacitive heating accounted for 29.35 percent and 20.07 percent, respectively, of the combined inductive and capacitive plasma power. Independently accumulated field-side and circuit-side powers, including conductor loss, agreed within approximately 0.5 percent. These results support turn-resolved bidirectional field-circuit coupling for axisymmetric plasma simulations using a fundamental-frequency circuit representation.
ER -