A Nonlinear Two-Sheath Circuit Model for Low-Pressure Symmetric and Asymmetric Capacitively Coupled Radio-Frequency Plasmas
Abstract
We develop a nonlinear self-consistent two-sheath circuit model for low-pressure capacitively coupled plasmas that applies to geometrically symmetric as well as asymmetric discharges. The quasineutral plasma bulk is represented by an inductive-resistive element and coupled to stationary particle and electron-energy balances. Both boundary sheaths are treated dynamically using a lncosh sheath charge-voltage model with bounded differential elastance, based on a Riccati closure for the differential sheath width. The model recovers the quadratic depletion-sheath relation in the small-charge limit, while the characteristic sheath scales are determined from the RF-averaged sheath voltages using a collisionless Child-Langmuir/Bohm closure. The resulting four-variable RF subsystem contains the two sheath charges, the blocking-capacitor voltage, and the discharge current. In the symmetric monofrequent limit, the two sheath nonlinearities compensate strongly and the dc self-bias vanishes, whereas geometrical or electrical asymmetry breaks this compensation and enhances harmonic generation and plasma-series-resonance oscillations.
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BibTeX
@misc{noesges2026nonlinear,
title = {{A Nonlinear Two-Sheath Circuit Model for Low-Pressure Symmetric and Asymmetric Capacitively Coupled Radio-Frequency Plasmas}},
author = {Katharina Noesges and Tim Bolles and Máté Vass and Ihor Korolov and Thomas Mussenbrock},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01528},
eprint = {2610.01528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01528},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Nonlinear Two-Sheath Circuit Model for Low-Pressure Symmetric and Asymmetric Capacitively Coupled Radio-Frequency Plasmas
AU - Katharina Noesges
AU - Tim Bolles
AU - Máté Vass
AU - Ihor Korolov
AU - Thomas Mussenbrock
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01528
UR - https://arxiv.org/abs/2610.01528
AB - We develop a nonlinear self-consistent two-sheath circuit model for low-pressure capacitively coupled plasmas that applies to geometrically symmetric as well as asymmetric discharges. The quasineutral plasma bulk is represented by an inductive-resistive element and coupled to stationary particle and electron-energy balances. Both boundary sheaths are treated dynamically using a lncosh sheath charge-voltage model with bounded differential elastance, based on a Riccati closure for the differential sheath width. The model recovers the quadratic depletion-sheath relation in the small-charge limit, while the characteristic sheath scales are determined from the RF-averaged sheath voltages using a collisionless Child-Langmuir/Bohm closure. The resulting four-variable RF subsystem contains the two sheath charges, the blocking-capacitor voltage, and the discharge current. In the symmetric monofrequent limit, the two sheath nonlinearities compensate strongly and the dc self-bias vanishes, whereas geometrical or electrical asymmetry breaks this compensation and enhances harmonic generation and plasma-series-resonance oscillations.
ER -