A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge

Wen, De-Qi; Kawamura, E.; Lieberman, M. A.; Lichtenberg, A. J.; Wang, You-Nian

doi:10.1063/1.4993798

Title: A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge

Journal Article · 23 August 2017 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.4993798 · OSTI ID:1474308

Wen, De-Qi ^[1]; Kawamura, E. ^[2]; Lieberman, M. A. ^[2]; Lichtenberg, A. J. ^[2];

^[3]

Dalian Univ. of Technology, Dalian (China). School of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science; University of California, Berkeley
Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science
Dalian Univ. of Technology, Dalian (China). School of Physics

It is well-known that standing waves having radially center-high voltage profiles exist in high frequency driven capacitive discharges. Capacitive sheaths can also nonlinearly excite driving frequency harmonics near the series resonance that can be spatially near-resonant, and therefore enhance the on-axis power deposition. The powered-electrode/plasma/grounded-electrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both z-symmetric and z-antisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially- and time-varying sheath widths, incorporating both symmetric and antisymmetric modes, and the plasma skin effect. Waves generated in the electrostatic wave limit are also treated. The discharge is modeled as a uniform density bulk plasma with either homogeneous or Child law sheaths at the electrodes, incorporating their nonlinear voltage versus charge relations. The model includes a finite power source resistance and a self-consistent calculation of the dc bias voltages. The resulting set of nonlinear partial differential equations is solved numerically to determine the symmetric and antisymmetric mode amplitudes and the nonlinearly-excited radially-varying harmonics. Two examples driven at lower frequency (30 MHz) or at higher frequency (60 MHz) are examined. The first case displays the excited dominant ninth harmonic near the series resonance frequency with the fundamental frequency having a weak standing wave. The higher frequency case shows a more obvious standing wave effect, enhanced by the nonlinear harmonics. Finally, the symmetric and antisymmetric modes are of similar amplitudes over the driving electrode, summing to give a larger bottom sheath.

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Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

Grant/Contract Number:: SC0001939

OSTI ID:: 1474308

Alternate ID(s):: OSTI ID: 1376737

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 8 Vol. 24; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited By (4)

Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges Zhao, Kai; Wen, De-Qi; Liu, Yong-Xin Physical Review Letters, Vol. 122, Issue 18 https://doi.org/10.1103/physrevlett.122.185002	journal	May 2019
Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges Wen, De-Qi; Kawamura, E.; Lieberman, M. A. Journal of Physics D: Applied Physics, Vol. 50, Issue 49 https://doi.org/10.1088/1361-6463/aa9627	journal	November 2017
Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source Zhao, Kai; Liu, Yong-Xin; Kawamura, E. Plasma Sources Science and Technology, Vol. 27, Issue 5 https://doi.org/10.1088/1361-6595/aac242	journal	May 2018
Symmetry breaking in high frequency, symmetric capacitively coupled plasmas Kawamura, E.; Lieberman, M. A.; Lichtenberg, A. J. Physics of Plasmas, Vol. 25, Issue 9 https://doi.org/10.1063/1.5048947	journal	September 2018

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