A nonlinear electromagnetics model of an asymmetricallydriven, low pressure capacitive discharge
It is wellknown that standing waves having radially centerhigh 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 nearresonant, and therefore enhance the onaxis power deposition. The poweredelectrode/plasma/groundedelectrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both zsymmetric and zantisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially and timevarying 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 selfconsistent 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 nonlinearlyexcited radiallyvarying 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 nearmore »
 Authors:

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 Dalian Univ. of Technology, Dalian (China). School of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science
 Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science
 Dalian Univ. of Technology, Dalian (China). School of Physics
 Publication Date:
 Grant/Contract Number:
 SC0001939
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 8; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Univ. of Michigan, Ann Arbor, MI (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
 OSTI Identifier:
 1474308
 Alternate Identifier(s):
 OSTI ID: 1376737
Wen, DeQi, Kawamura, E., Lieberman, M. A., Lichtenberg, A. J., and Wang, YouNian. A nonlinear electromagnetics model of an asymmetricallydriven, low pressure capacitive discharge. United States: N. p.,
Web. doi:10.1063/1.4993798.
Wen, DeQi, Kawamura, E., Lieberman, M. A., Lichtenberg, A. J., & Wang, YouNian. A nonlinear electromagnetics model of an asymmetricallydriven, low pressure capacitive discharge. United States. doi:10.1063/1.4993798.
Wen, DeQi, Kawamura, E., Lieberman, M. A., Lichtenberg, A. J., and Wang, YouNian. 2017.
"A nonlinear electromagnetics model of an asymmetricallydriven, low pressure capacitive discharge". United States.
doi:10.1063/1.4993798. https://www.osti.gov/servlets/purl/1474308.
@article{osti_1474308,
title = {A nonlinear electromagnetics model of an asymmetricallydriven, low pressure capacitive discharge},
author = {Wen, DeQi and Kawamura, E. and Lieberman, M. A. and Lichtenberg, A. J. and Wang, YouNian},
abstractNote = {It is wellknown that standing waves having radially centerhigh 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 nearresonant, and therefore enhance the onaxis power deposition. The poweredelectrode/plasma/groundedelectrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both zsymmetric and zantisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially and timevarying 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 selfconsistent 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 nonlinearlyexcited radiallyvarying 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.},
doi = {10.1063/1.4993798},
journal = {Physics of Plasmas},
number = 8,
volume = 24,
place = {United States},
year = {2017},
month = {8}
}