7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Similarity Rules for Inductive Radio Frequency Plasmas withThermohydrodynamic Coupling Effects

Huihui Wang1, Dong Yang2, Bocong Zheng3, Fei Wei1, Yangyang Fu2
1
Department of Chemical Engineering, Tsinghua University, 2 Department of ElectricalEngineering, Tsinghua University, 3 School of Physics, Beijing Institute of Technology
e-mail: huihuiwang@tsinghua.edu.cn

Similarity theory and scaling laws describe how
physical properties of plasma remain the same whencontrol parameters are changed. It is useful fordeveloping and optimizing plasma sources. Similarity
rules have been successfully verified in discharges driven
by direct current [1-5], radio frequency [6,7], microwave [8-11],
and pulsed power supplies [12]. More recently, thesimilarity rules were rigorously demonstrated in low
pressure plasmas with strong nonlocal kinetic effects
using electrostatic particle-in-cell simulation [13-15].
However, similarity rules were not verified fordischarges with electromagnetic and thermodynamic
coupling effects.
In this presentation, we report similarity rules forinductively coupled plasma (ICP) withthermohydrodynamic coupling effects using
two-dimensional fluid simulations and theoreticalanalyses of gas flow and heat transfer equations. Theresults show that the change of gas temperature withscaling factors causes the violation of similarity rule in
the ICP. The increase of gas temperature with scaling
factors causes the gas flow rate to increase, and theelectron density in the plasma bulk to decrease. Further,
it is found that the deviation of gas temperature can bemitigated by adding an external heat source, thus
maintaining the validity of the similarity relations.

References[1]. V. A. Lisovskiy, S. D. Yakovin, and V. D.
Yegorenkov, Low-pressure gas breakdown in
uniform dc electric field, J. Phys. D: Appl. Phys. 33,
2722 (2000).
[2]. Y. Fu and J. P. Verboncoeur, On the similarities of
low-temperature plasma discharges, IEEE Trans.
Plasma Sci. 47,1994 (2018).
[3]. M. Loveless and A. L. Garner, Scaling laws for gas
break-down for nanoscale to microscale gaps atatmospheric pressure, Appl. Phys. Lett. 108,234103 (2016).
[4]. Y. Fu, P. Zhang, and J. P. Verboncoeur, Paschen’s
curve in microgaps with an electrode surface
protrusion, Appl. Phys. Lett. 113, 054102 (2018).
[5]. Y. A. Astrov, A. N. Lodygin, and L. M. Portsel,
Dynamics and stability of the townsend discharge
in nitrogen in narrow gaps, Phys. Rev. E 89,033109 (2014)[6]. V. Lisovskiy, J. P. Booth, K. Landry, D. Douai, V.
Cassagne, and V. Yegorenkov, Similarity law for rf
breakdown, Europhys. Lett. 82, 15001 (2008).
[7]. M. Puaˇc, D. Mari ́c, M. Radmilovi ́c-Radjenovi ́c,M. Šuvakov, and Z. L. Petrovi ́c, Monte Carlomodeling of radio-frequency breakdown in argon,
Plasma Sources Sci. Technol. 27, 075013 (2018).
[8]. S. C. Brown, Basic Data of Plasma Physics (MITPress, Cambridge, 1959).
[9]. C. M. Ferreira and M. Moisan, The similarity laws
for the maintenance field and the absorbed power
per electron in low-pressure surface wave produced
plasmas and their extension to HF plasmas ingeneral, Phys. Scr. 38, 382 (1988).
[10]. A. Sola, A. Gamero, J. Cotrino, and V. Colomer,Empirical similarity laws for argon plasmas
produced by a surface wave at 2.45 GHz, J. Phys.
D: Appl. Phys. 21, 1112 (1988).
[11]. A. M. Loveless and A. L. Garner, A universal
theory for gas breakdown from microscale to theclassical Paschen law, Phys. Plasmas 24, 113522(2017).
[12]. G. A. Mesyats, Similarity laws for pulsed gas
discharges, Phys. Usp. 49, 1045 (2006).
[13]. Y. Fu, B. Zheng, P. Zhang, Q. H. Fan, J. P.
Verboncoeur, and X. Wang, Similarity of capacitive
radio-frequency discharges in nonlocal regimes,
Phys. Plasmas 27, 113501 (2020).
[14]. D. Yang, Y. Fu, B. Zheng, H. Wang, Q. H. Fan, X.
Zou, X. Wang, and J. P. Verboncoeur, Similarity
properties in capacitive radio frequency plasmas
with nonlinear collision processes, Plasma Sources
Sci. Technol. 30, 115009 (2021).
[15]. D. Yang, H. Wang, B. Zheng, X. Zou, X. Wang, andY. Fu, Application of similarity laws todual-frequency capacitively coupled radio
frequency plasmas with the electrical asymmetryeffect, Plasma Sources Sci. Technol. 31, 115002(2022).