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Title
Japanese: 
English:Multiple solutions in the Te–Ne parameter space of argon CR model via Monte Carlo optimization 
Author
Japanese: 叶宇晨, 土居謙太, 清田哲司, 菊地航行, 山下雄也, 根津篤, 赤塚洋.  
English: Yuchen Ye, Kenta Doi, Tetsuji Kiyota, Wataru Kikuchi, Yuya Yamashita, Atsushi Nezu, Hiroshi Akatsuka.  
Language English 
Journal/Book name
Japanese: 
English:Plasma Sources Science and Technology 
Volume, Number, Page Vol. 35    No. 5   
Published date May 6, 2026 
Publisher
Japanese: 
English:IOP Publishing 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Official URL https://iopscience.iop.org/article/10.1088/1361-6595/ae61f0
 
DOI https://doi.org/10.1088/1361-6595/ae61f0
Abstract The accurate determination of the electron temperature (Te) and density (Ne) is critical for understanding argon plasma characteristics, yet inverse solutions to the collisional-radiative (CR) model often suffer from non-uniqueness, complicating data interpretation. The core contribution of this study is the visualization of band-like solution structures within the CR inverse problem and the development of a practical strategy for handling this non-uniqueness. The results reveal band-like residual regions in the Te-Ne space, representing continuous zones where fitting residuals are insensitive to coupled Te-Ne variations, thereby corresponding to multiple solutions. These regions exhibit a change in monotonicity at Te ≈ 1.77 eV under the Maxwellian assumption, reflecting a transition in the dominant electron-collision kinetics governing the excited states. The structures of these regions are highly sensitive to spectral line selection and EEPF assumptions: higher excited-level sets shift the solutions toward higher Ne to balance the relative population distribution, whereas EEPF assumptions with greater high-energy depletion shift them toward higher Te to maintain the necessary excitation rates. The proposed optimization approach efficiently identifies these solutions while maintaining physical consistency. This strategy resolves the non-uniqueness of the inverse problem, ensuring reliable tomographic determinations of Te and Ne in argon inductively coupled plasmas.

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