Convenient analytical solution for vibrational distribution function of molecules colliding with a wall
Abstract
We study formation of the Vibrational Distribution Function (VDF) in a molecular gas at low pressure, when vibrational levels are excited by electron impact and deactivated in collisions with walls and show that this problem has a convenient analytical solution that can be used to obtain VDF and its dependence on external parameters. The VDF is determined by excitation of vibrational levels by an external source and deactivation in collisions with the wall. Deactivation in wall collisions is little known process. However, we found that the VDF is weakly dependent on the functional form of the actual form of probability $${\gamma }_{\upsilon ^{\prime} \to \upsilon }$$ for a vibrational number $$\upsilon ^{\prime} $$ to transfer into a lower level $$\upsilon $$ at the wall. Because for a given excitation source of vibrational states, the problem is linear the solution for VDF involves solving linear matrix equation. The matrix equation can be easily solved if we approximate probability, in the form: $${\gamma }_{\upsilon ^{\prime} \to \upsilon }=(1/\upsilon ^{\prime} )\theta (\upsilon ^{\prime} \upsilon ).$$ In this case, the steadystate solution for VDF($$\upsilon $$) simply involves a sum of source rates for levels above $$\upsilon ,$$ with a factor of $$1/(\upsilon +1).$$ As an example of application, we study the vibrational kinetics in a hydrogen gas and verify the analytical solution by comparing with a full model.
 Authors:

 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Donghua Univ., Shanghai (China); Dalian Univ. of Technology (China)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Dalian Univ. of Technology (China)
 Publication Date:
 Research Org.:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE
 Contributing Org.:
 China Scholarship Council (CSC), National Magnetic Confinement Fusion Science Program, China (Grant No. 2015GB114000), National Key R&D Program of China (Grant No. 2017YFE0300106) and Initial Research Funds for Young Teachers of Donghua University.
 OSTI Identifier:
 1663369
 Grant/Contract Number:
 AC0209CH11466; 2015GB114000; 2017YFE0300106
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Plasma Sources Science and Technology
 Additional Journal Information:
 Journal Volume: 28; Journal Issue: 10; Journal ID: ISSN 13616595
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Yang, Wei, Khrabrov, Alexander V., Kaganovich, Igor D., and Wang, YouNian. Convenient analytical solution for vibrational distribution function of molecules colliding with a wall. United States: N. p., 2019.
Web. doi:10.1088/13616595/ab4310.
Yang, Wei, Khrabrov, Alexander V., Kaganovich, Igor D., & Wang, YouNian. Convenient analytical solution for vibrational distribution function of molecules colliding with a wall. United States. doi:10.1088/13616595/ab4310.
Yang, Wei, Khrabrov, Alexander V., Kaganovich, Igor D., and Wang, YouNian. Tue .
"Convenient analytical solution for vibrational distribution function of molecules colliding with a wall". United States. doi:10.1088/13616595/ab4310. https://www.osti.gov/servlets/purl/1663369.
@article{osti_1663369,
title = {Convenient analytical solution for vibrational distribution function of molecules colliding with a wall},
author = {Yang, Wei and Khrabrov, Alexander V. and Kaganovich, Igor D. and Wang, YouNian},
abstractNote = {We study formation of the Vibrational Distribution Function (VDF) in a molecular gas at low pressure, when vibrational levels are excited by electron impact and deactivated in collisions with walls and show that this problem has a convenient analytical solution that can be used to obtain VDF and its dependence on external parameters. The VDF is determined by excitation of vibrational levels by an external source and deactivation in collisions with the wall. Deactivation in wall collisions is little known process. However, we found that the VDF is weakly dependent on the functional form of the actual form of probability ${\gamma }_{\upsilon ^{\prime} \to \upsilon }$ for a vibrational number $\upsilon ^{\prime} $ to transfer into a lower level $\upsilon $ at the wall. Because for a given excitation source of vibrational states, the problem is linear the solution for VDF involves solving linear matrix equation. The matrix equation can be easily solved if we approximate probability, in the form: ${\gamma }_{\upsilon ^{\prime} \to \upsilon }=(1/\upsilon ^{\prime} )\theta (\upsilon ^{\prime} \upsilon ).$ In this case, the steadystate solution for VDF($\upsilon $) simply involves a sum of source rates for levels above $\upsilon ,$ with a factor of $1/(\upsilon +1).$ As an example of application, we study the vibrational kinetics in a hydrogen gas and verify the analytical solution by comparing with a full model.},
doi = {10.1088/13616595/ab4310},
journal = {Plasma Sources Science and Technology},
number = 10,
volume = 28,
place = {United States},
year = {2019},
month = {10}
}
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