• Title/Summary/Keyword: The two-term approximation of the Boltzmann equation

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The study of electron drift velocity in $CF_4+Ar$ molecular gas mixture by 2-term and multi-term approximation of the Boltzmann equation (다항근사 및 2항근사 볼츠만 방정식을 이용한 $CF_4+Ar$ 혼합기체의 전자이동속도 연구)

  • Song, Byoung-Doo;Ha, Sung-Chul;Jeon, Byoung-Hoon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2004.07b
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    • pp.1179-1182
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    • 2004
  • This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients in $CF_4+Ar$ gas mixture by using two-term approximation of Boltzmann equation. but there is difference between the result of the two-term and the multi-term approximation of the Boltzmann equation in $CF_4$ gas. Therefore, in this paper, we calculated the electron drift velocity (W) in $CF_4+Ar$ gas mixture for range of E/N values from $0.01\sim500[Td}$ at the temperature was 300[K] and pressure was 1[Torr] by multi-term approximation of the Boltzmann equation by Robson and Ness. The results of two-term and multi-term approximation of the Boltzmann equation has been compared with each other for a range of E/N.

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The comparison of electron transport coefficients of gases for analysis of multi-term approximation of the Boltzmann equation (다항근사 볼츠만 방정식의 타당성 검토를 위한 가스의 전자수송계수 비교)

  • Song, Byoung-Doo;Ha, Sung-Chul;Jeon, Byoung-Hoon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2003.05e
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    • pp.69-72
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    • 2003
  • This paper describes the information for the difference between two-term and multi-term approximation of the Boltzmann. In previous paper, we calculated the electron transport coefficients in pure Oxygen and Argon gases by using two-term approximation of Boltzmann equation. Therefore, in this paper, we calculated the electron transport coefficients(W and $N{\cdot}D_L$) in pure Oxygen and Argon gases for range of E/N values from 0.01~500[Td] at the temperature was 300[K] and pressure was 1[Torr] by using multi-term approximation of the Boltzmann equation by Robson and Ness, The results of two-term and multi-term approximation of the Boltzmann equation has been compared with the experimental data for a range of E/N.

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The Study of Character of Electron Drift Velocity in CF4 Molecular Gas by the Boltzmann Equation (볼츠만 방정식에 의한 CF4 분자가스의 전자이동속도 특성에 관한 연구)

  • Song, Byoung-Doo;Ha, Sung-Chul
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.17 no.11
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    • pp.1252-1257
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    • 2004
  • This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients by using two-term approximation of Boltzmann equation. But there is difference between the result of the two-term approximation of the Boltzmann equation and experiments in pure CF$_4$ molecular gas and in CF$_4$+Ar gas mixture. Therefore, In this paper, we calculated the electron drift velocity (W) in pure CF$_4$ molecular gas and CF$_4$+Ar gas mixture (1 %, 5 %, 10 %) for range of E/N values from 0.17~300 Td at the temperature was 300 K and pressure was 1 Torr by multi-term approximation of the Boltzmann equation by Robson and Ness. The results of two-term and multi-term approximation of the Boltzmann equation have been compared with each other for a range of E/N.

An Application of Two-term and Multi-term Approximation of Boltzmann Equation to Electron Swarm Method (전자군 방법에 이용되는 2항근사와 다항근사 볼츠만 방정식의 적용)

  • 하성철;전병훈
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.15 no.1
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    • pp.79-84
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    • 2002
  • An accurate cross sections set is necessary for the quantitatively understanding and modeling of plasma phenomena. By using the electron swarm method, we determine an accurate electron cross sections set for objective atoms or molecule at low electron energy range. It is general calculation that used in this method to an two-term approximation of Boltzmann equation. But it may give erroneous transport coefficients for CF$_4$ molecule treated in this paper having \`C2v symmetry\`, therefore, multi-term approximation of the Boltzmann equation analysis which can consider anisotropic scattering exactly is carried out. It is necessary to require understanding of the fundamental principle of analysis method. Therefore, in this paper, we compared the electron transport coefficients(W and ND$\_$L/) in pure Ar, O$_2$, and CF$_4$ gas calculated by using two-term approximation of the Boltzmann equation analysis code uses the algorithm proposed by Tagashira et al. with those by multi-term approximation by Rubson and Ness which was developed at James-Cook university, and discussed an application and/or validity of the calculation method by comparing these calculated results.

The analysis of electron transport coefficients in Xenon gas by multi-term approximation of the Boltzmann equation (볼츠만 다항근사 방정식을 이용한 Xe 가스의 전자수송계수 해석)

  • Jeon, Byoung-Hoon;Ha, Sung-Chul;Song, Byoung-Doo
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2003.05e
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    • pp.73-76
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    • 2003
  • This paper describes the information for quantitative simulation of weakly ionized plasma. In previous paper, we calculated the electron transport coefficients in pure Xenon gas by using two-term approximation of Boltzmann equation. Therefore, in this paper, we calculated the electron transport coefficients(W, $N{\cdot}D_L$ and $D_{L/{\mu}}$) in pure Xenon gas for range of E/N values from 0.01 ~ 500[Td] at the temperature was 300[K] and pressure was 1[Torr] by using multi-term approximation of the Boltzmann equation by Robson and Ness, The results of two-term and multi-term approximation of the Boltzmann equation has been compared with the experimental data by L. S. Frost and A. V. Phelps for a range of E/N.

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The analysis of electron transport coefficients in $CF_4$ molecular gas by multi-term approximation of the Boltzmann equation (다항근사 볼츠만 방정식에 의한 $CF_4$ 분자가스의 전자수송계수 해석)

  • Jeon, Byung-Hoon;Park, Jae-June;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.11b
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    • pp.141-144
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    • 2001
  • An accurate cross sections set are necessary for the quantitatively understanding and modeling of plasma phenomena. By using the electron swarm method. we determine an accurate electron cross sections set for objective atoms or molecule at low electron energy range. In previous paper, we calculated the electron transport coefficients in pure $CF_4$ molecular gas by using two-term approximation of the Boltzmann equation. And by using this simulation method. we confirmed erroneous calculated results of transport coefficients for $CF_{4}$ molecule treated in this paper having 'C2v symmetry' as $C_{3}H_{8}$ and $C_{3}F_{8}$ which have large vibrational excitation cross sections which may exceed elastic momentum transfer cross section. Therefore, in this paper, we calculated the electron transport coefficients(W and $ND_L$) in pure $CF_4$ gas by using multi-term approximation of the Boltzmann equation by Robson and Ness which was developed at lames-Cook university, and discussed an application and/or validity of the calculation method by comparing the calculated results by two-term and multi-term approximation code.

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The analysis of electron transport coefficients in CF$_4$ molecular gas by multi-term approximation of the Boltzmann equation (다항근사 볼츠만 방정식에 의한 CF$_4$분자가스의 전자수송계수 해석)

  • 전병훈;박재준;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.11a
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    • pp.141-144
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    • 2001
  • An accurate cross sections set are necessary for the quantitatively understanding and modeling of plasma phenomena. By using the electron swarm method, we determine an accurate electron cross sections set for objective atoms or molecule at low electron energy range. In previous paper, we calculated the electron transport coefficients in pure CF$_4$ molecular gas by using two-term approximation of the Boltzmann equation. And by using this simulation method, we confirmed erroneous calculated results of transport coefficients for CF$_4$ molecule treated in this paper having 'C2v symmetry'as C$_3$H$_{8}$ and C$_3$F$_{8}$ which have large vibrational excitation cross sections which may exceed elastic momentum transfer cross section. Therefore, in this paper, we calculated the electron transport coefficients(W and ND$_{L}$) in pure CF$_4$ gas by using multi-term approximation of the Boltzmann equation by Robson and Ness which was developed at James-Cook university, and discussed an application and/or validity of the calculation method by comparing the calculated results by two-term and multi-term approximation code.e.

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The study of electron transport coefficients in pure $CO_2$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CO_2$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Kim, Ji-Yeon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.164-167
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure $CO_2$ were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of $CO_2$ molecular gas. And for propriety of two-term approximation of Boltzmann equation analysis, the calculated results compared with the electron transport coefficients measured by Nakamura.

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The study of electron transport coefficients in pure $CF_4$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CF_4$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.29-32
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    • 2001
  • We measured the electron transport coefficients(the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_L$) in pure $CF_4$ over the E/N range from 0.04 Td to 250 Td by the double shutter drift tube. And these electron transport coefficients in pure $CF_4$ were calculated over the E/N range from 0.01 to 250 Td at 1 Torr by using the two-term approximation of the Boltzmann equation.

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The study of electron transport coefficients in pure Xe by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 Xe분자가스의 전자수송계수의 해석)

  • Ma, Su-Young;Jeon, Byung-Hoon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.174-177
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    • 2001
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure Xe were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Xe molecular gas.

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